Fundamentals of Insurance
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- Fundamentals of Insurance
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PGP -II: 2003-04
Third Term
Fundamentals of Insurance
R Rajogopalan
□cxSiM
Indian Institute of Management
AH M E DABAD
Ahmedabad
$
g( S . H/) )V3 VzMTH
Course Title:
Fundamentals of Insurance
Batch and Term:
2002-04, Term VI
Credit:
0.5
No. of sessions:
13
Instructor:
R. Rajagopalan
TAPMI, Manipal
Context
The Indian Insurance sector has traversed a full circle. Till 1956, when life insurance was
nationalized, it was totally in the private sector. In 1971, commercial insurance was also
nationalized. After around four decades of this nationalized monopoly, private sector
participation has again been allowed. The ensuing competition is opening up challenging
career options for MBAs. This course seeks to prepare you for the same.
There are two kinds of career opportunities: one in the insurance companies per se and
the other in terms of risk management in corporate sector using insurance as one of the
tools. There are also other emerging career opportunities in insurance marketing and
distribution, insurance advisory services and third party administration (TPA) of
insurance contracts.
Course Objectives
This course will focus primarily on those concepts, techniques and issues in the context
of a person aspiring for a career in insurance and risk management. Wherever relevant,
concerns of individuals in managing their risks will be discussed to provide a ‘marketing’
perspective. Only those conceptual materials of common relevance to all types of
insurance products, life/ health insurance on the one hand and corporate/ general
insurance on the other, will be covered in this course.
Proposed Coverage
1.
2.
3.
4.
5.
6.
7.
8.
Risk: Alternative Definitions, Types of Risk
Risk Management Process and Methods
Objectives of Risk Management
Risk Pooling and Insurance
Institutions for Insurance and Reinsurance- Economic rationale and requirements
Insurance Laws and Regulation
Insurance Pricing
Asymmetric Information / Moral hazard / Adverse selection
Text Book
Scott E. Harrington and George R. Niehaus (1999), Risk Management and Insurance,
McGraw-Hill International Edition (Hereafter, referred to as H&N)
Suggested Books
1. Alan Waring and A. Ian Glendon (1998), Managing Risks: Critical Issues for
Survival and Success into the 21st Century, Thomson Business Press.
2. Insurance Act 1938 (plus amendments through IRDA Act 1999, see below)
3. The Insurance Regulatory and Development Authority (IRDA) Act, 1999
4. Peter L. Bernstein (1996) Against the Gods: The Remarkable Story ofRisk, John
Wiley & Sons
5. Trieschmann and Gustavson (1995) Risk Management & Insurance, SouthWestern (9th Edition)
6. George E. Rejda (2001) Principles of Risk Management and Insurance, Pearson
education, Seventh Edition
7. Williams, Jr, Smith and Young (1998) Risk Management and Insurance, McGraw
Hill, Eighth Edition
Websites
1- http://screwedbyinsurance.com/
2- http://www.actuaries.org.uk/interactives/front.html
3. http.7/www.swissre.com
4. http://business-insurance.galaxy.com/
5. http ://bestreview.com
6. http://irdaindia.org
7. http://bimaguru.com
8. http://licindia.com
Evaluation Scheme
Quizzes: 2*20%
End-Term:
40%
60%
1
S. No
1
2
3
4
5
6
7
8
9
Session Schedule
__________ Topics__________ _______ Readings/ Exercises
a) Risk and Pure Risk
• H&N, Chapters 1,3 &7
b) Approaches to managing pure Optional
risks
Bernstein’s Book: Against the Gods
c) How does insurance add
value?
d) Risk Pooling-Essential
Concepts_________________
Insurance Pricing- Generic
• H&N, Chapter 6
Format- Pricing Equation______
Estimating Net Claim Costs- Life • R. Rajagopalan, “The Two-State
Insurance Contracts
Markov Model of Life and Death”
• R. Rajagopalan “Exercises on
Mortality Tables and Valuing Cash
Flows of Insurance Products”:
Set 1: Questions of Life and Death
Set 2: Insurance in Bollywood_____
Risk Sharing in Insurance
• H&N, Chapter 23, pp 593-607
Contracts
• Judy Feldman Anderson and Robert
L. Brown (2000), “Risk and
Insurance”, Society of Actuaries,
USA.________________________
Information Asymmetry: Moral
• H&N, Chapter 8, Sec 8.1 and 8.2
Hazard and Adverse Selection
• Estelle James and Renuka Jain
“Annuity Markets in India: What are
the Key Public Policy Issues?”,
EPW, Feb 22, 2003_____________
Legal Doctrines related to
• H&N, Chapter 8, Sec 8.3
Insurance
• Case: “Developing Risk Skills: An
Investigation of Business Risks and
Controls at Prudential Insurance
Company of America”___________
Insurance Regulation in India
• R. Rajagopalan, “Indian Laws
Related to Insurance- What a
Manager Should Know”__________
Insurer’s Expenses: Accounting
• Mulgund & Balasubramanian
and Management
“Analysis of Expenses for Life
Insurers”_____________________
Insurer’s Capital Requirements
• H&N: Chapter 4
and Returns
a) Reserve Requirements
b) Cost of Capital: Insurance
Sector Specifics
c) Role of Reinsurance
10
-Continued-
•
11
Portfolio Approach to Risks
•
12
13
Corporate Liability Insurance
Employee Retirement Plans
•
•
Kenneth A. Froot “The Market for
Catastrophe Risk: A Clinical
Examination”__________________
Neil A. Doherty, “Risk Management
Strategy: Duality and Globality”,
Chapter 8 of “Integrated Risk
Management”__________________
H&N: Chapter 15_______________
H&N: Chapter 19
%
The Two-State Markov Model of Life and Death1
Introduction
The design of life insurance products is based on the conceptual foundation provided by
what is called a ‘Markov model’ of life and death. It is worthwhile to have a rudimentary
understanding of this model. This would improve our understanding of life insurance
products. This model can also be generalized to a three-state (healthy-ill-dead) model,
which again provides the conceptual foundation for health and disability insurance
products and retirement benefit plans.
Please read this note after completing the accompanying exercise titled “Exercises on
Mortality Tables and Valuing Cash Flows of Insurance Products”. That would help you
understand this note better. More importantly, some of the notations used in this note are
explained in the above exercise.
Two-State Markov Model
A life (person), currently aged x, can only be in one of the two possible states at any
future time: ‘alive’ or ‘dead’. A transition from the ‘alive’ state to the ‘dead’ state is
possible at any future time Z (i.e., at age x+Z). However, a transition from the ‘dead’ state
to the ‘alive’ state is not possible. The ‘dead’ state is thus called an absorbing state.
Dead at
x+Z
Alive at x
Alive at
x+Z
Dead at x
Dead at
x+Z
Assumption 1 (Markov Assumption)
It is assumed that the probabilities that a life at any given age (x) will be found in either
state (alive or dead) at any future time (x+Z) depend only on the ages involved (x and x+Z)
and on the current state (state atx). This is called the Markov assumption. What this
1 Prepared by Prof. R. Rajagopalan, TAPMI, Manipal.
1
implies is that we need to know only the age of a person (alive) now, to specify the
chances of his being alive or dead at any give time in the future. We need to know neither
his life history nor his current health status2.
Assumption 2
Consider a future time x+t at which the person is still alive. The chance that this person
will die in a very short time interval dt is given by3
dt Qx+t
~ fx+t
u, dt,t>0
/,ix+t is called the transition intensity at time x+t and can be interpreted as the
instantaneous force of mortality at x+t.
Assumption 3
Since mortality varies with age, we have to make some simplifying assumption to enable
empirical estimation. It is assumed that the transition intensity atx+^ is a constant /dx for
0< t<l for each integer value of x. That is, for each integer x,
0<t<l
In other words, we are assuming that one-year is too short a time for this intensity to
change significantly. We are also assuming, by implication, that this intensity jumps at
discrete times, at one-year intervals, on a person’s birthday. Though this assumption may
be reasonable for other ages, it may not be so for a newborn, that is when x=0.
Probabilities of Death and Survival
Given the above, it can be shown that
d
-^tPx =-tPxXPx+l
Intuitively, we can interpret the above as saying that the rate at which the probability of
survival declines at x+t is the product of probability of survival till x+t in the first place
Gpx), multiplied by the transition intensity at x+t, jux+tThe equation above implies4 that
For dealing with other factors affecting these probabilities, we can construct a separate model for each
such stratified population. Alternatively, we can treat them as static factors and incorporate them through a
regression model.
3 The exact equality will have a term o(dt) on the R.H.S which tends to 0 faster than dt itself
4 By solving this first order differential equation for tpx
2
I
f Mx+,ds
.Px = e o
The chance of death before reaching age x+t, denoted by tqx
1-//MS given by
= l-e-hds
Discrete Time Two-state Model
Suppose that a person is aged exactly x now. Instead of considering time as a continuous
variable, let us say we are interested in the status of this person only at discrete intervals
of time, that is, at t= 1, 2, 3....
In particular, let us consider his chance of survival till the end of the next one year, that
is, till he reaches age x+1 (px) and death within the next one year (gQ. The above
equations imply the following:
p. e
qx =l-e~Px
Please recall assumption 3.
If we look at the mortality tables in this light, our understanding would be better to that
extent.
Reference
Chapter 5 of the ActEd Study Materials: 2003 Examinations for Subject 104 “Survival
Models”, of The Institute of Actuaries, London
*)|C)|Cd|C^C3|C9|C)|C
3
Exercises on Mortality Tables and Valuing Cash Flows of Insurance Products1
Set 1
Questions of Life and Death
Life Table
Please refer to the table “Mortality Rates of Assured Lives in LIC of India - LIC 94-96
(ultimate)”2 while answering the following questions. The above table is reproduced at
the end of this set of exercises for your convenience. This table is based on LIC’s
experience amongst those whose life insurance policies were in force during 1994-96.
In that table, known as a life table, the column titled of people alive” can be used to
derive estimates of lots of quantities of relevance to life insurance. This table starts with
an arbitrary assumption3 that there are 100,000 people in a population who had just
completed 14 years of age4.
The entry in this column in each subsequent row, numbered as per completed age x, can
be interpreted as the expected number of survivors (ZQ at the end of that age x, out of
these original 100,000. Thus, as per this table, 93579 out of the original 100,000 people at
age 14 are expected to be still alive at the end of age 50. That is, Z5o= 93579.
The column “# of Deaths” gives the number of people (c/x), out of the original 100,000,
who are expected to die after completing the age in that row (x) but within the next one
year. For example, 545 out of the original 100,000 are expected to die after reaching age
50 but before age 51. That is, dso=545.
Suggestion
You may like to create a spreadsheet version of the above life table. Then you would be
able to avoid the computational drudgery. However, it might be worthwhile to do the
problems in set 1 manually to ensure that we understand well. Use of a spreadsheet would
be absolutely necessary for problems in Set 2.
Illustrations and Questions
a) What is the probability that a person who has just completed x years will die in the
next one year? This probability is denoted by qx. Please recall that in a binomial
probability model, the probability of failure in a trial is usually denoted by q. We
consider each person of age x as a ‘trial’ and death is ‘failure’.
1 Prepared by Prof. R. Rajagopalan, TAPMI, Manipal.
2 LIC’s life tables are the only published life tables on insured lives in India as of now. This is applicable to
males only
3 This is an useful interpretation of what is technically called the radix of a life table
4 There is nothing particular about starting at 14. LIC simply did not have sufficient data on younger ages who typically do not buy insurance products
1
w
For example, q5o
dso/ho = 545/93579 = .00582396
Exercise 1: Compute qx for x = 20, 30, 40, 50, 60, 70, 80 and 90. Plot qx against x
and comment. Enter these in the column qx in the table.
2. What is the probability that a person currently aged x will survive that year? This is
denoted by px. By definition, px = 1 - qx.
Exercise 2: Compute px for the various x in Exercise 1.
3. What is the probability that a person aged x will survive at least for the next n
years, i.e., till he attains age x+n? This is indicated by npx. For example, iopso
denotes the probability that a person now aged 50, will survive at least the next 10
years, that is, till he is 60. With a life table, computing this is a piece of cake!
For example, iopso
In general.9 nPx
ho/ ho 85350/93579 0.91206
h+n/ h
Exercise 3: Compute the probability of survival in the next 10 years at x
20, 30, 40, 50, 60, 70, 80 and 90.
4. What is the probability that a person aged x will die within the next n years, i.e.,
before he attains age x+n? This is indicated by nqx. For example, loqso denotes
the probability that a person now aged 50 will die within the next 10 years, that is,
before he reaches 60. Again, no problem (to compute!).
Simply put,„^= 1 - npx
For example, ioq5o
1- iopso — 1- 0.91206
.08794
Exercise 4: Compute nqx for n = 10, for x = 20, 30, 40, 50, 60, 70, 80 and
90.
5. What is the probability that a person aged x will live till he is x+n but die within
the subsequent m years, before he reaches x+n+ml Again not very difficult...
As per the life table,
•
•
The number of people alive at x is lx.
The number of deaths during the period x+n and x+n+m is
h+n
h+n+m
Therefore, this probability = (lx+n -h +n+m) / h
2
I
For example, the probability that a person now aged 50 will die between
ages 60 and 70 is = (l6o-l7o) / ho = (85350 - 67279) /93579= 0.19311
This probability is denoted by n\mqx
This notation can be interpreted as ‘something’ is deferred by n years,
denoted by the ‘n|’ part. The thing being deferred appears next, that is,
m Qx •
Exercise 5: Compute the above for x = 20, 30, 40, 60, 70, 80.
Exercise 5a: Repeat Exercise 5, assuming m = 1. In line with our earlier
notation, we may drop the ‘m’ part and denote this probability simply as
3
Set 2
Insurance in Bollywood
We assume that you have already learnt the notion of time value of money, discounting
cash flows, computing NPV etc., elsewhere. Combining these with the probabilities
defined and computed in Set 1, we can compute several financial values concerning
insurance products.
Let i denote the applicable interest rate. We will assume that all benefits due to a
policyholder will be paid at the end of the year in which the insured event (say, death)
occurs5. We will define the discount rate v = 1 / (1+i).
Consequently, the present value (PV) of Rs. 1 to be received at the end of n years is
= 1/(1 +i)n. Similarly, the PV of an annuity of Rs. 1 per year over the next n years
would be (l-vn)/i.
In insurance products, future cash flows are typically uncertain. For example, under a
term insurance contract, the sum assured needs to be paid only if the insured dies during
the coverage period or term. Premiums can be collected only if the policyholder is alive
and willing to continue with the policy. Similarly, in an annuity contract, we have to pay
the annuity only till the policyholder is alive. Therefore we have to treat such present
values as random variables. We would be using
• The expected present value (EPV)6 to value future premiums, benefits and
expenses.
• Variances in such present values to quantify risks.
Here we go!
Let us assume i - 6% for all the problems in set 2 and that the mortality is as per the life
table attached.
1. Suppose LIC has just sold a ‘non-participating whole life policy’ with a sum assured of
Rs. 1 to Mr. Anant Nag, aged 35. This policy would pay Rs 1 at the end of the year of
death of Mr. Anant. What is the EPV of Benefit payments (EPVB) under this policy?
Assume that Mr. Anant Nag dies between k and k+1 years from now, that is, between
ages 35+k and 35+k+l. The present value of benefits paid to him would then be vk+1. He
may die anywhere between ages 35 and 100 7. Therefore we have to consider the range of
integers k, 0 <k <64. The probability of death between k and k+1 is k\ q* = kPss x Q35+ k
(he has to live for the next k years and then die in the k+1^ year). Therefore,
5 In practice, such benefits may be paid quite soon after the event. There are corresponding expressions for
such situations.
6 There are standard notations used by actuaries for each of these expected present values, under the
“International Actuarial Notation”. We will avoid these as long as possible to ensure ‘user friendliness’!
7 Please note that the life table assumes that even an Anant dies by 100!
4
64
*+l
EPVB
^kPlS X ^35+k
*=0
Exercise 1: Please use a suitable spreadsheet to compute
a) The above EPVB.
b) The EPVB at x = 30,40,50,60,70,80,90
c) The EPVB at x = 30,40,50,60,70,80,90 but for a sum assured of
Rs. 10,00,000
2. Suppose that Mr. Markendeya, a stunt-man, currently aged 20, has just purchased
a 20-yr, ‘non-participating term insurance’ policy which would pay Rs I at the
end of the year in which Mr. Markendeya dies, but only if he dies within the next
20 years. Nothing will be paid if he survives beyond 20 yrs. What is the EPVB?
19
EPVB
X QlO+k
k=0
Exercise 2: Please use a suitable spreadsheet to compute
a) The above EPVB.
b) The EPVB at x = 30,40,50,60,70,80
c) The EPVB at x = 30,40,50,60,70,80 but for a sum assured of Rs. 10,00,000
3. Mr. Dev Anand, the evergreen hero, bought a 30-year ‘non-participating pure
endowment policy’ when he was 508. This insurance would pay him Rs 1 exactly
after 30 yrs, but only if he was still alive at that time. What is the EPVB?
EPVB = v30 X3OP5O
Exercise 3: Please use a suitable spreadsheet to compute
a) The above EPVB.
b) The EPVB at x = 30,40,50,60,70
c) The EPVB at x = 30,40,50,60,70 but for a sum assured of Rs. 10,00,000
4. Mr. Bacchhan9 purchased a 30-yr ‘non-participating endowment policy’ when he was
40. This policy will pay Rs 1 at the end of year in which he dies, if he dies within 30 yrs;
it would also pay Rs 1 on the day the policy matures if he is still alive. What is the
EPVB?
It is easier when we realize that a 30-yr endowment policy is nothing but a bundle
involving a 30-yr term insurance and a 30-yr pure endowment (See Exercises 2 and 3
8 The gossip at that time was that after all he had just spotted Ms. Zeenat Aman as his next heroine talent!
9 The only Bollywood hero to have died using a two-headed coin in reel life, but who typically wants to
have it both ways in real life
5
above). Hence, its EPVB is the sum of the EPVBs of the corresponding term and pure
endowment policies.
29
EPVB = (Z»“ X^40X940+t )+V
X30/?40
k=0
Exercise 4: Please use a suitable spreadsheet to compute
a) The above EPVB.
b) The EPVB at x = 30,40,50
c) The EPVB at x = 30,40,50 but for a sum assured of Rs. 10,00,000
d) The EPVB if the insurance is a special one: it would pay Rs. 10,00,000 for
death during term and Rs 5,00,000 only, if Mr. Bacchhan survives the 30yr term?
5. Mr. Wrakesh Ration, now aged 60, made a pile as the producer of the huge hit
Kaho Na Kitna Bana wanted to use part of that pile to buy a life long annuity which
would give him Rs 10,00,000 lakh per annum at the beginning of every year as long a
he is alive, starting today. What is his EVPB?
39
EVPB = \ 0,00,000
XkP60
k=G
Please note that he will get 10,00,000 at the beginning of every year as long as he is
alive and we need to discount it to now. In fact the factor vk *kpx is known as ‘the
actuarial discount factor’. This discounts for both time value of a payment as well as
the chance that the payment has to be made.
Exercise 5: Mr. Rajesh Khannot Anymore, another contemporary of Wrakesh, is 65
and he would like to buy an annuity of Rs 5 lakhs payable annually in the beginning
of each year till he reaches 80 or the year of his death, whichever is earlier. What is
his EVPB?
6. Mr. Writhik Ration, the one-film wonder hero10 of Bollywood landed a Rs 5 Cr
sponsorship deal as a brand ambassador for a hard drink Typsy Tola®, at an young
age of 25. He wanted to use this money to buy an annuity that would pay him a
regular amount at the beginning of each year starting with his 40th birthday11 till
the year of his actual death. If he dies before 40, nothing would be paid. How
much can he expect per year as annuity?
Obviously EPVB must be equal to Rs 5 Cr, the price he is paying. Let us assume that he
will get Rs A per annum as the annuity beginning when he is 40.
In these days of IPR, this name is hereby owned by me! Wrakesh was fond of names beginning with K.
Hence this precaution.
l0The name of his only hit was reportedly changed in the last minute from Kahaan Gaye Woh Din
11 Projected death date for his film career!
6
59
EPVB = 500,00,000 = ^x15p25 x v15 xEvix^o
k=0
Exercise 6:
a) Compute amount A that would be received by Writhik if and when he hits 40
yrs.
b) Mr. Share Dukhan, another star aged 35, wanted a life annuity beginning
when he is 50 using the Rs 20 Cr he has stashed in a Swiss Bank12. How much
can he hope for as annuity?
Exercise 7:
The Bollywood grapevine was all agog with rumours on the passionate real-life rivalry
between two reigning heroes, Mr. Barechest Khan (aged 35) and Mr. Awake Soberai
(aged 25). They were both wooing Ms. Surayya Ray (aged a constant 25 in the past 5
yrs!). Just when it seemed that the contest was all over in favour of Mr. Soberai, there
was an anonymous phone call to him, allegedly from the D company operating from
Dubai. The caller threatened him that he will be bumped off13 unless he stays clear of Ms.
Ray.
Now Ms. Ray wants Mr. Soberai to buy an insurance policy that would pay her Rs
10,00,000 at the beginning of every year as long as she is alive, in case Mr. Soberai dies
before he reaches 40 yrs of age. Otherwise she would not marry him14.
Please help Mr Soberai to develop a financial expression of his love for Ms. Ray and to
quantify it. Assume that Bollywood is the same as the ordinary people in real life (and in
death).
12
Allegedly earned through entertainment shows in Dubai, promoted by the famous D company
Through a supari contract to be executed by the local sharp shooter Mr. Taporiwala
14
As any other macho Bollywood hero, Mr. Soberai wanted Ms. Ray to give up her acting after marriage
13
7
TABLE - 19(1)
Mortality Rates of Assured Lives in LIC of India - LIC 94-96 ultimate
Basic data
Age
# of
#of
(x)
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
People
alive (/x)
100000
99923
99841
99754
99662
99567
99467
99365
99259
99151
99041
98929
98815
98701
98585
98470
98355
98240
98122
97999
97871
97735
97590
97435
97267
97085
96886
96668
96435
96184
95912
95613
95284
94920
94518
94072
93579
93034
92435
91777
91057
90273
89422
Deaths
W
77
82
87
92
96
100
102
105
108
110
112
114
115
115
115
115
115
118
123
128
136
145
155
168
182
199
218
234
251
272
298
329
364
402
446
493
545
599
658
720
784
851
920
.00582396
8
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
88502
87526
86480
85350
84121
82784
81326
79739
78015
76242
74289
72148
69812
67279
64546
61616
58496
55197
51734
48131
44413
40616
36777
32940
29152
25463
21922
18610
15590
12875
10472
8380
6590
5088
3851
2854
2069
1465
1011
680
445
282
174
0
976
1046
1130
1228
1338
1458
1587
1724
1772
1953
2141
2335
2533
2733
2930
3120
3299
3462
3604
3717
3797
3839
3837
3788
3689
3541
3312
3020
2715
2403
2092
1790
1503
1237
997
785
604
453
331
235
162
109
174
The last but one row is by assumption
9
EDUCATION AND EXAMINATION COMMITTEE
OF THE
SOCIETY OF ACTUARIES
RISK AND INSURANCE
by
Judy Feldman Anderson, FSA
and
Robert L. Brown, FSA
Copyright 2000 by the Society of Actuaries
The Education and Examination Committee provides study notes to persons preparing
for the examinations of the Society of Actuaries. They are intended to acquaint
candidates with some of the theoretical and practical considerations involved in the
various subjects. While varying opinions are presented where appropriate, limits on the
length of the material and other considerations sometimes prevent the inclusion of all
possible opinions. These study notes do not, however, represent any official opinion,
interpretations or endorsement of the Society of Actuaries or its Education and
Examination Committee. The Society is grateful to the authors for their contributions in
preparing the study notes.
1-21-00
Printed in U.S.A.
i
RISK AND INSURANCE
I.
INTRODUCTION
People seek security. A sense of security may be the next basic goal after food, clothing, and
shelter. An individual with economic security is fairly certain that he can satisfy his needs (food,
shelter, medical care, and so on) in the present and in the future. Economic risk (which we will
refer to simply as risk) is the possibility of losing economic security. Most economic risk derives
from variation from the expected outcome.
One measure of risk, used in this study note, is the standard deviation of the possible outcomes.
As an example, consider the cost of a car accident for two different cars, a Porsche and a Toyota.
In the event of an accident the expected value of repairs for both cars is 2500. However, the
standard deviation for the Porsche is 1000 and the standard deviation for the Toyota is 400. If the
cost of repairs is normally distributed, then the probability that the repairs will cost more than
3000 is 31% for the Porsche but only 11% for the Toyota.
Modem society provides many examples of risk. A homeowner faces a large potential for
variation associated with the possibility of economic loss caused by a house fire. A driver faces a
potential economic loss if his car is damaged. A larger possible economic risk exists with respect
to potential damages a driver might have to pay if he injures a third party in a car accident for
which he is responsible.
Historically, economic risk was managed through informal agreements within a defined
community. If someone’s bam burned down and a herd of milking cows was destroyed, the
community would pitch in to rebuild the bam and to provide the farmer with enough cows to
replenish the milking stock. This cooperative (pooling) concept became formalized in the
insurance industry. Under a formal insurance arrangement, each insurance policy purchaser
(policyholder) still implicitly pools his risk with all other policyholders. However, it is no longer
necessary for any individual policyholder to know or have any direct connection with any other
policyholder.
IL HOW INSURANCE WORKS
Insurance is an agreement where, for a stipulated payment called the premium, one party (the
insurer) agrees to pay to the other (the policyholder or his designated beneficiary) a defined
amount (the claim payment or benefit) upon the occurrence of a specific loss. This defined claim
payment amount can be a fixed amount or can reimburse all or a part of the loss that occurred.
The insurer considers the losses expected for the insurance pool and the potential for variation in
order to charge premiums that, in total, will be sufficient to cover all of the projected claim
payments for the insurance pool. The premium charged to each of the pool participants is that
participant’s share of the total premium for the pool. Each premium may be adjusted to reflect any
2
special characteristics of the particular policy. As will be seen in the next section, the larger the
policy pool, the more predictable its results.
Normally, only a small percentage of policyholders suffer losses. Their losses are paid out of the
premiums collected from the pool of policyholders. Thus, the entire pool compensates the
unfortunate few. Each policyholder exchanges an unknown loss for the payment of a known
premium.
Under the formal arrangement, the party agreeing to make the claim payments is the insurance
company or the insurer. The pool participant is the policyholder. The payments that the
policyholder makes to the insurer are premiums. The insurance contract is the policy. The risk of
any unanticipated losses is transferred from the policyholder to the insurer who has the right to
specify the rules and conditions for participating in the insurance pool.
The insurer may restrict the particular kinds of losses covered. For example, a peril is a potential
cause of a loss. Perils may include fires, hurricanes, theft, and heart attack. The insurance policy
may define specific perils that are covered, or it may cover all perils with certain named
exclusions (for example, loss as a result of war or loss of life due to suicide).
Hazards are conditions that increase the probability or expected magnitude of a loss. Examples
include smoking when considering potential healthcare losses, poor wiring in a house when
considering losses due to fires, or a California residence when considering earthquake damage.
In summary, an insurance contract covers a policyholder for economic loss caused by a peril
named in the policy. The policyholder pays a known premium to have the insurer guarantee
payment for the unknown loss. In this manner, the policyholder transfers the economic risk to the
insurance company. Risk, as discussed in Section I, is the variation in potential economic
outcomes. It is measured by the variation between possible outcomes and the expected outcome:
the greater the standard deviation, the greater the risk.
III. A MATHEMATICAL EXPLANATION
Losses depend on two random variables. The first is the number of losses that will occur in a
specified period. For example, a healthy policyholder with hospital insurance will have no losses
in most years, but in some years he could have one or more accidents or illnesses requiring
hospitalization. This random variable for the number of losses is commonly referred to as the
frequency of loss and its probability distribution is called the frequency distribution. The second
random variable is the amount of the loss, given that a loss has occurred. For example, the
hospital charges for an overnight hospital stay would be much lower than the charges for an
extended hospitalization. The amount of loss is often referred to as the severity and the probability
distribution for the amount of loss is called the severity distribution. By combining the frequency
distribution with the severity distribution we can determine the overall loss distribution.
Example: Consider a car owner who has an 80% chance ofno accidents in a year, a 20%
chance of being in a single accident in a year, and no chance of being in more than one accident
3
in a year. For simplicity, assume that there is a 50% probability that after the accident the car
will need repairs costing 500, a 40% probability that the repairs will cost 5000, and a 10%
probability that the- car
need to be replaced, which will cost 15,000. Combining the frequency
and severity distributions fo\
"mms the following distribution of the random variable X, loss due to
accident:
0.80 x = 0
0.10 x = 500
/«=
0.08 x = 5000
0.02 x = 15,000
The car owner’s expected loss is the mean of this distribution, £[%]:
£[ = X x ’ / W = 0-80 • 0 + 0.10 • 500 + 0.08 • 5000 + 0.02 • 15,000 =750
On average, the car owner spends 750 on repairs due to car accidents. A 750 loss may not seem
like much to the car owner, but the possibility of a 5000 or 15,000 loss could create real concern.
To measure the potential variability of the car owner’s loss, consider the standard deviation of the
loss distribution:
= 080 (-750)2 + 0.10 ■ (-250)2 + 0.08 ■ (4250)2 + 0.02 • (14,250)2
= 75,962,500 = 2442
5,962,500
If we look at a particular individual, we see that there can be an extremely large variation in
possible outcomes, each with a specific economic consequence. By purchasing an insurance
policy, the individual transfers this risk to an insurance company in exchange for a fixed premium.
We might conclude, therefore, that if an insurer sells n policies to n individuals, it assumes the
total risk of the n individuals. In reality, the risk assumed by the insurer is smaller in total than the
sum of the risks associated with each individual policyholder. These results are shown in the
following theorem.
Theorem: Let Xx, X2Xn be independent random variables such that each Xi has an
expected value of p and variance of cr2. Let S„ = Xt + X2 +... + Xn. Then:
= np, and
n • PartX'.]=n o2.
The standard deviation of Sn is
for each policy.
no, which is less than no, the sum of the standard deviations
Furthermore, the coefficient ofvariation, which is the ratio of the standard deviation to the mean,
is--------= —f=—. This is smaller than —, the coefficient of variation for each individual X .
n- p
fn • p
p
4
The coefficient of variation is useful for comparing variability between positive distributions with
different expected values. So, given n independent policyholders, as n becomes very large, the
insurer’s risk, as measured by the coefficient of variation, tends to zero.
Example: Going back to our example of the car owner, consider an insurance company that will
reimburse repair costs resultingfrom accidents for 100 car owners, each with the same risks as in
our earlier example. Each car owner has an expected loss of 150 and a standard deviation of
2442. As a group the expected loss is 75,000 and the variance is 596,250,000. The standard
deviation is -j596,250,000 = 24,418 which is significantly less than the sum of the standard
deviations, 244,182. The ratio of the standard deviation to the expected loss is
24,418/75,000 = 0.326, which is significantly less than the ratio of 2442/750 = 3.26 for one car
owner.
It should be clear that the existence of a private insurance industry in and of itself does not
decrease the frequency or severity of loss. Viewed another way, merely entering into an insurance
contract does not change the policyholder’s expectation of loss. Thus, given perfect information,
the amount that any policyholder should have to pay an insurer equals the expected claim
payments plus an amount to cover the insurer’s expenses for selling and servicing the policy,
including some profit. The expected amount of claim payments is called the net premium or
benefit premium. The term gross premium refers to the total of the net premium and the amount to
cover the insurer’s expenses and a margin for unanticipated claim payments.
Example: Again considering the 100 car owners, if the insurer will payfor all ofthe accidentrelated car repair losses, the insurer should collect a premium ofat least 75,000 because that is
the expected amount of claim payments to policyholders. The net premium or benefit premium
would amount to 750 per policy. The insurer might charge the policyholders an additional 30%
so that there would be 22,500 to help the insurer pay expenses related to the insurance policies
and cover any unanticipated claim payments. In this case 7500130%=975 would be the gross
premium for a policy.
Policyholders are willing to pay a gross premium for an insurance contract, which exceeds the
expected value of their losses, in order to substitute the fixed, zero-variance premium payment for
an unmanageable amount of risk inherent in not insuring.
IV. CHARACTERISTICS OF AN INSURABLE RISK
We have stated previously that individuals see the purchase of insurance as economically
advantageous. The insurer will agree to the arrangement if the risks can be pooled, but will need
some safeguards. With these principles in mind, what makes a risk insurable? What kinds of risk
would an insurer be willing to insure?
The potential loss must be significant and important enough that substituting a known insurance
premium for an unknown economic outcome (given no insurance) is desirable.
5
The loss and its economic value must be well-defined and out of the policyholder’s control. The
policyholder should not be allowed to cause or encourage a loss that will lead to a benefit or claim
payment. After the loss occurs, the policyholder should not be able to unfairly adjust the value of
the loss (for example, by lying) in order to increase the amount of the benefit or claim payment.
Covered losses should be reasonably independent. The fact that one policyholder experiences a
loss should not have a major effect on whether other policyholders do. For example, an insurer
would not insure all the stores in one area against fire, because a fire in one store could spread to
the others, resulting in many large claim payments to be made by the insurer.
These criteria, if fully satisfied, mean that the risk is insurable. The fact that a potential loss does
not fully satisfy the criteria does not necessarily mean that insurance will not be issued, but some
special care or additional risk sharing with other insurers may be necessary.
V.
EXAMPLES OF INSURANCE
Some readers of this note may already have used insurance to reduce economic risk. In many
places, to drive a car legally, you must have liability insurance, which will pay benefits to a person
that you might injure or for property damage from a car accident. You may purchase collision
insurance for your car, which will pay toward having your car repaired or replaced in case of an
accident. You can also buy coverage that will pay for damage to your car from causes other than
collision, for example, damage from hailstones or vandalism.
Insurance on your residence will pay toward repairing or replacing your home in case of damage
from a covered peril. The contents of your house will also be covered in case of damage or theft.
However, some perils may not be covered. For example, flood damage may not be covered if
your house is in a floodplain.
At some point, you will probably consider the purchase of life insurance to provide your family
with additional economic security should you die unexpectedly. Generally, life insurance provides
for a fixed benefit at death. However, the benefit may vary over time. In addition, the length of
the premium payment period and the period during which a death is eligible for a benefit may each
vary. Many combinations and variations exist.
When it is time to retire, you may wish to purchase an annuity that will provide regular income to
meet your expenses. A basic form of an annuity is called a life annuity, which pays a regular
amount for as long as you live. Annuities are the complement of life insurance. Since payments
are made until death, the peril is survival and the risk you have shifted to the insurer is the risk of
living longer than your savings would last. There are also annuities that combine the basic life
annuity with a benefit payable upon death. There are many different forms of death benefits that
can be combined with annuities.
Disability income insurance replaces all or a portion of your income should you become disabled.
Health insurance pays benefits to help offset the costs of medical care, hospitalization, dental care,
and so on.
6
Employers may provide many of the insurance coverages listed above to their employees.
VI. LIMITS ON POLICY BENEFITS
In all types of insurance there may be limits on benefits or claim payments. More specifically,
there may be a maximum limit on the total reimbursed; there may be a minimum limit on losses
that will be reimbursed; only a certain percentage of each loss may be reimbursed; or there may be
different limits applied to particular types of losses.
In each of these situations, the insurer does not reimburse the entire loss. Rather, the policyholder
must cover part of the loss himself. This is often referred to as coinsurance.
The next two sections discuss specific types of limits on policy benefits.
DEDUCTIBLES
A policy may stipulate that losses are to be reimbursed only in excess of a stated threshold
amount, called a deductible. For example, consider insurance that covers a loss resulting from an
accident but includes a 500 deductible. If the loss is less than 500 the insurer will not pay
anything to the policyholder. On the other hand, if the loss is more than 500, the insurer will pay
for the loss in excess of the deductible. In other words, if the loss is 2000, the insurer will pay
1500. Reasons for deductibles include the following:
(1) Small losses do not create a claim payment, thus saving the expenses of processing the claim.
(2) Claim payments are reduced by the amount of the deductible, which is translated into premium
savings.
(3) The deductible puts the policyholder at risk and, therefore, provides an economic incentive for
the policyholder to prevent losses that would lead to claim payments.
Problems associated with deductibles include the following:
(1) The policyholder may be disappointed that losses are not paid in full. Certainly, deductibles
increase the risk for which the policyholder remains responsible.
(2) Deductibles can lead to misunderstandings and bad public relations for the insurance company.
(3) Deductibles may make the marketing of the coverage more difficult for the insurance
company.
(4) The policyholder may overstate the loss to recover the deductible.
Note that if there is a deductible, there is a difference between the value of a loss and the
associated claim payment. In fact, for a very small loss there will be no claim payment. Thus, it is
essential to differentiate between losses and claim payments as to both frequency and severity.
7
Example: Consider the group of\W car owners that was discussed earlier. If the policy provides
for a 500 deductible, what would the expected claim payments and the insurer’s risk be?
The claim payment distribution for each policy would now be:
0.90 loss = 0 or 500 y = 0
/(y) = 0.08 loss = 5000
y = 4500
0.02 loss= 15,000
y = 14,500
The expected claim payments and standard deviation for one policy would be:
E[y] = 0.90 • 0 + 0.08 • 4500 + 0.02 • 14,500 = 650
a2r = 0.90- (-650)2 + 0.08 • (3850)2 +0.02 (13,850)2
5,402,500
ar = 75,402,500 = 2324
The expected claim payments for the hundred policies would be 65,000, the variance would be
540,250,000 and the standard deviation would be 23,243.
As shown in this example, the presence of the deductible will save the insurerfrom having to
process the relatively small claim payments of500. The probability ofa claim occurring drops
from 20% to 10%oper policy. The deductible lowers the expected claim payments for the hundred
policies from 75,000 to 65,000 and the standard deviation willfallfrom 24,418 to 23,243.
BENEFIT LIMITS
A benefit limit sets an upper bound on how much the insurer will pay for any loss. Reasons for
placing a limit on the benefits include the following:
(1) The limit prevents total claim payments from exceeding the insurer’s financial
capacity.
(2) In the context of risk, an upper bound to the benefit lessens the risk assumed by the
insurer.
(3) Having different benefit limits allows the policyholder to choose appropriate coverage
at an appropriate price, since the premium will be lower for lower benefit limits.
In general, the lower the benefit limit, the lower the premium. However, in some instances the
premium differences are relatively small. For example, an increase from 1 million to 2 million
liability coverage in an auto policy would result in a very small increase in premium. This is
because losses in excess of 1 million are rare events, and the premium determined by the insurer is
based primarily on the expected value of the claim payments.
As has been implied previously, a policy may have more than one limit, and, overall, there is more
than one way to provide limits on benefits. Different limits may be set for different perils. Limits
might also be set as a percentage of total loss. For example, a health insurance policy may pay
8
healthcare costs up to 5009, and it may only reimburse for 80% of these costs. In this case, if
costs were 6000, the insurance would reimburse 4000, which is 80% of the lesser of 5000 and the
actual cost.
Example: Looking again at the 100 insured car owners, assume that the insurer has not only
included a 500 deductible but has also placed a maximum on a claim payment of 12,500. fVhat
would the expected claim payments and the insurer’s risk be?
The claim payment distribution for each policy would now be:
0.90
loss = 0 or 500 y = 0
y = 4500
f(y) 0.08 loss = 5000
0.02
loss = 15,000
y = 12,500
The expected claim payments and standard deviation for one policy would be:
£[/] = 0.90 • 0+0.08 • 4500+0.02 • 12,500 = 610
CT2r = 0.90-(-610)2 +0.08-(3890)2 +0.02 (U,890)2 =4,372,900
(7r
74,372,900 = 2091
The expected claim payments for the hundred policies would be 61,000, the variance would be
437,290,000, and the standard deviation would be 20,911.
In this case, the presence of the deductible and the benefit limit lowers the insurer’s expected
claim payments for the hundred policies from 75,000 to 61,000 and the standard deviation willfall
from 24,418 to 20,911.
VII. INFLATION
Many insurance policies pay benefits based on the amount of loss at existing price levels. When
there is price inflation, the claim payments increase accordingly. However, many deductibles and
benefit limits are expressed in fixed amounts that do not increase automatically as inflation
increases claim payments. Thus, the impact of inflation is altered when deductibles and other
limits are not adjusted.
Example: Looking again at the 100 insured car owners with a 500 deductible and no benefit
limit, assume that there is 10% annual inflation. Over the next 5 years, what would the expected
claim payments and the insurer’s risk be?
Because of the 10% annual inflation in new car and repair costs, a 5000 loss in year 1 will be
equivalent to a loss 0/500001.10=5500 in year 2; a loss o/50009(1.10)2=6050 in year 3; and a
loss of50000(1.10)3=665 5 in year 4.
9
The claim payment distributions, expected losses, expected claim payments, and standard
deviations for each policy are:
Policy with a 500 Deductible
f(y,t)
0.80
0.10
0.08
0.02
Expected
Amount
Standard
Deviation
Loss
Claim
0
0
500
0
5000
4500
15,000
14,500
750
650
2324
Loss
Claim
0
0
550
50
5500
5000
16,500
16,000
825
725
2568
Loss
Claim
0
0
605
105
6050
5550
18,150
17,650
908
808
2836
Loss
Claim
0
0
666
166
6655
6155
19,965
19,465
998
898
3131
Loss
Claim
0
0
732
232
7321
6821
21,962
21,462
1098
998
3456
Year 1
Year 2
Year 3
Year 4
Year 5
Looking at the increases from one year to the next, the expected losses increase by 10% each year
but the expected claim payments increase by more than 10% annually. For example, expected
losses growfrom 750 in year 1 to 1098 in year 5, an increase of 46%. However, expected claim
payments growfrom 650 in year 1 to 998 in year 5, an increase of 54%. Similarly, the standard
deviation ofclaim payments also increases by more than 10% annually. Both phenomena are
caused by a deductible that does not increase with inflation.
Next, consider the effect of inflation ifthe policy also has a limit setting the maximum claim
payment at 12,500.
10
Policy with a Deductible of500 and Maximum Claim Payment of 12,500
Expected Standard
0.80
0.10
0.08
0.02
Amount Deviation
f(y.t)
Year 1
Loss
0
500
5000
15,000
750
Claim
0
0
4500
12,500
610
2091
Year 2
Loss
0
550
5500
16,500
825
Claim
0
50
5000
12,500
655
2167
Year 3
Loss
605
0
6050
18,150
908
Claim
0
105
5550
12,500
705
2257
Year 4
Loss
0
666
6655
19,965
998
Claim
0
166
6155
12,500
759
2363
Year 5
Loss
0
732
7321
21,962
1098
Claim
0
232
6821
12,500
819
2486
A fixed deductible with no maximum limit exaggerates the effect of inflation. Adding a fixed
maximum on claim payments limits the effect of inflation. Expected claim payments growfrom
610 in year 1 to 819 in year 5, an increase of34%, which is less than the 46% increase in
expected losses. Similarly, the standard deviation of claim payments increases by less than the
10% annual increase in the standard deviation oflosses. Both phenomena occur because the
benefit limit does not increase with inflation.
VIII. A CONTINUOUS SEVERITY EXAMPLE
In the car insurance example, we assumed that repair or replacement costs could take only a fixed
number of values. In this section we repeat some of the concepts and calculations introduced in
prior sections but in the context of a continuous severity distribution.
Consider an insurance policy that reimburses annual hospital charges for an insured individual.
The probability ofany individual being hospitalized in a year is 15%. That is, P(H =1) = 0.15 .
Once an individual is hospitalized, the charges X have a probability densityfunction (p.d.f.)
/.v(x|//=l) = 0.1e’°l'forx>0.
Determine the expected value, the standard deviation, and the ratio ofthe standard deviation to
the mean (coefficient ofvariation) of hospital charges for an insured individual.
11
The expected value of hospital charges is:
£[AT] = P(H 1)£[ X\H * 1] + P{H = 1)£[^|# = 1]
= 0.85-0 + 0.15 J 0.1 x-e-°'xdx = -0.15 x e^•lx| +0.15 j e-QAxdx
o
0
0o
^r=i.5
= -0.1510e
0
E[X2 ] = P(H
l)£[y2\H * 1] + P(H = 1)£■[ JT21 // = 1]
= 0.85 02 +0.15jo.lx2e -01X6&
0
= -0.15x2e■~01x| +0.15-10j 0.1 ■Ix-e^dx = 30
0
o
The variance is: cs\ = £'[Ar2]-(£'[^])2 =30-(15)2
27.75
The standard deviation is: <JX =V27.75=5.27
The coefficient of variation is: cr jV/£[Z] = 5.27/1.5 = 3.51
An alternative solution would recognize and use the fact that fx^X\H= 1) is an exponential
distribution to simplify the calculations.
Determine the expected claim payments, standard deviation and coefficient of variation for an
insurance pool that reimburses hospital charges for 200 individuals. Assume that claims for each
individual are independent ofthe other individuals.
200
Let S =
1=1
£'[S]= 200 £[y] = 300
200 <j2v =5550
7200o\ = 74.50
12
Coefficient of variation = ^s/
Ze[S] = 0.25
If the insurer includes a deductible of 5 on annual claim payments for each individual, what would
the expected claim payments and the standard deviation be for the pool?
The relationship of claim payments to hospital charges is shown in the graph below:
Claim Payment with Deductible=5
Y=max(0,X-5)
5
4 >
■w
E
3 -
cS 2
E
C3
Q
1 0 *
2
0
4
6
8
10
Hospital Charges (X)
There are three different cases to consider for an individual:
(1) There is no hospitalization and thus no claim payments.
(2) There is hospitalization, but the charges are less than the deductible.
(3) There is hospitalization and the charges are greater than the deductible.
In the third case, the p.d.f. of claim payments is:
/>(^4-5|jy = l) _ 0.1 e-0 ^+5’
P(^>5|//= 1) “ P[X > 5|W = 1)
Summing the three cases:
£[y] = P(H l)£[r|77 1] + P(X < 5, H =
X < 5, H = 1] + P{X > 5, H = l)£[y|X > 5,H = 1]
= P(H * 1) • 0 + P(H = 1) ■ P(X < 5|/f = 1) ■ 0 + P(H= 1) • P(X > 5|JZ = 1)
> 5>H = i]
= O.isjo.l y e^'^dy = O.15 e'05J0.1 y e~QAydy
0
o
= 0.15e-°5 •10 = 0.91
13
E[Y2 ] = P(H
1) ■ 02 + P(H = 1) • P(X < 5|H = 1) • 02 + 0.15j 0.1 y1 ■ e -0.1(^+5)
0
= 0.15 e-05 J 0.1 y2
0
= 30 e-0,5 = 18.20
dr = 18.20-(0.91)2 = 17.37
(yY =
17.37 =4.17
200
For the pool of 200 individuals, let Sy = ^Yi
i=l
£’[Sr] = 200 £'[^=182
= 200 ci2 = 3474
72000^=58.94
Assume further that the insurer only reimburses 80% of the charges in excess of the 5 deductible.
What would the expected claim payments and the standard deviation be for the pool?
480%-5r] = 0.8£[5y] = 146
^SO’/oSy
(0.8)2.<t.2 = 2223
^SO’/oS,
0.8 (Tn
47.15
IX. THE ROLE OF THE ACTUARY
This study note has outlined some of the fundamentals of insurance. Now the question is: what is
the role of the actuary?
At the most basic level, actuaries have the mathematical, statistical and business skills needed to
determine the expected costs and risks in any situation where there is financial uncertainty and
14
data for creating a model of those risks. For insurance, this includes developing net premiums
(benefit premiums), gross premiums, and the amount of assets the insurer should have on hand to
assure that benefits and expenses can be paid as they arise.
The actuary would begin by trying to estimate the frequency and severity distribution for a
particular insurance pool. This process usually begins with an analysis of past experience. The
actuary will try to use data gathered from the insurance pool or from a group as similar to the
insurance pool as possible. For instance, if a group of active workers were being insured for
healthcare expenditures, the actuary would not want to use data that included disabled or retired
individuals.
In analyzing past experience, the actuary must also consider how reliable the past experience is as
a predictor of the future. Assuming that the experience collected is representative of the insurance
pool, the more data, the more assurance that it will be a good predictor of the true underlying
probability distributions. This is illustrated in the following example:
An actuary is trying to determine the underlying probability that a 70-year-old woman will die
within one year. The actuary gathers data using a large random sample of 70-year-old women
from previous years and identifies how many of them died within one year. The probability is
estimated by the ratio of the number of deaths in the sample to the total number of 70-year-old
women in the sample. The Central Limit Theorem tells us that ifthe underlying distribution has a
mean of p and standard deviation of O’ then the mean ofa large random sample ofsize n is
approximately normally distributed with mean jp and' standard
' ’ ’ deviation
’ ' "
—j=. The larger the size
yin
of the sample, the smaller the variation between the sample mean and the underlying value of p.
When evaluating past experience the actuary must also watch for fundamental changes that will
alter the underlying probability distributions. For example, when estimating healthcare costs, if
new but expensive techniques for treatment are discovered and implemented then the distribution
of healthcare costs will shift up to reflect the use of the new techniques.
The frequency and severity distributions are developed from the analysis of the past experience
and combined to develop the loss distribution. The claim payment distribution can then be
derived by adjusting the loss distribution to reflect the provisions in the policies, such as
deductibles and benefit limits.
If the claim payments could be affected by inflation, the actuary will need to estimate future
inflation based on past experience and information about the current state of the economy. In the
case of insurance coverages where today’s premiums are invested to cover claim payments in the
years to come, the actuary will also need to estimate expected investment returns.
At this point the actuary has the tools to determine the net premium.
15
The actuary can use similar techniques to estimate a sufficient margin to build into the gross
premium in order to cover both the insurer’s expenses and a reasonable level of unanticipated
claim payments.
Aside from establishing sufficient premium levels for future risks, actuaries also use their skills to
determine whether the insurer’s assets on hand are sufficient for the risks that the insurer has
already committed to cover. Typically this involves at least two steps. The first is to estimate the
current amount of assets necessary for the particular insurance pool. The second is to estimate the
flow of claim payments, premiums collected, expenses and other income to assure that at each
point in time the insurer has enough cash (as opposed to long-term investments) to make the
payments.
Actuaries will also do a variety of other projections of the insurer’s future financial situation under
given circumstances. For instance, if an insurer is considering offering a new kind of policy, the
actuary will project potential profit or loss. The actuary will also use projections to assess
potential difficulties before they become significant.
These are some of the common actuarial projects done for businesses facing risk. In addition,
actuaries are involved in the design of new financial products, company management and strategic
planning.
X.
CONCLUSION
This study note is an introduction to the ideas and concepts behind actuarial work. The examples
have been restricted to insurance, though many of the concepts can be applied to any situation
where uncertain events create financial risks.
Later Casualty Actuarial Society and Society of Actuaries courses cover topics including:
adjustment for investment earnings; economics; frequency models; severity models; aggregate
loss models; survival models; fitting models to actual data; and the credibility that can be
attributed to past data. In addition, both societies offer courses on the nature of particular perils
and related business issues that need to be considered.
16
)
Annuity Market in India
What Are the Key Public Policy Issues?
Annuities markets around the world are small but are likely to grow as a result of
reforms in the public social security systems and private pensions plans, which partially
replace the defined benefit plans with funded defined contribution plans. When people retire,
they may choose or are sometimes required to annuitise these defined contribution
savings. Therefore, it is important to learn whether or not annuities markets exist and what
kinds of market failure can be anticipated. Several papers have analysed markets in the
US, UK, Canada, Switzerland, Australia, Israel, Chile and Singapore. This paper extends the
analysis by examining the annuities market in India. The paper focuses on the analyses of
the expected present discounted value (EPDV) of cash flows from the annuity, and the
money's worth ratio (MWR), which is the EPDV divided by the initial premium cost.
It points to several key weaknesses in the annuities market that need to be corrected to
enable the development of a healthy annuity industry in India. It also summarises
some of the key policy choices that must be made to enable it to ploy an effective
role in the broader pension reform.
Estelle James, Renuka Sane
tance of a vibrant annuity industry. Most
attention so far, both in India and else
where, has focused on the accumulation
A ccording to the Project Oasis re- stage, during which retirement savings
/\ port, less than 11 per cent of the accounts are built up, without giving much
JL X. estimated working population in thought to the decumulation phase, which
India is eligible to participate in a formal appears to be far off in the future. How
pension system and about 90 per cent of ever, retirement savings will eventually be
the population does not come under the withdrawn and consumed. The challenge
purview of any such mechanism.! The is to design a decumulation phase such that
pension system for government employees people don’t run out of income before they
is running into troubled due to the strain die, and also make this cost-effective. If
it is placing on government finances. Mean EPF is reformed to permit higher rates of
while, private sector workers covered by return and accumulations, annuities will
the Employees Provident Fund (EPF), a assume greater importance as they provide
defined contribution scheme, are faced an opportunity to convert these savings
with inadequate terminal accumulations, into a guaranteed flow of retirement in
primarily as a result of low returns and come for life. Therefore, it is important to
liberal withdrawals. Moreover, the EPF learn how the annuities markets operate,
does not provide a lifetime income stream. to analyse whether the annuity market in
Rather, participants.receive their money India can be relied on to provide reliable
upon retirement in a lump sum. If they live retirement income at reasonable prices,
15-20 years after retirement, as many and to anticipate possible market failures
undoubtedly will, they may run out of in order to take preventative action.
The annuity industry m India is small.
money. Doubts also persist over the effi
ciency, transparency and sustainability of Both demand and supply are minimal. The
the defined benefit plan for private sector opening of the insurance sector has ush
workers, the Employees Pension Scheme ered in new potential players, but the variety
of products offered has been limited and
(EPS).
The impending pension reforms and the response of the industry cautious. In
subsequent transition to a social security this paper, we deal with issues that are
system that incorporates more productive central to the healthy development of this
individual accounts heighten the impor industry. Taking the present situation as
I
Introduction
Economic and Political Weekly
February 22, 2003
a starting point, we ask: do annuities in
India provide good value for money? Are
annuitants likely to get back the premium
they pay in, plus interest, over time? The
money’s wonh ratio (MWR) analysis is
one measure of the value of an annuity.
The MWR tells us how much of the initial
premium the annuitant eventually gets back
as income. It is the ratio of expected dis
counted lifetime benefits to initial capital
cost. An MWR of 1 indicates that the
consumer is getting back in present ex
pected value exactly what he put in, plus
interest that equals the discount rate. The
MWR depends on payouts of annuity
products (how much is received each
month), mortality of the population (how
long the annuitant will live) and the in
terest rate used for discounting. Consumers
want to be sure that they can expect to get
back their premium plus a reasonable rate
of return, companies want to be sure they
are not paying more than is affordable, and
regulators want to be sure that consumers
are treated fairly and that companies will
keep their promises. Thus, they all care
about the MWR.
This study summarises what we already
know about the Indian annuity market
and identifies steps that must be taken
by the government and the industry to
enable the industry to grow. Specifically,
we argue that:
729
- Better data are needed on expected months. Section VI discusses the key
(2) In 2000, new annuity business vat
was;
mortality rates of different sub-groups policy choices that government and still only 1.3 per cent of new life business
within the diverse Indian population, and industry leaders must make in the near
in terms of new policies, and 2.3 per cent
on probable improvements in these rates future, to enable healthy growth of this in terms of new premiums.
over time.
industry. The conclusion summarises our
(3) Added to this individual annuity
- Long-term financial instruments, in empirical results and the next steps
business is a large group business from
cluding long-term government bonds (pos forward.
superannuation plans, which include pen
sibly price-indexed), must be further
sion investments and annuities.
developed to enable insurance companies
II
While we focus on the individual busito match the long-term liabilities implied
Annuity Market in India
ness* lhe group annuity business is sub
by annuities.
stantial, as it is mandatory in employer- Investment regulations and regulatory
One would expect that the absence of run superannuation funds to annuitise twoauthority
should
be
modernised.
M
....
asocialsecuritysystemthatpaysalifetime thirds of the account upon retirement
New products, including variable (par- income stream, combined with low cov- During the accumulation stage, employers
ticipating, for-profit) annuities, with and erage of formal company schemes, would place the accounts in trust funds or insurwithout
wimoui floors,
noors, need to be constructed to lead to a high demand among people ance company for management. At retire
auract consumers with diverse preferences approaching retirement for annuity prod- ment, the funds are handed over to an
i
for risk. TkThis, in ».turn, implies
more com ucts Qn the contraryt the demand for
insurance company (usually LIC), which
plex standards and regulations.
annuities in India has been minuscule. then offers a group annuity. Recently, the
- Mechanisms should be developed for The annuity industry has not been able to trend has been towards offering an‘open
dispensing information about products and penetrate the insurance market, or for that market option’ that allows individuals the
payouts offered by insurance companies, matter the psyche
of the Indian
customer,
• •
------- ---------- choice of insurance company for
as they enter the market.
The
The Indian
Indian annuity
annuity industry
industry is
is annuitisation. This open-market option
Section II presents key statistics on the characterised by low rates of participation could facilitate the development ofa mai ket
annuity industry in India - its size, prod by the public, a small number of providers, for individual annuities. However, expeucts and potential growth. Section III and limited product innovation. The in- rience from the UK suggests that most
analyses the money’s worth ratio. We dustry is currently dominated by the Life workers do not exercise this option or are
present data on payouts of different annu Insurance Corporation of
.rrIndia
.• (LIC).
z,
even aware of it.
ity products as well as the interest and With the opening of the insurance sector,
Most annuities in India are taxmortality rates that are used to determine e£s exPCCjed from HDFC Standard advantaged savings vehicles that take the
these payouts, and we show how the in Life, Tata AIG, and ICICI Prudential.
—-------- ------------- form of deferred annuities, rather than
dustry
has reacted rto recent
changes
in ’Mutual
funds are also
<' in the process of immediate life annuities. LIC used to offer
rh^evariaMAcQ
tw
u
."T-------------tnese variables. Sections IV and V exam- cobtaining permission
• . from
- Will the
. Securities
UUJJIUII 11
U1V JUVUlll
two deferred annuities - Jeevan Suraksha
me data on administrative and marketing and Exchange Board of India (SEBI)) to and Jeevan Dhara. Recently these schemes
costs, • and ..on investment
, returns, which
71 otterannuily Products. But as of now, LIC were merged into one and there is now only
enter i _ o tbe company s calculations m is virtually the entire market.
one deferred annuity plan, called the New
an important way. We argue that compa
Table 1 presents summary data on the Jeevan Suraksha-I/ New Jeevan Dhara -1,
nies cover their costs and ‘profits
out of
thr
SIZe-°f ^e annuity business versus the life LIC also sells an immediate annuity, New
the spread between the rate of return they insurance business for the industry. We see Jeevan Akshay - I, Prudential ICICI and
Jeevan Akshay - I, Prudential ICICI and
earn on their investments and the rate they that:
HDFC Standard Li fe also provide deferred
pay consumers. Falling interest rates in
(I)
(1) T\
Thew annuity uuoiuvoa
business naa
has ibeen annuity schemes. Prudential ICICI has a
the Indian markets and non-availability of growing since 1996, but the growthi rate
scheme similar to that of an immediate
long-term bonds, combined with increas has been \ ery uneven, ranging from - 64
annuity. Third company sells variable
ing longevity among annuitants, have per cent to +1555 per cent in various
annuities in its group superannuation
resulted in decreased payouts in recent years.
schemes.
A recent study by the National Council
Table 1: Size of Annuity and Life Insurance Markets in India
for Applied Economic Research (NCAER)
1996
1997
1998
1999
2000
and SEBI throws some light on the low
Annuities-new business
present and projected demand for annu
Premiums (lakh Rs)
183
14494
4893
9789
17262
ities and the growth of deferred annuities.
* policies (lakh)
.11
1.82
.66
1.05
2.23
The
most popular savings vehicle, by far,
Av Rs per policy
1664
7964
7414
9323
7741
per cent growth (# policies)
consists of fixed deposits. Only the group
1555
-64
59
112
Business in force-# policies (lakh)
that had income exceeding Rs 10,000
7.58
9.59
Life insurance-new bus
(USS 208) monthly had a large share of
Premiums (lakh of Rs)
281363
334539
384112
486341
600828
» policies (lakh)
savings in LIC, and practically none of this
110.21
122.68
133.11
148.44
169.77
Av Rs per policy
1706
was in immediate annuities, insurance
1867
2010
2208
2423
Business in force-#policies (lakh)
708.78
776.66
849.15
916.37
clearly is a luxury of the higher income
1012.9
Annuities as per cent of life
class and annuities are viewed by them as
insurance-new business
Premiums
- tax-advantaged saving instead of old-age
.065
4.33
1.27
2.01
# policies
.09
1.48
.49
security. Between 1987 and 1992. tax relief
.71
1.31
was provided for Jeevan Dhara and Jeevan
730
Economic and Political Weekly
February 22. 2003
Askha) and growth in demand was phe (sickness, dowries or weddings), annuities MWR for a single life annuity is:
nomenal. When the tax-relief was with normally do not allow flexibility in the
MWR = | (T-a)’l2 PM. AJ ,
drawn in April 1992, the individual pen time stream of income.
z
ca
- Control over investment strategy.
sion business stopped growing and many
1=1
d + i,)'
Jeevan Dhara policies were surrendered. Annuities may be seen as inflexible instru
In 1996. tax relief was provided for a new- ments, which do not give the annuitant any where:
deferred annuity, the Jeevan Suraksha plan. control over risk-return trade-offs or in T = Maximum attainable age.
a = Age (in years) of annuitant at start
Accordingly.as Table 1 shows, the number vestment strategy.
- Adverse selection. The high longevity
of contract,
of individual policies sold increased by
1554.5 per cent. In 2000-01, LIC sold a of annuitants (see below) leads to low t = Number of months beyond annuity
starting date,
total of 3.44 lakh annuity policies, of which payouts, which in turn makes annuities
Jeevan Suraksha accounted for 3.07 lakh, unattractive to the average population Pa.. = Probability of individual being alive
l months after age a,
and other (immediate) annuities were a member.
- High discount rates. While the insur Aa = Monthly annuity payment for annu
mere 0.37 lakh.
ity purchased at age a,
The fact that deferred annuity schemes, ance company must discount according to
which are basically accumulation instru rales they receive on investments, many Ca = Cost of policy for individual pur
chasing annuity at age a,
ments, are much more popular than imme people have higher discount rates; this
diate annuity is consistent with the expe may be true, in particular, of middle and it = Nominal monthly t-period spot rate.
The numerator of the expression is the
rience of countries such as the US, Canada low-income groups who need their money
and Australia. However, unlike these other for immediate or near-term consumption. ‘expected present discounted value’
While the last reason may prevent people (EPDV) of the lifetime income stream from
countries, purchasers of ‘deferred annu
ities’ in India are required to annuitise from annuitising unless it becomes man the annuity, while the denominator Ca is
upon retirement. They can take out 25 per datory, the other reasons for low demand the initial capital cost. If the MWR is 100
cent of their premiums plus interest as a can be mitigated by innovative product per cent, this means that consumers can
lump sum, but 75 per cent must be con development that gives people an oppor expect to get back what they paid in, in
verted into a life annuity - so ultimately tunity to incorporate bequests into annu addition to longevity and investment in
longevity insurance is involved. In the ities, allows some flexibility in liming of surance. The 100 per cent MWR is often
past, LIC specified the conversion terms payouts, gives annuitants a choice of in referred to as the ‘load factor’. If the MWR
on the date the deferred annuity was ini vestment strategy, with corresponding is considerably less than 100 percent (a high
tially purchased, so the company was sharing of risks and returns, and includes load factor), consumers are getting back
bearing the full longevity and reinvest options attractive to groups with low life a lot less than they put in, and this may
ment risk, for a period that might span 70 expectancies.3 It is important, both for not be a good deal for them. If it is much
years from date of purchase to date of industry and for public policy, to analyse greater than 100 per cent this raises the
death. Recently, this arrangement was the reasons for the low purchase of annu prospect that insurance companies are
changed and the conversion terms are now ities as a first step towards reversing this offering too much in order to gain market
share in the short run and may not be able
unspecified until retirement; the terms trend.
to keep their promises in the long run;
prevailing on the date of conversion then
possibly regulators should be concerned.
III
apply. In effect, this passes the interme
The MWR clearly depends on market
diary investment and mortality risk on to
Money’s Worth Ratio
payouts, interest rates and mortality rates.
the prospective annuitants and greatly
We structure this paper as a search by Interest rates turn future payouts into
shortens the period over which the com
pany bears this risk. This change in LIC financial analysts for the MWR. However, present discounted values while mortality
policy may be a response to declining insurance companies, consumers, regula rates turn them into expected values,
interest and mortality rates and a realisation tors and policy-makers must carry out the depending on survival probabilities.
that these declines may continue. It is same search for their own reasons. Com
consistent with the higher load that LIC panies must figure out how large are the
Payouts and Their Variation
now imposes on immediate annuities - the payouts that they can offer, consumers
by Product
topic of this paper. Later wediscuss possible must calculate the expected value to them
Suppose a worker starts his career by
interactions between the deferred and of alternative annuity products (versus no
annuitisation at all), regulators must en earning Rs 31,043 per year, works for 40
immediate annuity markets.
Some reasons for the low participation sure that the system as a whole is solvent, years with a real annual wage growth of
and policy-makers must understand the 2 per cent (due to economywide growth
in the annuity market may be:2
- Myopia. People do not see a need for industry in order io set the rules of the + age earnings growth) and contributes
game.
2 per cent of his wage every year to a
annuitising their savings.
Do annuities provide good value for retirement savings account on which he
- Bequests. People may wish to leave
their assets to their families rather than money? Are annuitants likely to get back earns a real rate of return of 5 per cent.
the premiums they pay in. over time? To Then at the end of 40 years his final annual
using it all up in an annuity.
- Precautionary saving and desire for answer these questions, we calculate the wage is Rs 67.200 and his retirement saving
liquidity. People may save for precaution MWR, that is, the present value of the . accumulation is Rs 1,00,000 (abstracting
ary reasons and want access to their money expected future payments relative to from inflation). If he turns this accumu
when needed for emergency purposes the initial premium cost. Concretely, the lation into an annuity, what will he earn
d.l
Economic and Political Weekly
February 22, 2003
I
f
731
in exchange for his Rs 1,00,000? In this
section we investigate how the answer to
this question varies by product that is
chosen.
Table 2 shows the payouts an annuitant
will get if he purchases an immediate
annuity through the New Jeevan AkshayI scheme floated by LIC. The data allows
us to measure trade-offs between differ
ent types of insurance that a worker might
want to buy. In June 2002, an annuitant
could get Rs 844 per month for an indi
vidual nominal single premium immedi
ate annuity (SPIA), but if he wants to
purchase a partial bequest in the form of
10-yearguaranteed payment he must forego
5.5 per cent of the monthly benefit and gets
only Rs 800. If he wants a joint annuity
that will provide 50 per cent of the
benefit to the spouse upon his death, he
will have to forego 12.9 per cent and
receive only Rs 747. Annuities that esca
late at a fixed rate of 3 per cent per year
start out with a monthly payout of Rs
707. The payout automatically increases
each year, so after six years it passes the
Rs 844 that the annuitant would have got
with a non-escalating SPIA. An escalating
annuity may be a crude way for payouts
to keep pace with expected inflation; but
it does not protect workers against unex
pected increases in inflation. Only an
annuity indexed to the price level will offer
this, and this insurance is not offered in
India.
Interest Rates
Ideally, the discount rate used should
reflect consumers’ time and risk prefer
ences, which should also coincide with
the rates available on alternative invest
ments. Using the term structure of gov
ernment interest rates as a risk-free rate
would be appropriate for consumers who
hold other savings, prefer (or are at the
margin of making) risk-free investments,
and consider annuities completely safe.
For consumers with a preference for riskier
assets, or those who consider annuities
unsafe, a higher discount rate is appropri
ate Brown et al (2000) used the AA
corporate bond structure as their risky
discount rate James et al (2001) use trea
sury + 1.4 per cent, as a better reflection
of the risk in the typical insurance com
pany portfolio. Consumers who have no
voluntary savings, are liquidity con
strained or are borrowing rather than
investing might have an even higher
discount rate.4
732
Figure: Sovereign Yield Curve
11.00-1
10.50
10.00
9.50
9.00
(5
8.50
q>
8.00
7.50
7.00
6.50
6.00
i
1
3
5
7
i
i
11
13
15
17
Years
- -October 19,2001. — January 7,2002, - June 17,2002, _ July 1.2002
We use the government rate as a risk
free benchmark by which to measure the
relative return to consumers. However,
since most low earners have little volun
tary savings and many high earners
probably want to invest in riskier assets
with a higher expected return, it is likely
that for many potential annuitants the
appropriate discount rate is higher than
the government rate. Moreover, the port
folios in which insurance companies in
vest are not completely safe. Therefore,
we also present results for a ‘risky’ rate:
the government term structure + 1.4 per
cent. As we shall see, it roughly corre
sponds to the rate of return on invest
ments that would be just high enough
to cover insurance company costs, and
is a better approximation of their actual
portfolios.
Interest rates in the Indian economy were
regulated until 1997-98, when mediumand long-term rates were approximately
12-13 per cent. In the deregulated world
they started falling and by 2000-01 had
dropped by 2-3 percentage points. As
discussed below, the interest rate on govern
ment bonds has continued falling during
the past year, and this should change annuity
payouts and possibly the MWR. We col
lected payout data for two points in lime
- October 31, 2001 and June 19, 2002.
Over this period, medium- and long-term
rates fell from 9-10 per cent to less than
8 per cent. Additionally, the term structure
became much less sleep, as short-term
rates continued to hover around 7 per cent
(see Figure). This drop in nominal rates
occurred because of changes in the broad
macroeconomy, and corresponded to a drop
9
19
in real rates, as the inflation rate was roughly
constant at 5 per cent.
We would expect the falling and flatter
term structure to have the following effects
on payouts and MWR:
(1) Lower interest rates overall would
lead to lower payouts (because they pro
vide a lower return on insurance company
investments), but if the payouts were
actuarially fair the MWR would be unaf
fected, by definition.
(2) In contrast, a flatter yield curve - i e,
a drop that is concentrated in the mediumand long-term - might lead to lower MWRs
(because insurance companies may have
previously obtained higher rates of return
by mismatching assets and liabilities and
investing in long-term instruments, but
can no longer reap such gains if long-term
rates fall disproportionately; hence, to cover
their costs insurance companies must
increase their load).
(3) Insurance companies may follow
smoothing policies that temporarily hold
annuity prices constant through time as
interest rates change. In such cases, current
interest rates would not be a good predictor
of current annuity payouts or MWRs. This
may be happeningdue to regulations or due
to the absence of competitive pressures (in
monopolised markets, as in India).5
Mortality Tables
India-specific vs UK data\ Calculation of
the present value of expected lifetime
payouts depends on mortality rates of
annuitants. Annuitant mortality rates are
likely to be much lower than population
wide mortality data, because annuitants
Economic and Political Weekly
February 22. 2003
come from higher income urban groups we refer to the 1994-96 data as the EPF estimate how much adverse selection is
with longer expected lifetimes. Moreover, population mortality and the 1996-98 data taking place, but we do observe that life
the relevant mortality rates must be ad as the annuitant mortality. Note that life expectancy for the annuity purchasers is
justed for improvements that have been expectancy for the population as a whole greater than for the EPF population or for
taking place from year to year, in expected is two-three years lower than our estimates the population as a whole (see further
lifespans. Such mortality tables, adjusted for the EPF population. LIC has not been discussion of adverse selection below).
for expected improvements, are known as able to calculate impaired life mortality as Estimating the mortality improvement
cohort mortality tables, since they change it docs not have data on which lives are factor: Even if India knew the life expect
for each birth cohort. Unfortunately, until impaired. Nor has it been able to obtain ancy of retirees in the past, this would not
recently annuitant mortality data did not the trend of mortality improvement in the accurately tell us how long an average 65
exist in India and even now the data that past, which might help in estimating ex year-old would live in the present or fu
exist are from ‘period table', based on pected future improvement. All insurance ture, because life expectancy has been
cross sectional data, unadjusted for antici companies in India follow these same improving over time. We will live longer
pated mortality improvements.
period mortality tables, although in their than our parents and our children will live
In the absence of India-specific data, pricing policies they include an ad hoc longer than us. In pricing annuities, insur
LIC has been using different British tables. ‘safety factor’ that they were not willing ance companies must take longevity im
In 1985 LIC adopted the a(90) ultimate to divulge to us, in lieu of a formal mortality provements into account and in evaluating
table, which is based on mortality expe improvement factor.
their expected value, prospective consum
rience of male and female annuitants in Need for data on differentiated mortality-. ers must do so loo. This is the way period
the UK over the period 1967-70. Different Given the heterogeneity in the Indian mortality tables are converted into cohort
adjustments have been made to this table market, one would expect vast differences tables.
from time to lime for pricing immediate in mortality across various sections of
However, it is very difficult to estimate
annuities for Indian and European lives - society. Different population groups, in how rapidly life expectancy will grow.
both male and female—as well as for effect, represent different risks and should Some demographers believe that biogenetic
arriving at total liabilities of the annuity therefore be placed in different pricing research will extend human life indefi
business. Without carefully corrected data, payout categories. If this does not happen, nitely, while others believe we are close
however, the basis for such adjustments the large body of low and middle earners, to the limit. Uncertainty about future
whose life expectancy is likely to be lower mortality improvements is particularly great
is questionable.
Population versus annuitant mortality: In than that of high earners, will feel that in countries like India, because they de
1994-96 LIC carried out an investigation annuities are not a good deal for them and pend on broad factors such as improve
of mortality among all its insured lives, will not purchase annuities voluntarily. ment in water, sanitation and nutrition, and
primarily those covered by life insurance. This can imply market inefficiency be the diffusion of medical technology and
The latest investigation was carried out for cause low-risk (low longevity) workers are products from more industrialised coun
the period 1996-98, where only group thereby excluded from the insurance tries, which may proceed at a very uneven
immediate annuities purchased by trustees market, or perverse redistribution if every
Table 2: Monthly Payout for New
of occupational pension schemes were one is required to purchase annuities, since
Jeevan Akshay-I, Rs 1,00,000
low
earners
will
end
up
subsidising
high
considered. (Individual annuities were not
Premium - Immediate Annuities
included.) The report on the new data was earners. For risk differentiation to lake
at 65, June 2002
submitted in January 2000. During 2000- place (in order to avoid perverse redistri
Product
Monthly Payout
01, LIC had to decide how to react to this bution and to encourage the voluntary
SPIA
844
purchase of annuities), India requires
new information.
5 YG
833
mortality
data
that
are
broken
down
by
The 1996-98 table exhibits much lower
10 YG
800
mortality rates than the 1994-96 tables, as population groups - men versus women, 15 YG
756
707
members under occupational pension plans urban versus rural, and lower versus higher 20 YG
Joint SPIA
747
education.
As
of
today,
such
disaggre
are officers, executives and higher paid
Escalating SPIA
707
Return of purchase price
employees, who lend to live longer. Ac gated data do not exist.
580
In most countries differentiation by
cordingly, our calculations for the 199698 table show a very high life expectancy gender is most basic, as women at 65
Table 3: Annual Payout for Rs 1,00,000
Premium in New Jeevan Akshay-I
at age 65 of 82.3, which is comparable to typically live three-four years longer than
Immediate Annuities at Age 65-June 19,
developed countries and therefore not a men. However, female longevity seems
2002 versus October 31,2001
correct estimate of the life-expectancy of very close to male longevity in India (ac
2002
2001 New/Old Ratio
the total Indian population. The 1994-96 cording to World Bank population data). Product
life table captures a wider population as Since virtually all purchasers of annuities SPIA
10,128 13,240
.77
it includes all sorts of working as well as are men, we use male mortality in (he fol 5YG
9996
13,020
.77
9600
12,540
.77
non-working groups. Moreover, purchas lowing calculations. In selected countries 10 YG
15 YG
9072
11,970
.76
ers of life insurance would be expected to breakdowns by socio-economic status are 20
YG
8484
.74
11,410
have higher mortality than annuitants, due available. Given the wide variation in Joint SPIA
8964
.74
to adverse selection. With a life expect incomes and access to medical facilities (50 per cent)
12,140
.74
ancy al 65 of 79.3, it is probably more in India, such differentiation would be Escalating SPIA 8484 11,400
Return of
representative of the broad EPF popula particularly crucial here. The paucity of purchase price
6960
.67
10,330
tion. Therefore, in the discussion below data makes it extremely difficult to
Economic and Political Weekly
February 22, 2003
733
pace, in addition to more predictable
steadier forces. One possible approach is
to make the MWR calculations for two sets
of improvement factors, so we obtain some
perspective on the degree of uncertainty
involved. In the past, much of the improve
ment in life expectancy has occurred in the
first year of a child’s life, but in the future
much of it will be concentrated in the final
years of an old person’s life. In other
countries, life expectancy at 65 has in
creased at a rate close to 1 month per year,
but this has varied considerably across
time and regions. In some countries the
shift from period to cohort tables increases
life expectancy by 1-2 years, or 5-10 per
cent, while in other countries the projected
improvement is close to 0.
A fundamental prerequisite to a well
functioning annuity market is a set of
mortality tables that captures mortality
differences across the population and make
it possible for companies to offer suitable
products. If the annuity market in India has
to evolve, well developed mortality tables,
including estimated improvement factors,
are the first step.
Changing Value of MWR
We calculate the MWR using the gov
ernment bond term structure as the riskfree discount rate and the government bond
rate + 1.4 per cent as the risky discount
rate. Additionally, we use two alternative
mortality tables - the 1994-96 table and
the 1996-98 table. The latter applies to a
select group of high-income annuitants
with much greater longevity, the former
is a more general cross section of the EPF
population, and both have much lighter
mortality than the average population
member. Previous studies of the MWR in
other countries have shown rates that are
close to, and sometimes exceed 100 per
cent. But many of these other countries
have quite competitive insurance indus
tries. We sought to determine whether the
MWR would also be high in India, in
which LIC has had a near-monopoly for
many years.
We first obtained payout data for Oc
tober 31, 2001. During 2001-02, as ob
served above, interest rates fell dramati
cally. Therefore, we obtained a second set
of payout data for July 19.2002, to measure
the response of the annuity market. Table 3
shows that most payouts fell by 23-26 per
cent, and for the product that guaranteed
return of purchase price, payouts fell by
33 per cent.
734
We sought to determine the degree to
which this sharp drop in payouts is ex
plained by: (1) changes in interest rates,
(2) the shift in mortality tables from 1994-.
96 to 1996-98, or (3) other factors. We
hypothesised above that falling interest
rate levels would lead to lower payouts but
constant MWRs, ceteris paribus, and
greater longevity would have this same
effect, but other factors might reduce the
MWR. Table 4 throws light on how much
each of these factors contributes to the
change in payouts.
Columns 1 and 2 display the MWRs
calculated using original payouts with the
old interest rates; column 1 shows MWRs
for the average EPF population member
and column 2 for the average annuitant.
For the single premium immediate annuity
(SPIA), the difference in MWRs due to
selection is 8 per cent. But for both groups,
the MWRs on all products are very high
- approximately 100 per cent for the EPF
population and 107-11 per cent for annu
itants. From the vantage point ofthe average
annuitant who used this discount rate, the
expected value of payouts far exceeded the
initial premium (col 2). From the vantage
point of the supplier, LIC, it was coming
to realise that this pricing policy involved
a large potential loss, given the greater
longevity of its annuitant group compared
with the EPF population ((MWR in col 1
around 100 per cent but in col 2 far > 100
per cent). The MWR is particularly high
for the 15 and 20-year guaranteed prod
ucts. Such high MWRs indicate that in
surance companies felt they would be able
to earn a higher, possibly riskier rate of
return in the long run, to cover their costs
and profits and, furthermore, they did not
anticipate sharply higher mortality. Both
of these expectations were undercut in
2000-02.
Columns 3 and 4 show what happened
to these MWRs when interest rates fell in
2002 - suddenly MWRs shot up by 8-9
per cent. LIC now found itself in a perilous
position - it was returning an expected
stream of benefits that were 18 per cent
more than the present value of premiums
collected. Of this 18 per cent total, about
half was attributable to the fact that an
nuitant life expectancy was greater than
that for the EPF population as a whole (the
difference between columns 1 and 2) information that they had developed two
years previously. The other half was due
to the sudden decrease in interest rates,
which meant that they could no longer earn
as high a rate of return on investments as
they had in the.21past (the difference
between columns 2 and 4). We conjecture
that LIC (correctly) found this to be a nonsustainable situation and decided to adjust
payouts downward.
Columns 5 and 6 show the MWRs based
on the new payouts and new interest rates.
For annuitants, the MWRs have fallen to
roughly 90 per cent for most products, and
for the average EPF population member,
they have fallen considerably below that.
(For the SPIA, the MWRs are 89 per cent
and 81 per cent, respectively). Therefore
we find that payouts were adjusted by
much more than was necessary to restore
financial balance. If the object of LIC had
been to get back to its 2001 position (MWRs
in col 2), payouts could have been adjusted
downward by only 7 per cent. If the object
was to use this opportunity, as well, to take
account of the new information about life
expectancy, and get the MWR of annu
itants back to 100 per cent, payouts could
have been adjusted downward by 15 per
cent. Instead, payouts were adjusted down
ward by 25 per cent, on average. Thus,
about 30 per cent of the cut in payouts is
explained by the interest rates drop and
another 30 per cent by the shift to the use
of lighter annuitant mortality tables. The
decision to impose a much higher load
factor - about 10 per cent of the premium
- explains the remaining 40 per cent of the
cut. This experience in India contrasts with
cross-country comparisons in which inter
est rate differentials play the major role in
explaining payouts differentials [James and
Song 2001].
Why has the load factor risen so dramati
cally, from less than nothing to 10 per cent
of the premium? We hypothesised above
that a flattening out of the yield curve
would lead to higher loads, because this
would reduce the gain to LIC from mis
matching short-term liabilities against long
term assets (expecting that sufficient li
quidity would be provided by new premi
ums). These results are consistent with that
hypothesis. It is also possible that the drop
in interest rates led LIC to expect still
further drops, and therefore to greater
reinvestment risk. It would require a higher
load to cover that risk.
Closely related, regulatory and/or socio
political factors may have led LIC to follow
a smoothing policy and delay reductions
in payouts in 2001, even when annuities
were known to be underpriced based on
the new longevity information. The sharp
drop in interest rates in 2002 may have
given LIC a political opportunity to adjust
Economic and Political Weekly
February 22. 2003
payouts to these longer-term factors.
Moreover, the re-evaluation of expected
longevity may have led to a realisation that
the company had lost money on previous
annuity sales, and it may have decided to
recoup this loss by making a larger profit
on its new annuitants. This would imply
an ex post inter-generational redistribu
tion from new retirees who will receive
inferior payouts, to old retirees, w-ho are
already locked in higher payouts. As the
insurance market becomes more competi
tive, LIC will not have the market power
to bring about such inter-generational
redistributions, but it still has that capacity
now. Along similar lines, the company
may have decided to build in an ad hoc
safety factor in view of future mortality
improvements, and part of the new load
undoubtedly reflects that decision.
Finally, the interaction between the
immediate and deferred markets may have
played a role in reducing the MWR. The
biggest loss to the company will accrue
because, in the past, it had guaranteed
payouts to holders of deferred annuities
that were based on the old high interest
rates. These payouts are now locked in for
many years to come; many of the holders
of deferred annuities are still 10-20 years
away from retirement. When they retire,
LIC w'ill begin to show a loss that will have
to be made up somehow - at a time when
the market is likely to be much more
competitive. As discussed above, to fore
stall further loss-making obligations, LIC
changed its policy and on future sales of
deferred annuities the conversion terms
will depend on prevailing rates at date of
retirement. At that point, the holders of
deferred annuities will be a captive market
of consumers, since they are required to
annuitise with LIC. Moreover, this group
is much larger than the purchasers of
immediate annuities have been in the past.
LIC is therefore in a good position to make
a profit on the new group of deferred
annuitants, by reducing the MWR it offers
in the immediate market.6 In other words,
2002 may have been seen as an opportune
moment for delayed and anticipatory
adjustments (reacting to past actuarial
losses and anticipated future drops in
interest and interest rates), as well as the
changing nature of the annuity market,
rather than simply a moment for adjusting
to the immediate interest rate changes.
We do not know which of these expla
nations played the largest role in LIC’s
decision to cut payouts, but we do know
that this decision means that the expected
present value of payments that annuitants
will receive is only 90 percent of the initial
premium, instead of over 109 per cent, as
it was one year ago. (For other MWR
calculations see Appendix).
Lower MWR When Discounting
at ‘Risky’ Discount Rate
Some individuals may use a higher
discount rate in evaluating the worth of an
annuity. This would include people with
a higher time preference and those who
prefer to accept higher risk in exchange
for a higher expected return. Some people
would prefer to have a consumption stream
that is more heavily weighted towards early
retirement, rather than later retirement by
which time they may die or be too ill to
enjoy their money. We therefore evaluated
the old and new payouts at a riskier rate
of treasuries + 1.4 per cent. Not surpris
ingly, the MWR falls substantially. Com
paring columns 1 and 2 in Table 5 with
columns 1 and 6 of Table 4, we see that
the higher discount rate leads to a drop of
about 7 per cent in the MWR. Recent
studies indicate that the rate of time pre
ference may be much higher than govern
ment + 1.4 per cent for many people.7 For
individuals with higher discount rates, the
perceived load factor from current payouts
would be higher still. The smaller MWR
Table 4: Impact on the MWR of the Shift to Lower Payouts: How Much Was Due to
Lower Interest Rates, Higher Mortality or Other Factors?
Old Payouts Old Payouts Old Payouts, Old Payouts,
and Interest and Interest New Interest New Interest
Rates.
Rates,
EPF Pop
Annuitants
EPF Pop
Annuitants
SPIA
5YG
10YG
15YG
20YG
50 per cent to
spouse on death
3 per cent escalating
736
New Payouts New Payouts
and Interest
and Interest
Rales,
Rates.
EPF Pop
Annuitants
99.8
101.3
104.7
107.8
109.6
108.8
109.1
110.0
110.8
110.9
105.9
107.3
110.9
115.4
118.8
116.5
116.7
117.6
119.2
120.6
81J
82.4
84.9
87.5
88.4
89.2
89.6
90.1
90.4
89.6
99.7
103.5
107.1
115.1
106.4
111.2
115.4
125.1
78.6
82.7
85.2
93.1
perceived by many potential consumers
may go far towards explaining why the
demand for annuities has been low in India
and most other countries. Giving consum
ers the possibility of a higher return through
a variable annuity in which risk is shared
between annuitant and insurance company
may be a way to satisfy one segment of
this excluded market.
Lower MWR for Average
Population Member - Adverse
Selection?
Table 4 also exhibits lower MWRs for
the 1994-96 assured life table than the
1996-1998 annuitants table (compare
columns 1 versus 2, 5 versus 6). As a
typical example: using the risk-free rate,
an average EPF worker who bought an
individual level SPIA in June 2002 will
get an MWR of only 81 per cent compared
with 89 per cent for the average annuitant.
The average population mamber, who does
not purchase insurance, would have a still
lower MWR. This phenomenon, some
times ascribed to adverse selection, is often
given as the reason for low purchase of
annuities. In interpreting these data, it is
important to distinguish between ‘active’
selection that is due to asymmetric infor
mation about expected longevity and ‘pas
sive’ selection that is due to positive
correlations between socio-economic sta
tus, longevity and purchase of annuities.
The latter can be handled by the judicious
use of risk classification by insurance
companies (placing individuals in appro
priate risk categories according to observ
able characteristics that are correlated with
risk) while the former is an example of
market failure due to unobservable risk
factors.8 This is discussed further in the
section on policy issues.
Here we simply note that some annuity
products imply much less selection than
others. For example, the MWR of annu
ities with 15 or 20-yearguarantees is almost
the same for the EPF and annuitant popu
lations. Since payment over a long period
is required, to the estate if the primary
beneficiary dies early, such products do
not place the shortlived annuitant at a big
disadvantage (although it may be his fam
ily rather than he himself who enjoys the
benefits). This is an illustration of a pro
duct that is likely to have much appeal if
the annuity industry plays an important
role in a reformed pension system. In
contrast, the accelerating annuity, whose
benefits are back-loaded, will appeal to
Economic and Political Weekly
February 22, 2003
people who expect to live a long time. As
discussed funher in the Conclusion, such
product variation is one way to accommo
date population diversity.
IV
Administrative Costs
Insurance companies must cover their
costs and profits out of the load they charge
on annuities and other products, plus their
investment earnings. To understand their
loads, therefore, it is necessary to under
stand theiradministrative costs and invest
ment returns. This section and the next
deal with these issues.
It is difficult to obtain cost information,
but we present data from LIC’s annual
reports and from the Pocketbook of Sta
tistics. Unfortunately, these data do not
disaggregate between annuities and life
insurance. One of the biggest cost items
internationally is marketing costs - much
as it is for the accumulation stage of retail
retirement accounts. According to the LIC
report, commissions to agents and salaries
to other staff account for 9.13 per cent and
9.52 per cent of total premium income
respectively, and other management costs
amount to 2.5 per cent. LIC officials claim
that sales commissions on annuities are
much lower - on immediate annuities only
2 per cent and on deferred annuities 7.5
per cent on first year premiums and 2 per
cent thereafter, rates that are quite low by
international standards. Immediate annu
ity commissions may be lower than for life
insurance because the entire premium is
paid-up front and doesn’t require constant
new ‘selling’ each year, in contrast to other
policies that must be renewed annually.
The absence of product differentiation
further limits opportunities for marketing
and sales commissions. However, the
openiflg up of the insurance sector in India
combined with a growth in the number of
private players may increase marketing
expenses in the future.
In addition to marketing expenses, an
nuities involve record-keeping and com
munication costs. These are likely to be
low as a percentage of total premium
because each annuity policy is relatively
large compared with the average life in
surance account and costs are a fixed
amount per account, hence small relative
to premiums (Table 1). The need to invest
reserves incurs another cost element.
Bond investments by large investors
incur costs of less than 30 basis points
elsewhere, but costs may be higher in
Economic and Political Weekly
India. Finally, reinvestment and mortality
risk are real costs that must be compen
sated.
International evidence suggests that the
keys to lower administrative costs in the
annuity stage, as in theaccumulation stage,
of retirement savings accounts, are large
account size and low marketing expenses.
These conditions, especially the second
one, seem to be satisfied reasonably well
in India compared with other countries. In
all, it seems unlikely that administrative
and marketing costs exceed 12 per cent of
premiums, a range that is consistent with
that in other countries [James et al 2001].
This could be paid through a 12 percent
load (if MWR = 88 per cent), or (if MWR
= 100 per cent) through investment earn
ings that exceed the government term
structure by at least 1.5 percentage points.
It is possible that LIC counted on higher
investment earnings in the past but is now
relying on a higher load.
V
Investment Portfolios and
Returns of Annuity
Companies
In well-developed insurance markets,
insurance is a spread business. Companies
pay annuitants the risk-free government
rate but invest in a mixed portfolio that
includes corporate bonds, mortgage-backed
securities and some equities. They cover
theircosts and profits, in part, on the spread
between the risk-free and the risky rate.
They intermediate this risk, providing a
safer investment to annuitants, by a variety
of techniques including portfolio diversi
fication, product diversification, reinsur
ance, using stockholders as buffers in case
of financial difficulty, and giving policyholders high priority in case of bankruptcy.
The spread enables insurance companies
to provide a high MWR, sometimes ex
ceeding 100 per cent, to annuitants.
Of course, the spread comes at the
expense of a riskier portfolio, including
higher default risk and reinvestment risk.
Regulation is required to prevent exces
sive risk that will make it difficult for
companies to keep their promises later on.
However, over-regulation prevents the
companies from earning the spread, and
results in higher cost to potential consum
ers. Therefore, a narrow line must be walked
by regulators. In India it is possible that
in the past regulators have crossed over the
line towards excessive regulation.
The Insurance Regulatory Development
February 22, 2003
Authority (IRDA) regulates the annuity
industry. All the players have to seek
permission from IRDA to float annuity
products. IRDA also has laid down strict
regulations regarding investment for in
surancecompanies. Il stipulates maximum
limits for investment in various areas,
leaving government securities as the main
allowable investment. Accordingly, LIC
invests its funds in government bonds,
special deposits, debentures, and loans to
government, with only a small equity share.
During 1999-00, the public sector share
of investments was 84.2 per cent, the co
operative sector was 1.5 per cent, and the
private sector 14.3 per cent. Unfortunately
we do not have the investment portfolios
of the annuity business alone since this
business is usually merged with the life
insurance business, which dominates.
However, we do have data on the annual
yield on pension assets during the 1990s.
Assets backing retirees are probably in
vested in a similar way to assets backing
annuitants, so their yields are probably
similar also. (Note that these assets earn
more than assets backing workers, as they
can be invested for well-defined long-term
periods.) During the 1990s these yields
ranged between 13 per cent and 15 per
cent, which was 1-2 per cent above the
government long-term bond rateduring this
period.10 Currently the rate on the 10-year
bond is below 7.5 per cent. Falling interest
rates in the Indian markets has clearly
reduced payouts. And we have seen that
Table 5: Money’s Worth Ratio
with Risky Rate
Old Payouts,
New Payouts,
Old Risky Rate, New Risky Rate,
1994-96 Mortality
1996-98
Table
Mortality Table
SPIA
5YG
10YG
15YG
20YG
50 percent to
spouse ondeath
3 per cent
escalating
92.75
94.22
97.15
' 81.72
82.16
99.5
82.55
82.49
100.35
81.24
92.2
77.69
95.3
84.26
Table 6: Annual Yield on Pension
Business’
Year
1992-93
1993- 94
1994- 95
1995- 96
1996- 97
1997- 98
Assets
Assets
Backing Workers Backing Retirees
12.92
13.66
13.63
13.79
14.35
14.08
1318
14.87
15.02
15.04
14.82
14.65
737
it has also reduced the MWR. The annuity
industry will be able to provide a high
MWR in the long run only if new invest
mentopportunities develop that yield more
than the government rate, are reasonably
safe, and are allowed by regulators.
A particular gap in the Indian financial
market at present is the absence of very
long term instruments. The average term
of corporate bonds in India is about seven
years. Only recently were government se
curities with a term of 20 years introduced.
Most companies are therefore at risk of a
huge asset-liability mismatch. According
to one official from Tata AIG, new en
trants to the annuities market would be
deterred by the high reinvestment risk,
given that the annuity liability is very long
term, yet long-term financial instruments
are scarce. All market players we spoke to
were consonant with the view that a vibrant
secondary market for securities is needed
if the annuity industry is to take off. Further,
the development of the debt market be
comes crucial for the development of the
annuity industry. Regulators will also have
to face the critical question of whether and
how much investment to permit in Indian
and foreign equity markets. Another bottle
neck is the unavailability of index-linked
bonds, which makes it difficult for Indian
insurers to provide a real annuity or other
price-indexed insurance products, as they
can in the UK and Chile [Brown et al 2000,
James et al 2001].
VI
Policy Issues
We have alluded, jn this paper, to several
controversial issues that need to be thought
through at the policy level at an early
stage of the industry’s development.
For example:
Should Insurance Companies Be
Permitted to Put People into
Different Risk Categories?
Whenever permitted, insurance compa
nies operating in well-developed markets
generally collect information that allows
them to place people in different risk
categories, which will be charged different
prices. This helps companies avoid ad
verse selection due to asymmetric infor
mation and it permits pricing that low-risk
(low longevity) groups would find attrac
tive. If annuity companies were to face a
potentially increased market due to pension
reform, we can predict that they would
738
begin to categorise people according to
characteristics that are known to be cor
related with longevity - gender, caste,
income, education, or health status. This
gathering of information and risk
categorisation would benefit groups such
as the poor, uneducated and sick, who are
expected to die at a relatively early age.
It avoids the perverse redistributions away
from these groups towards more
advantaged groups that occurs when ev
eryone is placed in a common pool. If
differentiated, these vulnerable groups will
get better monthly payouts for a given
premium and their financial wealth will
improve. However, such information col
lection and risk categorisation might vio
late important social norms and personal
privacy. For example, in the US it would
probably be illegal to differentiate accord
ing to gender or race. Indian policy-makers
need to think through which kinds of risk
classification would be permitted, encour
aged, and prohibited, in the Indian context.
And then they would have to begin build
ing the differentiated mortality tables that
would allow the desirable kinds of risk
classification to take place.
How Much and What Kinds
of Product Variety Should Be
Encouraged?
On the one hand, having a range of
permissible products enables people to
satisfy their diverse preferences about
bequests, timing of distributions or control
over investments. On the other hand,
consumers will be better able to evaluate
the risks and make price comparisons, and
regulators will be better able to determine
appropriate standards, if the product is
somewhat standardised. Some limited
range of products would satisfy both sets
of objectives, but policy-makers need to
decide where to draw the line. In thinking
this through, at least two types of products
ought to be strongly encouraged: joint
annuities and annuities with guaranteed
payment periods.
Many women will not work in the formal
labour market for most of their adult lives,
and therefore don’t acquire a pension of
their own. Yet, they may outlive their
husbands for many years. How will they
have some reasonable financial security in
their old age, as the informal extended
family system of support weakens? Joint
annuities are probably the best way to
provide security to surviving spouses and
for this reason, many countries with funded
individual accounts require this.11 It
should probably be strongly encouraged
in India also. (Of course, joint annuities
imply a smaller monthly payout to the
primary beneficiary, as we have already
noted.)
Appendix
Table A: MWR Using New and Old
Payouts for Both Sets of Mortality
Tables,Using the Government Term
Structure of Interest Rates Prevailing at
the Relevant Times (October 31, 2001 for
Old Payouts and June 19, 2002
for New Payouts)
_________ Mortality Table________
1994-96___ 1996-98
New
Old
New
Old
Payouts Payouts Payouts Payouts
SPIA
81.05
5YG
82.36
10YG
84.93
15YG
87.45
20YG
88.35
50 per cent to
spouse on
death
78.59
Escalating
at 3 per cent 82.72
99.83
101.32
104.65
107.82
109.63
89.15
89.57
90.06
90.37
89.64
108.79
109.12
109.98
110.78
110.94
99.69
85.23
107.09
103.49
93.13
115.05
Table B: Comparison of MWRs
Calculated Using Old and New Interest
Rates For New Payouts
________ Mortality Table______
1994-96
1996-98
Old
New
Old
New
Interest Interest Interest Interest
Rates Rates Rates Rates
SPIA
76.42
77.79
5YG
10YG
80.11
15YG
81.72
81.52
20YG
50 per cent to
spouse on death 73.61
Escalating
at 3 percent
77.02
81.05
82.36
84.93
87.46
88.36
83.22
83.72
84.14
83.9
82.44
89.16
89.57
90.1
90.4
89.64
78.6
79.02
85.23
82.72
85.6
93.13
Table C: MWR With the Risky Rate Government Term Structure + a 1.4 Per
Cent. (Old payouts Using Interest Rates
as of October 31, 2001 and New Payouts
Using Interest Rates as of June 19, 2002)
_______ Mortality Table_______
1994-96
1996-98
New
Old
New
Old
PayoutsPayouts Payouts Payouts
SPIA
74.9
5YG
79.19
10YG
78.45
15YG
80.25
20YG
80.3
50 per cent to
spouse on death 75.24
Escalating
at 3 percent
75.66
Economic and Political Weekly
92.75
94.22
97.15
99 5
100.35
81.72
82.16
82.55
82.49
81 24
100.38
100.75
101.47
101.8
101 32
92.2
77.69
98.33
953
84 26
104.95
February 22, 2003
Companies should also be encouraged
or required to provide annuity products
with guarantee payment periods, such
as 15 or 20 years, and indeed we see that
LIC does this already. Guaranteed terms
and joint annuities reduce cross-subsidies
between groups with high and low life
expectancies and thereby reduce adverse
selection. Our MWR analysis showed
that the low longevity population and
high longevity annuitants received
similar expected payments from the 15and 20-year period products. Low risk
workers are therefore likely to choose
these products, which give them better
terms than other products. If risk classi
fication is limited by social policy or
absence of good mortality data, offering
such products in which the low risks can
self-select themselves is a plausible way
to prevent perverse redistributions and
adverse selection out of the annuity market
altogether. In the context of a pension
reform, it is vital to provide information
to consumers in a way that allows them
to figure out which product is best for
them.
Another form of product is the variable
(participating) annuities in which annual
payouts vary with investment returns.
Usually such annuities feature some
annuitant control over investment strat
egy, and part of the investment is in stocks.
Low-income annuitants may feel they
cannot take this risk - a fixed joint
annuity may be best for them. But, as
we saw at the beginning of this paper,
high-income annuitants have a strong
preference for variable annuities, and
for the higher investment return they
allow. The challenge is to develop a
regulatory regime that permits variable
annuities while limiting the risk and
ensuring that consumers understand their
pros and cons.
Price-indexed annuities are another
product with great appeal to analysts and
policy-makers, since they protect annu
itants from unexpected inflation. If the
inflation rate is 5 percent, the purchasing
power of a nominal annuity will be cut
in half in 14 years. Many annuitants will
live longer than 14 years after retirement.
Without an indexed annuity they may find
themselves in relative poverty when they
like this trade-off. Moreover, in India it
will be costly and practically impossible
for insurance companies to provide
price-indexed annuities in the absence
of index-linked financial instruments for
investment. As noted above, the absence
of indexed government bonds is one of
the weaknesses of the Indian financial
market. Until they are available, a prom
ise by insurance companies to index
annuities is not credible; they would
probably be dubious about providing
such a product and it should not be
encouraged.
Should Annuitisation of Retirement
Savings Be Mandatory or
Voluntary?
This is likely to be one of the most
controversial issues in India. On the one
hand, the rationale for mandatory social
security is that people are myopic, may
not save enough for their old age, and may
live in poverty or become a charge on the
public treasury when they become very
old - the moral hazard problem. This
suggests that steps are needed to ensure
that people who have accumulated sav
ings in mandatory pension accounts don’t
spend these savings too quickly. More
over, mandatory annuitisation is some
times seen as a way to avoid adverse
selection and thereby increase payouts.
On the other hand, people have many
legitimate reasons for not wanting to turn
their entire savings accumulation into a
fixed income stream. Those with no other
resources to meet emergency needs have
a large precautionary demand for sav
ings and a high discount rate for a fixed
income stream. Those in poor health or
with low survival probabilities for other
reasons see a small expected value from
a long-term income stream. Forcing these
groups to annuitise may not make them
better off. While mandatory annuiti
sation provides longevity insurance to
everyone, it redistributes to those with
long expected lifetimes - unless exten
sive risk and price differentiation are
permitted. In India, most industry people
we spoke to favoured mandatory an
nuitisation as the only way to prevent
a quick consumption of retirement sav
are very old. However, to acquire an in
ings. But mandatory annuitisation pre
dexed annuity means taking a sharp re supposes a well-developed annuity in
duction in the initial monthly payout, to dustry with the potential for risk and
compensate for the fact that it will rise product differentiation, and many steps
through time - and many potential annu need to be taken before this is achieved
itants with high discount rates would not in India.
Economic and Political Weekly
February 22, 2003
Finally, What Special Regulations
Are Needed?
Currently, most insurance companies do
not segregate the assets backing their
annuity business, making it difficult to
apply different investment regulations. Is
asset segregation advisable as the annuity
business grows? Annuity guarantees span
long time periods - as much as 40 years
after retirement and even longer in the case
of deferred annuities. How do we avoid
the danger that companies may make
overly-optimistic assumptions regarding
future mortality rates and investment re
turns, in order to increase their current
market share, even though this may result
in large future losses and inability to pay?
What kinds of reserves, reinsurance, or use
of derivatives are needed to back their
guarantees credibly? What provisions
should be made for good disclosure and
consumer education? Also, as pointed out
earlier, taxation policy serves as a major
incentive/disincentive for purchasing an
nuities. On the one hand, tax incentives
seem to have a large impact on the demand
for annuities, and so can be viewed as an
attractive alternative to mandatory
annuitisation. On the other hand, tax in
centives cost the government foregone
revenues and imply a non-transparent tax
redistribution towards high earners who
are most likely to purchase annuities.
Mandatory annuitisation avoids these tax
costs but incurs other disadvantages men
tioned above.
Conclusion
The underdevelopment of the Indian
annuity industry manifests itself in its
small size relative to other kinds of insur
ance, the absence of well-developed
mortality tables which are a prerequisite
to sound pricing and funding policies, and
the paucity of long-term financial instru
ments with which to match assets and
liabilities. It is perhaps symptomatic of
the undeveloped state of the industry
that unrealistically generous payouts
with very high money’s worth ratios, far
exceeding 100 per cent, were offered
until this year. However, the substantial
drop in payouts by L1C in 2002 was much
greater than that warranted by falling
interest rates and resulted in a decline in
MWRs to 90 per cent, an increase in the
load from less than nothing to over 10 per
cent. Further a nalysis is needed to un
derstand why l.IC decided on such a
739
dramatic cut at this time, but we have
suggested several reasons, including
fears of further drops in interest and
mortality rates, recognition of actuarial
losses in the past, and the interaction
between the deferred and immediate an
nuity market.
We have identified institutional gaps
that the industry and government will have
to address expeditiously, in order for
annuities to play an important role in the
forthcoming pension reform
• Long-term securities, including gov
ernment and corporate bonds and mort
gage-backed securities, will have to be
issued to reduce reinvestment risk and
permit a better matching of assets and
liabilities.
• Debt markets and secondary markets
for securities will have to be better deve
loped.
• Mortality tables must be constructed
for different segments of the population,
and careful estimates made of potential
improvement factors, with sensitivity
analysis for alternative scenarios.
• New annuity products should be cre
ated that have broader popular appeal.
• Analyses should be undertaken of
administrative and marketing costs, with
the object of determining ways to keep
them low.
• New regulatory procedures and indi
cators are needed to govern an industry
that is expected to increase in size and
complexity. This must include mechanisms
for communicating information to potential
consumers about the benefits, costs and
risks of alternative annuity products. Tax
policy also needs to be rethought-should
annuitisation be encouraged by tax advan
tages (but will this have adverse distri
butional consequences, in view of the
high income elasticity of demand for
annuities)?
We have also discussed key controver
sial issues that need to be thought through
at the policy level. The most important
include:
• Should insurance companies be per
mitted to put people into different risk
categories based on gender, race, caste,
location, health, family history’, DNA or
occupation?
• How much and what kinds of product
variety should be encouraged?
• Should annuitisation of retirement
savings be mandatory or voluntary?
• Finally, what special regulations are
needed?
740
We hope that this paper has laid out an
agenda for future empirical research and
policy analysis that would enable annuity
markets to efficiently play the important
role they are likely to have in India’s
forthcoming pension reform. [U3
Address for correspondence:
ejames@estellejames.com and
renuka_s@vsnl.net.
8 For analyses of active and passive adverse
selection in the UK, see Finkelstein and Poterba
(2000) and Murthi. et al (1999).
9 See Gupta (1998).
10 See ’Reports on Currency and Finance’, RBI.
11 For empirical evidence that families carry out
insufficient saving and insurance to cover
surviving spouses, see Bedmheim et al (2002).
For evidence on the importance of joint annu
ities in maintaining the standard of living of
widows in social security systems that include
individual accounts, see James, et al 2002.
Notes
References
[We thank Ajay Shah, Arpan Thanawala, Sanjay
Shah, S P Subhedar, officials of LIC, Tata AIG
and AIG India for their helpful comments and
insights. We especially thank Xue Song for her
calculations of the MWR.)
Brown, Jeffery, Olivia Mitchell and James Poterba
(2000): The Role ofRealAnnuities and Indexed
Bonds in an Individual Account Retirement
Program.
Bemheim, Douglas, Lorenzo Fomi, Jagadeesh
Gokhale and Lawrence Kotlikoff (2002):
‘Mismatch Between Life Insurance Holdings
and Financial Vulnerabilities - Evidence from
the Health and Retirement Survey’, American
Economic Review, forthcoming.
Finkelstein. Amy and James Poterba (2000):
‘Adverse Selection in Insurance Markets:
Policyholder Evidence from the UK Annuity
Market’, MIT and NBER.
Gupta, P C (1998): ‘LIC’s Experience with
Management of Pension and Superannuation
Funds’, commissioned by project OASIS.
James. Estelle, Alejandra Cox-Edwards and Rebeca
Wong (2002): ‘The Gender Impact of Pension
Reform: A Cross-Country Analysis'. World
Bank discussion paper.
James. Estelle and Xue Song (2001): ‘Annuities
Markets Around the World: Money’s Worth
and Risk Intermediation’. CeRP working
paper 16/01.
James. Estelle. Xue Song and Dimitri Villas
(2001):‘AnnuitiesMarkets Around (he World’.
American Economic Association Meetings,
January 2001.
James. Estelle and Dimitri Villas (1999a):
‘Annuities Markets in Comparative
Perspective: Do Consumers Get Their Money’s
Worth?’ Conference on ‘New Ideas for Old
Age Security’. World Bank.
- (1999b): ‘The Decumulation (Payout) Phase of
Defined Contribution Pillars’, presented at
APEC meeting, Chile. 1999, and published in
conference volume
Mitchell. Olivia. James Poterba and Mark
J Warshawsky (1997): ‘New Evidence on
Money’s Worth of Individual Annuities',
working paper 6002. National Bureau of
Economic Research.
Murthi, Mamta. J Michael Orszag and Peter
R Orszag (1999): 77ie Valuefar Money of Annu
ities in the UK: Theory. Experience and Policy.
The Project OASIS Report (2000): Submitted to
the Ministry of Social Justice and Empower
ment.
Shane. Frederick. George Loewenstein and Ted
O'Donoghue (2002): ‘Time discounting and
Time Preference: A Critical Review’. Journal of
Economic Literature. Vol XL. No 2. June 2002.
Wadsworth. Mike. Alec Findlater and Tom
Boardman (2001): ‘Reinventing Annuities'.
Presented to the Actuarial Inn Staple Society.
1 The formal system consists of: (1) a pay-asyou-go defined benefit (DB) scheme for
government employees, (2) a defined
contribution (DC) scheme for private sector
workers called the Employees Provident
Fund (EPF), which takes in contributions
from the employee, employer and the
government, and (3) the Employees Pension
Scheme (EPS) which offers defined benefits
of up to a maximum of 50 per cent of the
average of the last 12 months salary. Besides
these are gratuity and superannuation schemes
(which can be DB or DC), run by the employer.
Under the superannuation scheme, one-third
of assets can be commuted tax-free upon
retirement. Other retirement plans include the
UTI retirement plan and the Kothari Pioneer
Pension Plan, which are mutual fund schemes
in which the worker saves until age 58. At
the age of 58. the worker can take the money
out as a lump sum or leave it invested and
receive a pension in the form of dividends
declared on the underlying securities in the
plan.
2 For further elaboration of the reasons for low
levels of annuitisation see James and Villas
1999.
3 For a further discussion see ‘Reinventing
Annuities', Wadsworth, et al (2001); James
and Song (2001).
4 For a comprehensive discussion of discount
rates see Shane et al (2002).
5 This was the case, for example, in Switzerland,
where insurance companies were required to
guarantee at least 4 per cent nominal during
the accumulation stage and to use a 7.2 per
cent actuarial factor at the payout stage, since
1985.With interest rates falling, these
requirements have decreased only recently. In
Singapore, companies are expected to hold
their annuity rales constant for six months. In
contrast, in the freer and more competitive
Canadian and US markets, annuity payouts
can change every day.
6 The possibility of less attractive conversion
rates in the future may deter people from
buying deferred annuities today. However,
given the fact that retirement is many years
away, (he more immediate tax benefits arc
likely to dominate.
7 For many references see Shane, et al (2002).
Economic and Political Weekly
February 22. 2003
Issues in Accounting Education
Vol. 16, No. 2
May 2001
Developing Risk Skills: An
Investigation of Business Risks and
Controls at Prudential Insurance
Company of America
Paul L. Walker, William G. Shenkir, and C. Stephen Hunn
ABSTRACT: The Prudential Insurance Company was involved in the largest life
insurance churning scam of the 1980s and early 1990s. At the time, Prudential had
weak business controls, and its corporate culture was characterized as ineffective
and loose. However, this scandal is rooted in something deeper than a poor control
environment. Prudential was a company facing several risks; many company deci
sions allowed these risks to have a dramatic impact on the company. As a result, its
weak control environment came to the forefront, allowing the churning scam to reach
its record levels. This case demonstrates the value of identifying and assessing
risks in an organization. Further, the case demonstrates how to build control solu
tions to match the risks. Learning how to manage risks is a valuable skill for busi
ness professionals. In fact, the AICPA’s Special Committee on Assurance Services
(AICPA 1997), also known as the Elliott Committee, identified risk assessment as
one of the emerging assurance services offered by CPAs.
“Let’s get beyond the word ‘insurance. ’ Let’s don’t be concerned with what
we call a plan. Let’s just look at the end result.”
—Prudential Training Video (ABC NewsPrimetime Live 1996)
| prudential Insurance Company of America, whose symbol is the Rock of
Gibraltar, assures its customers that “for financial security and peace of
-L mind” they could depend on the Rock (Prudential 1993 Annual Report, 5).
For years its advertisements built its “ROCK-SOLID” image (Prudential 1991
Annual Report, 5). Prudential (the Rock) was created around its people, who were
committed to a set of core values lauded by management: client focus, winning,
Paul L. Walker is an Associate Professor and William G. Shenkir is a Professor,
both at the University of Virginia, and C. Stephen Hunn is a Senior Associate in
the Assurance Practice at Ernst & Young.
The Coopers & Lybrand Foundation provided a grant to develop a course on business risks
and controls. This case is based on work derived from teaching that course. Professor Shenkir
acknowledges support ofa summer grant provided to the McIntire School by Ed Legard and
Professor Walker acknowledges the support of a Coopers & Lybrand Research Fellowship.
The research assistance of Duane Carling is greatly appreciated. Stephen Hunn partici
pated as a co-author of the case while serving as a graduate student assistant for Professors
Walker and Shenkir. This case was partially funded by a grant from the Coopers & Lybrand
Foundation. The information contained in the case was obtained from publicly available
sources, and its accuracy is somewhat dependent on those sources. Coopers & Lybrand did
not provide access to any Prudential data nor assist in any way in developing this case.
Copyright©2001 All Rights Reserved
€*
292
Issues in Accounting Education
trust, and respect for each other. The company was dedicated to “selling the right
product, to the right client, in the right way” (Parsons and Engdale 1995, 12-13).
Yet for Prudential s customers, selling the right product in the right way proved
to result in something less than “peace of mind.”
The Nicholsons’ Story
Keith and Carol Nicholson trusted their financial security to the Rock when
they purchased a rather sizable life insurance policy from their Prudential agent.
At one point, the policy’s cash value was $103,000 (ABC Netos Primetime Live
1996). Since Keith suffered from leukemia, this policy was comfort for the un
stable times that lay ahead of them. Carol Nicholson needed to know that this
money was going to be there.
Carol had been known to say that she trusted her Prudential agent as she
trusted her pastor. He was going to play a vital role in smoothing a very uncer
tain future. Therefore, when her agent suggested that she and her husband take
out a new life insurance policy on Keith “at no additional cost,” the couple agreed,
no questions asked. They just signed the forms, believing that they had brought
even more certainty to the unpredictable future.
Eventually, Keith succumbed to leukemia. Much to Carol’s surprise, the sixfigure nest egg that she thought would be awaiting her was now a mere $22,000
(ABC News Primetime Live 1996). Carol’s agent had not been honest when he had
Carol and her husband change his life insurance policy. The Nicholsons’ agent
had taken advantage of the couple’s trust by having them borrow against their
old policy to purchase a new and more expensive policy.1 Without even realizing
it, Carol and Keith had signed a blank withdrawal form that allowed their agent
to raid the cash value of the old policy to begin to pay for the new policy. Carol
Nicholson’s only reaction was a tearful plea of “How could they?”
The Nicholsons’ Problem: A Decade in the Making
Prudential is a massive entity whose asset base is equivalent to the economy of
Sweden (see Exhibits 1 and 2). In late 1994, Prudential’s primary businesses were
life insurance, health care, investments, and property and casualty insurance.
1 Such a tactic is referred to as a “churning,” “financing,” or “refinancing.”
EXHIBIT 1
Top 10 Life/Health Insurers in 1990
Ranked by Assets
1990 Assets
Ranking Company Name ____________
(in billions)
1
Prudential Ins. Co. of America
$133.5
2
Metropolitan Life Ins. Co.
103.2
3
Aetna Life Insurance Co.
52.3
4
Equitable Life Assurance Soc.
50.3
5
Teachers Ins. & Annuity Assoc.
49.9
6
New York Life Insurance Co.
39.9
7
Connecticut General Life Ins. Co.
37.4
8
John Hancock Mutual Life
33.7
9
Travelers Insurance Co.
33.0
10
Northwestern Mutual Ins.
31.4
Source: Best’s Review., July 1991.
Copyright©2001 All Rights Reserved
~
% of Total
Industry
8.7
6.7
3.4
3.3
3.2
2.6
2.4
2.2
2.2
2.0
Walker, Shenkir, and Hunn
293
EXHIBIT 2
Life Insurers Ranked Based on Premium Income
1990
Ranking
1
2
3
4
5
6
7
8
9
10
Company Name
Prudential Ins. Co. of America
Metropolitan Life Ins. Co.
Aetna Insurance Co.
New York Life Insurance Co.
John Hancock Mutual Life
Principal Mutual Life
Travelers Insurance Co.
Lincoln National Life Ins. Co.
Massachusetts Mutual Life Ins.
Connecticut General Life Ins. Co.
1990 Premium
(in billions)
1989
Ranking
1980
Ranking
$24.1
19.5
9.6
7.7
6.8
6.5
4.9
4.8
4.5
4.4
1
2
3
4
5
6
7
9
16
22
1
2
3
6
7
9
5
20
13
8
Source: Best’s Review, July 1991.
EXHIBIT 3
Prudential’s Total Life Insurance Sales 1982-1987
Year
1982
1983
1984
1985
1986
1987
Total Life Insurance Sales (in millions)
$59,779
65,854
66,645
80,167
87,312
92,654
Source: 1987 Prudential Annual Report. Note that this breakout of life insurance sales numbers is not
available for other years.
Of all the different types of insurance being offered by Prudential and its com
petitors, life insurance was the most lucrative for both the company and its agents.
From 1983-1987, Prudential saw record-breaking increases in its sales of life in
surance policies (see Exhibit 3), even though the industry saw a decline in sales
(see Exhibit 4).
Carol and Keith Nicholson were not the only victims of Prudential’s churning
scam. Before the end of 1995, over 10.7 million life insurance policyholders had alleg
edly fallen prey to the scam and a class action lawsuit was soon filed. Additionally,
investigations of the nation’s largest life insurer spanned the country, from New Jer
sey to Florida to Arizona, in an effort to answer the question, “How could they?”
In 1996, as part of the Florida Department of Insurance’s investigation of Pru
dential, a former Prudential Vice-President of Regional Marketing testified regard
ing sales practices. In part of his testimony, the witness discussed the process of
how customers buy life insurance (Florida Department of Insurance 1996b, 29).
WITNESS: They said that their agent sits there, and he says sign there,
sign here, sign here, sign here, and I have to trust in the agent. I sign, he
turns it over and says sign here, sign here, and sign here. I sign.
Copyright ©2001 All Rights Reserved
294
Issues in Accounting Education
EXHIBIT 4
Industry Life Insurance Purchases in the United States
(policies and certificates in thousands, amounts in $ millions)
_____ Individual
Year
1960
1965
1970
1975
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Policies
21,021
20,429
18,550
18,946
17,628
17,629
16,964
18,571
18,407
17,637
17,116
16,455
15,798
14,850
14,199
13,583
13,452
13,664
13,894
13,830
12,333
Group
Total
Amount
Certificates
Amount
Policies
$ 59,763
90,781
129,432
194,732
389,184
484,412
587,342
754,832
821,258
911,666
934,010
986,984
996,006
1,020,971
1,069,880
1,041,706
1,048,357
1,101,476
1,107,448
1,101,349
1,118,451
3,734
7,007
5,219
8,146
11,379
11,923
11,930
13,450
14,605
16,243
17,507
16,698
15,793
15,110
14,592
16,230
14,930
17,574
18,061
18,105
17,575
$ 14,645
24,755
27,436
23,769
27,092
29,007
29,552
28,894
32,021
33,012
33,880
34,623
33,153
31,591
29,960
28,791
29,813
28,382
31,238
31,955
31,935
29,908
51,385
63,690
95,190
183,418
346,702
250,532
271,609
293,521
319,503
374,741
365,529
410,848
420,707
459,271
573,953
440,143
576,823
549,984
499,024
581,366
Amount
74,408
142,166
193,122
289,922
572,602
831,114
837,874
1,026,441
1,114,779
1,231,169
1,308,751
1,352,513
1,406,854
1,441,678
1,529,151
1,615,659
1,488,500
1,678,299
1,657,432
1,600,373
1,699,817
$
Source: American Council of Life Insurance and LIMRA International.
Most people, even after they signed them, didn’t take them home and
read them. That is what it’s like applying for life insurance.
The Nicholsons were among the many insurance customers who just signed
forms as instructed by their agent. According to this ex-Prudential employee, the
most prevalent financing scam at Prudential was selling a new policy as “free life
insurance” by essentially using the accumulated cash value of an older policy to
pay the new, increased premiums. In many cases, the old “whole life” or “univer
sal policy was replaced with a “term” policy. The former policies build up cash
value, whereas term policies do not. In some cases, insured persons would in
crease their total life insurance coverage because they had more overall coverage
from the term policy. In his two days of testimony, the confidential witness com
mented as follows (Florida Department of Insurance 1996a, 53):
WITNESS: I would say financing was minuscule in ‘82, ‘83, ‘84—and then
started growing rapidly in ‘85, ‘86, ‘87, ‘88, and then started to level off prob
ably in ‘90, ‘91, ‘92, and then may have gone down a little bit in ‘93, ‘94.
Prudential contended that such practices were never condoned. Under oath,
the ex-employee stated otherwise (Florida Department of Insurance 1996a, 13): ’
WITNESS: That has always been Prudential’s public statement, financ
ing and replacement is bad; not generally in the best interests of the
Copyright ©2001 All Rights Reserved
Walker, Shenkir, and Hunn
295
policyholder... .At the peak, it was used in at least 30 percent of the cases
and probably higher.
According to a Coopers & Lybrand’s (1994, 5) assessment of Prudential’s
controls:
Training of field management with respect to supervising sales practices
and identifying and dealing with compliance-related issues has been in
consistent at best. As such, managers are not alw ays sure as to what con
stitutes “good” vs. ‘“bad”’ sales practices, are reactive toward compliance
issues, and are not held accountable for their own actions or those of their
representatives.
Prudential Insurance, like many life insurers during this period (1982-1993),
offered a very complex product. Without adequate instruction, many agents felt
as if they had been misled about what they were selling. Even so, it should be
noted that many Prudential employees were fully aware of the consequences of
their actions. The deposed former employee noted that there existed an informal
system of training on refinancing policies. The witness told how this manipula
tive practice was able to spread (Florida Department of Insurance 1996a, 54):
WITNESS: What happens is because there is no formal training of this kind
of thing, it passes by word of mouth or by transfer of people. So it doesn’t
surprise me that you will find it pop up here or pop up there. Then after these
people got to be very successful, they would go to conferences and say, ‘this is
how we do it.’ And then it spread countrywide, and my belief is it really got
heavy in ‘84 and ‘85 because illustration sold so nicely, too.
The ex-employee remarked that many agents set up booths at the Regional
Business Conference in an effort to “illustrate” the art of selling financed insur
ance (Florida Department of Insurance 1996b, 55). The employee also claimed
that, in support of these practices, many agents developed and used their own
sales materials, as revealed by testimony on these self-developed materials (Florida
Department of Insurance 1996b, 54 and 56):
QUESTION: Typically, would he [management] say anything about it?
Would he care?
WITNESS: I don’t know. I’m not sure. But keep in mind that the manag
ers are paid overrides. If there is a piece that appears to be working, they’re
not going to stop using it, because it affects their pocketbook.
The former Prudential worker also discussed the monetary consequences of
churning (Florida Department of Insurance 1996a, 14-16):
QUESTION: So...this document [a memo] would indicate that the
company knew way back in ‘76 that financed insurance was regularly
producing unacceptable results?
WITNESS: Correct. And the next question is why it was producing unac
ceptable results. Did you [Prudential] look into it? Did you [Prudential] as
certain what occurred in the sale that produced unacceptable results? The
answer is nothing. The reason that Prudential didn’t care was they were
sales driven. Everything was measured off new sales....There was a benefit
to the agents, to management, to individuals working for the company,
because their bonuses grew dramatically...
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296
Issues in Accounting Education
If you look at the pay scale of management in 1976, a senior vice presi
dent in 1976 probably made $100,000 a year, a lot of money. A senior vice
president in the company today probably in the same position might make
a million dollars a year. Now inflation has been eating away a lot since
1976, but I don’t think it ate ten times....So there was a financial incen
tive for the employees, all employees, not just senior people.
The incentive for the salesperson was simply commissions. Characteristically,
a large percentage of the premium paid by the consumer in the first year went
directly to the agent. That commission shrunk in later years. The ex-employee
further elaborated upon this subject in the second day of his testimony (Florida
Department of Insurance 1996b, 3 and 49):
WITNESS: Another file you would want to look at is Phoenix West. That
was an investigation done last year [1995]....As a result of that investiga
tion there were recommendations with regard to the discipline of many,
many people; but if you look at that whole investigation, you will see the
attitude of the company toward people who were engaged in wrongful fi
nancial insurance transactions over a long period of time, with the knowl
edge of many people...They merely state that we did it because we made
money and we didn’t care... .And Phoenix West is just a microcosm of what
was really going on in the country.
John Vetter, an insurance representative in the beleaguered Phoenix West
Agency, admitted to some questionable sales. In an investigation of the Phoenix
West Agency, the Florida Department of Insurance (Parsons and Engdale 1995,
7) documented that:
He [Vetter] said your judgment gets clouded out in the field when you are
pressured to sell, sell, sell. In response to questions on how he could ex
plain a case where he had rewritten a policy instead of reinstating it when
the rewrite resulted in a higher premium for the insured, he responded
that it was “pure greed.”
With everyone in Prudential benefiting financially from refinanced life insur
ance policies, there seemed to be no need to stop, regardless of management’s
“official” stance on the issue (Florida Department of Insurance 1996a, 9):
WITNESS: You will probably see that in Prudential all the documents
that you see or the bulk of the documents you see will be very good on
their face, they’ll say “you shall not do this.” The problem was that there
was nothing behind “you shall not do this.” There was no mechanism to
punish. In fact, I don’t believe you’ll find a single termination of an agent
or member of management for financing insurance outside of Cedar Rap
ids and a couple of other districts in the 80s.
The ex-employee felt not only that churning was condoned by management,
but also that management explicitly allowed it. Many Prudential customers com
plained about their new life insurance policies before this scandal fully surfaced
in 1994, and, according to this ex-employee, Prudential addressed such complaints
in the following manner (Florida Department of Insurance 1996a, 35):
WITNESS: ...whenever they [the customer] had a complaint, the first thing
they had to do if they had an oral complaint, they had to put it in writing.
Copyright © 2001 All Rights Reserved
Walker, Shenkir, and Hunn
297
That knocked down a number of the complaints right away because most
of our customers, because most of their educational level and because of
their financial circumstances, hesitated to put things in writing.
The second thing we did is we would get the complaint and then would
ask the agent what the agent did. If the agent said he did it right, we
would deny the complaint and we would hold to that denial through three
or four subsequent complaints. And basically we didn’t actually do an in
vestigation except to get the statement of the person who was complained
about, and that was the position in Prudential probably until late 1994.
Some Prudential executives did seek changes, given the growing number of
customer complaints (although it was later alleged that not all complaints were
logged into the company’s database). One such measure was having the customer
sign a release verifying that he or she fully understood the terms and conditions
of his or her new policy. Testimony recounts the reaction to such a measure (Florida
Department of Insurance 1996a, 39):
WITNESS: The next one is a memo [dated August 29, 1995] from Bill
Hunt [head of Ordinary Agencies]: “I do not believe we should have the
applicant sign off on anything. Not only does this imply a lack of trust
toward agents, it also has the potential to build skepticism from the pro
spective insured regarding what they are being sold.” Basically what he is
saying is he is not going to ask him to sign anything because it could dis
rupt the sale.
The selling of life insurance has become a complex process. Clearly, custom
ers frequently do not understand the product they are buying, but instead appear
to place a high level of trust in their agent. That trust places additional burdens
and responsibilities on agents and Prudential itself. It also appears evident that
sales practices such as churning and refinancings were not only widespread but
may have been occurring for an extended period of time. The witness implied that
financial incentives may have encouraged this activity and that management’s
attitude toward controls and problems was questionable.
A New CEO
As early as 1982, the company’s internal auditors reported to the Board of
Directors fraudulent practices on the part of sales agents. In addition, internal
audits of individual divisions and regional offices in the early 1990s detailed a
failure by management to enforce consumer-protection laws and regulations. In a
June 1994 report commissioned by Prudential in the wake of regulatory inquiries
about insurance sales practices, Coopers & Lybrand stated that Prudential offi
cials failed to act adequately upon such warnings. The Board admitted that it
had been made aware of “major irregularities,” but they continually asserted that
they trusted management’s claims that the problems were being properly moni
tored (Seism and Paltrow 1997).
In November 1994, Prudential’s board turned to Arthur Ryan (the president
of Chase Manhattan Corp.). This was the first time in over 120 years that Pru
dential had looked outside the company to fill the position of CEO. Lacking any
formal background in the field of insurance, his reputation was built upon his
ability to streamline operations and introduce new technology. He is renowned
for rolling up his sleeves at his own computer. He enjoys working one-on-one, but
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298
Issues in Accounting Education
is perfectly comfortable at center stage of the company auditorium (Treaster 1997).
Simply put, Ryan is direct, open, focused, and engaged.
Ryan’s Reaction and Changes
Ryan had made a conscious choice to change Prudential’s business approach.
Under Ryan’s command, Prudential would no longer be a “series of independent
silos, freewheeling subsidiaries working at cross-purposes with fragmented game
plans” (Treaster 1997). The buzzword at Ryan’s Prudential was “One Prudential”
(Prudential 1996 Annual Report, 2). This “One Prudential” would be about facili
tating teamwork and cooperation.
To break from the past, Ryan began recreating Prudential’s management team.
Much of the old guard was released. Twelve of the 14 executives who reported
directly to the CEO were hired by Ryan. Of the top 150 executives, two-thirds
were new, and half of these replacements were newcomers to Prudential.
Ryan also decided on cutbacks like those that had won him much praise at
Chase Manhattan. Within two years of Ryan’s arrival, a workforce of 100,000 had
been reduced to 83,000 (Treaster 1997). Ryan also eliminated about $790 million
in overhead (Seism 1997b) by shutting down five regional headquarters (that had
once been proud outposts for the company’s management). He also sold the home
mortgage operation, thereby reducing the company’s exposure in the homeowner’s
insurance side of the business (Treaster 1997). By the end of 1995, Ryan’s re
structuring had resulted in seven major operating groups: individual insurance,
money management, securities, healthcare, private asset management, interna
tional insurance, and a diversified group (Schwartz 1995, 26).
Although Ryan’s actions would appear to be a step in the right direction, not
all of his streamlining was met with open arms. The company’s insurance sales
force, which numbered 20,000 when Ryan came to Prudential, was cut in half
within four years. The company fired or counseled out agents who could barely
sell enough insurance to cover the costs of their employee benefits. During the
first months of 1997, more than 1,600 junior and senior insurance-sales manag
ers were still going through “very severe reviews.” As a result, about 100 of these
employees left Prudential.
Arthur Ryan’s labor troubles did not end with complaints from the sales force
over tighter controls. In an effort to mitigate some of the damage to Prudential’s
bottom line resulting from the churning scandal, Prudential attempted to increase
agent production quotas. The proposed labor contract would have increased quo
tas by 25 percent, but the union representing Prudential’s insurance agents re
jected the deal (Seism 1997a).
In 1998, Prudential officials estimated that the class-action suit could cost
Prudential as much as $2 billion. Many questions still remain for Arthur Ryan,
but for the customers of Prudential Insurance Co. of America, the most signifi
cant question remaining is, “Has enough been done to ensure that they will not be
the next Carol Nicholson?”
Discussion Questions
1. The Committee of Sponsoring Organizations (COSO) Internal ControlIntegrated Framework document states that companies must set objectives in
three areas: operations, financial reporting, and compliance. COSO further states
Copyright © 2001 All Rights Reserved
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Walker, Shenkir, and Hunn
2.
3.
4.
5.
6.
299
that to achieve those objectives, companies must have five components in place:
control environment, risk assessment, control activities, information and com
munication, and monitoring. To what extent are the aspects in the case related
to the COSO components and objectives?2
Read the risk framework suggested by the Special Committee on Assurance
Services at the AICPA’s web site (http://www.aicpa.org). If you were a business
risk advisor to Prudential, what sales, marketing, and strategy risks could you
identify for the period from the 1980s and the early 1990s, and how were the
risks related to the company’s problems seen in the case?
As their business risk advisor, assess the importance of the risks you identified
in Question 2. First, consider whether the dollar significance for each risk is
low, medium, or high. This dollar significance is not necessarily related to “au
dit materiality,” but rather to what you would consider significant. Second,
evaluate the likelihood of occurrence of each risk as low, medium, or high.
Having evaluated each risk on the basis of significance and likelihood, con
sider how Prudential should factor in the costs vs. the benefits of any solutions
to manage the risks.
Consider the risks you identified in Question 2. Has Prudential done enough to
adequately manage these risks? Why or why not?
If you were engaged by Prudential to advise them, what are some possible
business control solutions to the risks identified in Question 2? Consider con
trols to ensure that situations like the one experienced by the Nicholsons are
eliminated or at least minimized.
What other industries/companies face problems similar to Prudential’s “churn
ing” of policies?
2 In 1992, the Committee of Sponsoring Organizations (COSO) of the Treadway Commission issued a final
report Internal Controls-Integrated Framework, which is a comprehensive way of looking at business
controls. COSO set the standard for internal control. Using COSO’s document as a guide, management
can assess and report on their internal control. Additionally, professional auditing standards have adopted
portions of the COSO document.
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Indian Laws Related to Insurance- What a Manager Should Know1
Introduction
The two acts directly governing the Indian insurance industry are:
• The Insurance Act, 1938
• The Insurance Regulatory and Development Authority Act, 1999 (IRDA act)
This note is a ‘managerial summary’ of the major provisions of the above acts, meant to
provide the necessary background to the students of the elective course on ‘Risk and
Insurance’. There are also other laws like Company Law, Contract Law etc., which are
relevant but this note will not deal with these laws.
IRDA Act
As will be clear from our discussions elsewhere in the course, insurance industry needs a
strong supervisor and regulator. As per the Insurance Act, 1938, the Controller of
Insurance was such an authority. However, with the nationalization of the Life Insurance
business in 1956, and that of the General Insurance business in 1972, the regulatory role
of the Controller of Insurance lost its significance.
With the initiation of the liberalization process in 1991, the so called Malhotra
Committee, made two crucial recommendations:
• Permitting private sector entry into insurance
• Establishing a statutory and autonomous Insurance Regulatory Authority similar to
the Security and Exchange Board of India (SEBI)
Though successive governments agreed to the recommendations, the passing of the
requisite legislation was a long drawn affair, culminating in the passage of the IRDA act
in 1999. The main provisions of the IRDA Act
• Ended the exclusive monopoly of the Life Insurance Corporation of India (LIC) and
the General Insurance Corporation of India (GIC) and its subsidiaries
• Established the Insurance Regulatory and Development Authority (IRDA), consisting
of a Chairperson and not more than five full-time and four part-time members, as the
regulator, in place of the “Controller of Insurance” or the “Central Government”
• Introduced certain crucial amendments to the Insurance Act 1938, for example,
defining an “Indian Insurance Company”; capital requirements for insurers etc.
Some Duties, Powers and Functions of IRDA
a) To issue certificates of registration to applicants for carrying on insurance business;
and to renew, withdraw, suspend or cancel such registration
b) Protecting the interest of the (insurance) policy-holders
1 Prepared by R. Rajagopalan, T. A. Pai Management Institute (TAPMI), Manipal. This note is meant only
for class discussions at TAPMI.
1
c) Specifying requisite qualifications, code of conduct and practical training for
insurance intermediaries or agents
d) Specifying code of conduct for surveyors and loss assessors
e) Calling for information, conducting enquiries and investigations including audit of
insurers, intermediaries and other organizations connected with insurance
f) Specifying the form and manner in which books of accounts are to be maintained and
accounting statements to be rendered by insurers and intermediaries
g) Regulating investment of funds by insurance companies
h) Regulating maintenance of margin of solvency (by insurers)
i) Supervising the functioning of the Tariff Advisory committee (which regulates the
rates, advantages, terms and conditions of general insurance business)
j) Control and regulation of rates etc of general insurance not so covered by the Tariff
Advisory committee
k) Adjudication of disputes between insurers and insurance intermediaries
l) Specifying the percentage life insurance and general insurance business to be
undertaken by the insurer in the rural areas or social sector (this was to respond to a
major objection to privatization and to provide a “level playing field” vis-a-vis LIC
and GIC)
There are others like promoting efficiency of insurance business, professional
organizations related to insurance and collecting fees and levies for purposes of the act.
IRDA is subject to audit by the Comptroller and Auditor General of India (CAG). It is
also bound by policy directions, if any, given by the Central Government.
As we can see from the later discussion on the provisions of the Insurance Act, 1938,
from which the IRDA draws its powers, the IRDA has enormous powers as the
supervisor and regulator of the Indian Insurance Industry.
Insurance Act, 1938
This is a fairly large act (by our standards!), with more than hundred ‘sections’ in five
parts; and eight ‘schedules’ giving specific formats/ details. Of course each ‘section’, in
turn, may have ‘subsections’ and ‘provisos’ and so on. This act has been amended several
times, the latest being through the IRDA Bill of 1999. Therefore, with an emphatic
disclaimer on the comprehensiveness or correctness, my layman’s ‘managerial
summary’, as I see relevant to our course, follows.
Some Definitions
Contract of Insurance
A contract between two parties, where the ‘insurer’ agrees to pay a sum of money or its
equivalent, to another person, on the payment of ‘premium’ by the assured and on the
happening of some specified event or risk.
2
Life Insurance Business: Contracts of insurance on human life or the happening of any
contingency of human life. Thus death, disabilities, accidents etc come under life
insurance; so are annuities upon human life, superannuation allowances and annuities
General Insurance Business: Includes fire, marine or miscellaneous insurance
Fire Insurance Business: Self-explanatory(?)
Marine Insurance Business: Includes insurance upon vessels of any type, including
cargoes, freights etc, for any transit by land or water or both, including warehousing and
other activities incidental to transit.
Miscellaneous Insurance Business: Any insurance other than life, fire or marine
insurance.
Provisions Applicable to Insurers
1. No insurer, other than an ‘Indian insurance company’, can begin to carry on any class
of insurance business in India, after the commencement of IRDA Act. ( Through a
proposed amendment, co-operative societies are likely to be permitted to carry on
insurance business)
2. An ‘Indian insurance company’ is any company
a) formed and registered under the Companies Act, 1956
b) in which the aggregate direct and indirect holdings of equity shares by a
foreign company (as defined under clause 23 A of Section 2 of Income Tax
Act, 1961), do not exceed 26% of the paid-up equity capital
c) whose sole purpose is to carry on life insurance, general insurance or
reinsurance business
3. A certificate of registration must be obtained from IRDA before commencing any
class of insurance business.
4. A copy of the published prospectus, standard forms, terms and conditions of the
proposed insurance policies must accompany an application for registration. In the
case of life insurance policies, a certificate from an actuary that the terms and
conditions are workable and sound is also necessary.
5. The IRDA has the power to suspend or cancel the certificate of registration, for
violation of any of the several conditions/ provisions of the act. IRDA can also apply
to a court for winding up such an insurance company.
6. The registration has to be annually renewed. Renewal fee to be fixed by IRDA Max
[Rs 50,000, Min (0.25% of premium income, Rs 5 Cr)], for each class of insurance
business.
7. Requirement of minimum paid-up capital: Rs 100 Cr for any insurer and Rs 200 Cr
for any reinsurer.
8. No promoter shall hold more than 26% share capital; if he does, he has to divest the
excess in a phased manner after 10 yrs (or as prescribed by central government) from
the commencement of business.
3
9. Every insurer must keep a deposit, in favour of the central government, of either cash
or approved securities amounting to the following:
a) Life insurance: Min (1% of gross premium during the financial year, Rs 10 Cr)
b) General Insurance: Min (3% of gross premium during the financial year, Rs 10
Cr)
c) Reinsurance : Rs 20 Cr.
These deposits, though included in the assets of the insurer, can be used only for
discharging the liability of the insurer to his policyholders.
10. Separation of accounts and funds:
• An insurer has to keep a separate account of all receipts and payments related to
each class of insurance business.
• An insurer carrying on life insurance business has to maintain a separate fund
called the ‘life insurance fund’. The assets of this fund will be kept distinct from
all other assets of the insurer. This fund can not be applied for any other purpose
than the life insurance business of the insurer.
11. At the end of each financial year, every insurer has to prepare a balance sheet, profit
& loss account, a separate account of receipts and payments and a revenue account in
accordance with the regulations of IRDA. Every insurer has to keep separate accounts
related to the funds of shareholders and policy-holders.
12. Every insurer providing life insurance should get an actuarial investigation done
every year of its life insurance business, including the valuation of its liabilities and
prepare an abstract as per requirements of IRDA.
13. Investment of Funds
• Every life insurer has to keep investments not less than liabilities to holders of
policies issued by him which have matured or maturing claims. However, the amount
of premiums due but within grace period and loans granted to policy holders within
the surrender value of the respective policies may be subtracted from the above
investment requirements. This required investment will be adjusted downward
(upward) by an amount equal to the amount of reinsurance ceded (accepted).
• A minimum of 85% of investments out of the ‘controlled fund’ by any life insurer
have to be only in the ‘approved securities’, as specified by IRDA under Sec 27 of the
Insurance act. ‘Controlled fund’ means the all the funds in India related to life
insurance business.
• Similarly a minimum of 75% of all assets of a general insurer has to be in securities
approved by IRDA for that purpose.
• In addition, the above investments have to meet several conditions laid down in this
section
• At least 90% of the above investments have to be held free of any encumbrance,
charge, hypothecation or lien.
• No insurer can directly or indirectly invest the funds of the policyholders outside
India.
• The IRDA can issue regulations on the investments out of the funds of policyholders
in infrastructure/ social sectors. These regulations will apply uniformly to all life
insurers, general insurers and reinsurers.
4
14. No insurer will be directed or managed by or employ anyone whose remuneration or
any part therof, takes the form of a commission or bonus or a share in the ‘valuation
surplus’ in respect of the life insurance business; similarly remuneration as a
commission or bonus in respect of general insurance business is also prohibited,
(please think over why?). However, commissions to agents, or bonus paid on a
uniform basis to all salaried employees, are not prohibited.
15. A managing director or officer of an insurer carrying on life insurance business can
not be a managing director or officer of some other insurer carrying on life insurance
business or of a banking or of an investment company, (why?)
16. If an insurer has a life insurance fund of more than Rs 25 lakhs or an insurance fund
of more than Rs 50 lakhs, the managing director/ officer etc will be full time
employees.
17. Every insurer has to undertake such percentages of life insurance and general
insurance business in the rural or social sectors, unorganized or informal sectors,
economically vulnerable or backward classes, including crop insurance, as specified
by IRDA.
18. The IRDA has the power to investigate/ inspect any insurer and the insurer is duty
bound to provide all necessary records, books etc to the investigators.
19. IRDA can direct an insurer to modify suitably, any reinsurance treaty/ contract when
it comes up for renewal, if the IRDA is of the opinion that the terms and conditions
are detrimental to the insurer or public interest. In addition, IRDA might require an
insurer to get IRDA’s prior approval if it is of the opinion that the insurer is likely or
about to enter into such detrimental reinsurance treaties or contracts (why?)
20. IRDA has the power of search and seizure.
21. No life insurance business can be transferred or amalgamated with the life insurance
business of any other insurer except in accordance with a scheme prepared under
Section 35 and sanctioned by the IRDA. In fact, in the interest of the public,
policyholders, proper management of the life insurance business, IRDA can order
such an amalgamation of the life business insurance of an insurer, with the consent of
the other insurer.
22. The benefits due to a policyholder of life insurance can be assigned to another person.
Similarly, the policyholder can nominate the person(s) to whom the money will be
paid in the event of his death. (What is the difference between an assignment and
nomination? Which can cancel what?)
23. No insurer can pay any remuneration or commission etc to procure or solicit
Insurance business in India to any person except an insurance agent (or principal or
special agent). By a proposed amendment, banks are expected to be permitted to
distribute insurance products (known as Bancassurance)
24. Limitations on Commissions (as a % of premium)
• Life Insurance______
Policy Type__________
Immediate or Deferred
annuity based on single
premium_____________
Deferred annuity based on
Insurance Agent
2%
Special Agent
0.5%
7.5% of first year premium
2% of first year’s premium ~
5
more than one premium
2% of each renewal
premium____________
Other cases
35% (40% in the first ten
year’s of an insurer’s
business) of the first year
premium
7.5% of 2nd and 3rd yr
premium
5% for other premium
Note: Commission includes remuneration in any form
15% (17.5% in the first ten
year’s of an insurer’s
business) of first year
premium
General Insurance
Type of Policy
Fire or marine
Insurance Agent
5%
Miscellaneous
10%
Principal Agent______
20% less commission
payable to any insurance
agent_______________
15% less commission
payable to any insurance
agent
Note: Commission includes remuneration in any form
25. Limitations on expenses of management
Expenses on management include commission payments. Every insurer has to submit
annual returns to IRDA certifying that expenses on management has been fully debited to
the respective account of each class of insurance business.
Such expenses on management can not exceed limits prescribed by IRDA, with due
regard to the size and age of the insurer. Any excess thereof, in any particular year, has to
be within such excess permitted by IRDA.
26. No person can offer any inducements to any person to take or renew any insurance
policy; or any rebate on commissions or premiums payable. (Thus the currently
widely prevalent practice of sharing of a part of the first year commissions with the
policy holders by life insurance agents is strictly speaking illegal- how will it affect
the proposed bancassurance?)
27. No person can act as an insurance agent, chief/ principal/ special agent or an
insurance intermediary unless licensed to do so by the IRDA. IRDA has laid down
the grounds for disqualification, including lack of specified professional
qualifications. This license has to be renewed periodically as per IRDA’s regulations.
28. Except when an insurer can show that the policyholder has willfully suppressed a
material fact known to him at the time of taking out a life insurance policy, no
insurance policy can be questioned on the ground that some statements made were
false or inaccurate. The only exception is proof regarding age.
6
29. At least one fourth of the whole time Directors of an insurance company offering life
insurance has to be elected from amongst its (eligible) policy holders. No insurance
agent can become a Director.
30. Restrictions on Dividends and Bonus
No insurer carrying on life insurance business or any miscellaneous insurance specified
for this purpose by IRDA, can declare or pay any dividends to shareholders, bonus to
policy holders or any payments to service debentures etc from any such specified
insurance fund, except a surplus shown in the valuation of that fund done as per IRDA’s
regulations.
In addition:
a) such payments for servicing debentures, including interest, can not exceed 50% of
such surplus
b) Interest on debentures can not exceed 10% of such surplus, unless offset against
interest credited to the fund in deciding the interest basis during valuation
The
share of the surplus reserved for shareholders can not exceed 7.5% of such
c)
surplus.
31. No insurer can carry on any insurance business based on ‘the dividing principle’, i.e.,
any insurance where the premiums and or benefits (except for bonus) is not fixed but
depends on the number of policies becoming claims within a certain period.
32. Under specified situations/ cases, the act provides for the appointment of an
administrator by the IRDA for managing an insurance business; for takeover of an
insurer business by the Central Government; and winding up of an insurance business
by a Court or otherwise.
33. Tariff Advisory Committee: A committee called the Tariff Advisory Committee
(TAC) under the Chairmanship of the Chairperson of IRDA will be set up. The TAC
will control and regulate the rates, advantages, terms and conditions that may be
offered by insurers in respect of general insurance business.
34. No person can act as a surveyor or loss assessor unless licensed by IRDA to do so as
per provisions of the act and regulations thereof.
35. Solvency Margins
a) Assets of an insurer shall be valued at values not exceeding their market or realisable
values. Several assets specifically mentioned in the regulations made by IRDA in this
regard will be excluded.
b) Similarly, a proper value shall be placed on all liabilities.
c) Liabilities will exclude share capital, general and other reserves not created to meet
specific liabilities, investment reserve, reserve for bad and doubtful debts and
depreciation fund.
d) Liabilities shall include i) provisions for dividends declared and outstanding in full,
ii) reserves to the extent of 50% of the unexpired risks in fire and marine cargo
business and 100% of unexpired risk in marine full business, net of reinsurance, iii)
7
estimated liabilities on outstanding claims and dues to other insurers, sundry creditors
and tax dues.
e) Every insurer shall, at all times, maintain an excess of assets over liabilities as valued
above, known as the ‘Required Solvency Margin’, as follows:
Life Insurance Business
Mathematical Reserves: means the provisions made by an insurer to cover liabilities
(excluding liabilities which have fallen due and on ‘deposit back’ arrangements with
reinsurers), arising under policies of life insurance. Will also include provisions for
adverse deviations of the bases such as mortality and morbidity rates, interest rates,
expense rates, and provisions made as per regulations of IRDA.
Sum at Risk: Compute the sum of a) amounts payable on death except as annuities b) the
present value of any annuities/ periodic payments payable on death. From this sum,
subtract the mathematical reserves in respect of such policies.
Higher of Items (a) and (b) below.
a) Rs 50 Cr (Rs 100 Cr for reinsurer)
b) Aggregate of sums arrived at in items I and II below
Aggregate of results of the calculations in A and B below.
1)
A)
A.l. A percentage determined by regulation (not exceeding 5%) of the
‘mathematical reserves’ for direct business and reinsurance acceptances
without any deductions for reinsurance cessions
A.2. Compute the following in percentage terms:
(Mathematical reserves less reinsurance cessions as of last
financial year) divided by (mathematical reserves before such
deductions).
A.3. The sum in A.l shall be multiplied by the max (85% or the % in
A.2); in case of an insurer carrying on exclusively reinsurance, instead of
85%, use 50% on the above multiplier.
B)
B. 1. A sum equal to a percentage to be determined by regulation (not
exceeding 1%) of the ‘sum at risk’ for the policies on which sum at risk is
not negative (can it be negative?)
B.2. Compute the following in percentage terms
(Sum at risk as used in B.l. less reinsurance cessions) divided by
(Sum at risk as used in B. 1.before any such deduction)
B.3. Multiply the sum arrived at B. 1. by Max (50% or the % arrived at in
B.2).
H)
a percentage to be determined by regulation of IRDA of the value of the
‘assets’.
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General Insurance Business
Highest of the following:
a) Rs 50 Cr (Rs 100 Cr for reinsurers)
b) 20% of ‘net premium income’
c) 30% of‘net incurred claims’
subject to credit for reinsurance in computing net premiums and net incurred claims
amounting to min (actuals, % determined by regulation not exceeding 50%)
‘Net incurred claims’ means the average during the specified period (not exceeding three
preceding financial years)
36. No insurer will assume any risk unless the premium payable is paid in advance or
guaranteed to be paid as in prescribed manner, (why not?)
37. Re-insurance
Every insurer shall re-insure with Indian re-insurers such percentages of the sum assured
under each class of policies as may be specified by the IRDA. The percentage so
specified can not exceed 30%. The IRDA may also specify the proportion in which the
specified percentage will be allocated among the Indian re-insurers.
38. Acquisition of surrender values by policy
Consider any life insurance policy in which the whole of the benefits become payable
after the occurrence of a contingency which is bound to happen (e.g. death). If all
premiums payable on such a policy have been paid for at least three consecutive years,
the policy will acquire a guaranteed surrender value, to which will be added the surrender
value of any subsisting bonuses already attached to that policy. The policies issued shall
show such surrender values at the close of each year after the second year, and method of
calculating the surrender value of the bonus.
39. Restriction on the extent of shareholding by a promoter in an insurance company
Under section 6AA of the amended Insurance act, no promoter can hold more than 26%
or such other prescribed percentage of the paid up capital. The promoter will divest such
excess holding, if any, in a phased manner, after a period of ten years after
commencement. The IRDA may specify the manner and procedure for divesting such
excess holdings.
Regulation Issued under the Insurance Act or IRDA Act
Please note that specific details and procedures involved in implementing the various
provisions are contained in the detailed regulations issued in this regard by IRDA. The
details can be obtained from their website www.irdaonline.org or www.irdaindia.org .
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Analysis of Expenses for Life Insurers
By - Shriram Mulgund, P.A.Balasubramanian
1.
Introduction
In pricing a product, the actuary has to take into account a number of parameters, such as, mortality,
policy terminations, interest, expenses, taxation, profit objectives, and so on. For parameters
such as mortality, some industry tables would generally be available. For parameters such as
interest, the actuary can form some expectations for the trend of future interest rates. The expense
parameter can be considered to be somewhat unique. This will be very much company-specific.
No guidance will be available in the form of any inter-company study (apart from any published
financial statements). The success of a life insurer would depend, among other things, on its
ability to charge proper expenses in the products and to monitor and control the actual expense
levels.
This paper examines the manner in which the expenses can be analysed so as to reflect them in
pricing and valuation in an appropriate manner.
2.
Explicit Recognition of Expenses
When a block of business is placed on the books, the insurer receives premiums and then looks
after the outgo consisting of benefits, expenses and taxes. The balance is invested to generate
income.
The assumptions for mortality and policy terminations determine the benefits. The assumption
for interest determines the investment income (and, in some situations, the benefits payable in
the form of bonuses as well). A separate set of assumptions will then be needed to determine the
expense level.
Many times, there may be a temptation to provide for the expenses in an implicit manner - e.g.
through a margin in the interest assumption. While this may be an convenient way for minor
benefits, it will not be a desirable course to follow for major blocks of business. Use of implicit
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approach clouds the picture and makes the task of monitoring and controlling expenses very
difficult. As a result, recognising expenses in an explicit manner will always be desirable.
It may be borne in mind that the IRDA regulations on valuation envisage that the actuary will be
using explicit assumptions for all important parameters. This will of course include expenses.
3.
Nature of Analysis for Expenses
One of the objectives of analysing expenses is to enable the actuary to reflect them in pricing and
valuation in an appropriate manner. This will ensure the following:
The premiums in respect of any products sold by the insurer will include an
appropriate share of expenses in respect of that block business.
The reserves set up for any block of business will make an appropriate
provision for future expenses in respect of that block.
In order to achieve the above objectives, it will be necessary to analyse the expenses to reflect
the variations by the following characteristics:
Variations by product type.
Variations by first year and renewal years.
Variations by nature of activity for which the expenses are incurred.
These variations are discussed in the following paragraphs.
4.
Investment Expenses
In the discussion on allocation of expenses, a special mention should be made of expenses
associated with investments. These expenses are incurred in the process of earning investment
income. It is logical to deduct these expenses from the investment income. Any interest
assumption should be considered net of investment expenses.
Allocation of any expenses associated with the investment operation should follow the approach
discussed in the ensuing paragraphs.
5.
Direct and Allocated Expenses
In the process of allocation of expenses, some expenses can be very readily allocable to the
appropriate categories. For example,
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Commissions.
Any taxes payable on premiums or expenses associated with the sum assured
(e.g.stamp duty).
Any income taxes directly allocable to a specific line of business.
Expenses associated with printing, sales conferences, etc.
Other expenses will have to be allocated to the different categories using a variety of methods,
which take into account the nature of the underlying activity. These are discussed in the following
paragraphs.
6.
Variations by Product Type
Different product types could have very widely varying expense patterns and levels. If the
expenses of two (or more) of such groups are combined, appropriate expense provision in
premiums and valuation will take place only if the relative proportions of future new business
and business in force will be the same as that on which the expenses were combined. As it will
be impossible to ensure this, it will be more appropriate to deal with such blocks of business
separately.
Generally speaking, separation by the following classes of business will be necessary :
Individual and group.
With profits and without profits.
Life insurance, life annuities (including pensions) and health.
For some of the classes, some further sub-classification may be called for. For example, under
without profits life insurance, different expenses may have to be provided for permanent
(e.g.endowment) and term. Or, under annuities, different expenses may be involved for deferred
and immediate annuities.
The manner in which different lines or blocks of business are handled will depend on the volume
of business. Smaller blocks may have to be grouped with larger blocks of similar nature. Any
system that is put in place should be flexible, so that any new types of products that need a
separate analysis can be easily accommodated.
7.
Fund Accounting
The task of identifying expenses for different lines of business will be greatly facilitated by
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setting up of separate funds for such lines. With such funds set up, the income and outgo of each
fund can be dealt with separately. For each fund, its premium revenue will be credited, claims
and expenses (direct or allocated) are paid out and separate investments are made. This will
permit specifying different investment strategies for different funds. The profitability of each
line can then be determined separately. Such treatment can minimise subsidies between different
classes of business.
In situations where setting up separate funds is not possible or practical (due to small size),
notional allocation of various items will be required.
8.
First Year and Renewal Expenses
It has been recognised all along that placing a policy on the books of an insurer is expensive.
This requires differentiating between the first year and renewal expenses. Identification of the
first year expenses will be easy for some expenses (e.g. commissions). For others, this may not
be obvious. In such situation, the key test will be that the expense involved should be in respect
of an activity that is associated (directly or indirectly) with placing the business on the company’s
books. Foi activities that are directly associated with new business, the expenses will be roughly
proportional to the amount of new business generated. In the discussion in the following
paiagraphs, this test should be borne in mind (except, of course, for the investment expenses).
9.
Allocation of Expenses by Activity
Apart from diiect expenses such as commissions, all expenses are associated with certain activities,
e.g. underwriting, policy issue, premium collection, policy servicing, claims administration, and
so on. These activities can relate to different lines of business or relate to first year/renewal.
Allocating the expenses to the proper category will be critical for an appropriate analysis. For
example, consider the following activities:
•
Expenses associated with premium collections and accounting. These would
be incurred only for premium paying policies.
•
Expenses associated with loans and surrenders. These would be incurred
only for the policies having cash values and availability of loans.
•
Underwriting expenses. These will not be associated with annuity business.
There will be some activities that will be considered as “overhead”. These have to be spread
over the direct functions in an equitable manner.
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The objective of the allocation process will be to ensure that all the expenses incurred by the
insurer are eventually allocated to some function dealing with the issue or maintenance of business.
The allocation of expenses to the various activities can be carried out by the process of Functional
Allocation of Expenses discussed below.
10.
Functional Allocation of Expenses
All the work relating to the business issued and maintained by an insurer is done by people. All
expenses, other than the direct expenses such as commissions, medical fees, etc., can be associated
with people. Once all the expenses have been allocated to people, they can then be apportioned
between different activities or functions in proportion to the time the person spends on those
activities.
(a) Allocation to Employees
The expenses associated with each employee would consist of the following:
Salaries and employee benefits (such as vacation, pension, provident fund,
group life and health benefits, car allowance, and so on).
Rent for space needed for work along with the associated costs of electricity,
water, telephone and other utilities, property taxes, etc.
Furniture and other equipment such as calculators, computers, etc.
Office supplies, printing and postage charges, etc.
Different methods may have to be employed in allocating the total costs amongst the employees.
Following approaches can be considered:
The salaries and allowances paid to the employees will be directly available.
All employee benefits that are related to these can be allocated in proportion
to the salaries and allowances paid.
Each employee will be eligible for a specified office space. This would
generally be dependent on the position held by the employee (clerical,
supervisor, manager, etc.). All expenses related to the office space (office
rent, property taxes, electricity, etc.) can be allocated in proportion to the
office space.
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Each employee will be eligible for the office furniture and equipment
(telephone, computers, etc.) depending on the position held. It may be possible
to allocate the expense directly to the employee.
(h) Allocation to the Functions
Sections 11 to 14 below describe the various functions to which allocation is to take place. The
ultimate objective is to establish the total allocation to cells with different combinations in respect
of the following:
Line of business (or a sub-business category within a given line)
First year or renewal.
The different functions set out in Sections 11 to 14 below.
The employees can be asked to indicate their estimates of the proportion of time spent for the
different cells. There would be some employees who will be working on specific functions, e.g.
new business or underwriting. For such employees, the allocation between different lines of
business may be needed. There would be others whose work would be spread across different
lines of business and functions. For such employees, the time allocation to different cells will be
important. The total expense allocated to that employee can then be allocated in proportion to
the time spent on various components.
Different methods of allocation to the cells could be used for certain activities where time allocation
method may not be appropriate. For example:
Foi the premium accounting area, the number of collections processed will
be i elevant. The costs can be allocated in proportion to the number of
collections applicable to different lines of business.
For areas such as valuation, the allocation to different lines of business can
be done in proportion to the number of policies in force.
For areas such as policy issue, the allocation can be done in proportion to the
number of new policies issued.
Different allocation approaches may have to be used in different circumstances. The objective
will be to make sure that the allocation method is reasonable and easy to use.
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Description of Functions - First Year
In allocating the expenses, the following first year functions will be taken into account.
(a)
Acquisition
This will cover all expenses involved in securing the new business. This will include the following
activities:
Recruitment and Training of Agents
This will cover all the activities related to recruitment of agents (advertising, interviews,
evaluation, testing, etc.), training workshops, training material, conferences, etc.
Administration and Supervision of Agents
This will cover all the administrative support needed to agents’ activities, such as agency contracts,
maintenance of agency records, administration of agency financing plans, etc.
Recruitment and Training of Sales Supervisory Personnel
This will cover recruitment and training for the “second line” sales personnel.
Market Research and New Product Development
This will include any market research undertaken to understand the market needs and the work
of developing new products, preparation of premium rate manuals, new policy forms, etc.
Advertising
This will cover the direct costs of advertising through the various media and general administration
of these programs.
Sales Promotion
This will cover the tasks of preparing sales material, any assistance to sales people, sales
confererices and campaigns, etc. If the sales personnel use any software in establishing the
clients’ insurance needs, the development costs will also be included.
General Supervision
This will include the supervision for sales administration, branch work, field management,.etc.
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Selection
This function will include all the activities from the receipt of the proposal form from the agent
to its underwriting decision. This will encompass the following
Arranging medical examinations and obtaining special reports.
Reviewing all the evidence of insurability and arriving at the underwriting
decision, including any correspondence involved in the process.
Establishing underwriting policies and setting up of underwriting procedures.
(C)
Policy Issue
This function will include all work from the time the proposal is accepted until the policy has
been issued and the record has been placed on the computer system or the policy is cancelled as
not taken. This will cover the work of checking accuracy of premiums, checking proof of age,
reviewing nominations and/or assignments, delivery of policies, etc.
12.
Description of Functions - Renewal (Maintenance)
This will include all activities that will be necessary to service the policyholders and to keep the
policies on the company’s books. These will include a wide ranging activities as follows:
Billing and Collection of Premiums
This will encompass the activities relating to preparation and sending of premium notices,
collection and accounting of premiums, sending reminders, etc. If a major portion of the business
is of salary savings type (or through automatic bank deductions), the expenses should be separately
identified.
Work relating to Premium Paying Policies
This will encompass the following activities:
Commission accounting. Calculation and payment of agency commissions
and allowances, maintenance of agency commission records and preparation
of statements, etc.
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Business conservation. This will involve efforts to maintain the business on
the books of the company - usually after the grace period allowed for the
payment of premiums.
Reinstatements. This will include seeking evidence (if necessary), restoration
of premium paying basis, restoration or records, etc.
Benefit Payments
This will include the work relating to payment of policy benefits as follows:
Death benefits. Dealing with death notifications, claims investigations, dealing
with contested claims, payment of benefits, checking of beneficiary
designations, following up of unpaid claims, recording of claims on policy
master files, maintaining claims statistics, etc.
Maturity benefits. Payment of benefits, following up on unpaid benefits,
recording maturities on policy master files, etc.
Cash Surrenders. Handling requests for surrender, calculation of surrender
values, payment of benefits, recording surrenders on policy masterfiles, etc.
It may be noted that if any disability or health business is on the books, it will have to be dealt
with separately.
Policy Loans
This will cover all the work relating to policy loans-quotations, granting of loans, maintenance
of loan records, accounting of loan interest and repayments, etc.
Policy Valuation
This will cover the work relating to the year-end valuation.
General Policy Maintenance
This will include all other policyholder servicing such as
Address changes.
Policy changes (including any associated underwriting).
Maintenance of policy files.
General policy correspondence.
Research work relating to mortality, lapses, etc.
Admission of age, changes in nominations or assignments, etc.
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From time to time, some special projects may be undertaken (e.g. implementation of new systems
and procedures, changes in existing systems, etc.). Its treatment will depend on the nature of
these special projects. If the projects are likely to be recurring (say, every two or three years),
then the cost can be included in general maintenance. If they are likely to be recurring after a
long-term interval (or are of one-time nature), the cost could be amortised over a few years.
13.
Description of Functions - Overhead
The discussion above deals with functions that are directly associated with issue or maintenance
of policies. There will be a variety of functions that are not directly associated - e.g. legal,
human resources, statutory reporting, corporate work, etc. These can be dealt with on the following
lines:
To the extent the activity can be directly associated with a function, the
corresponding expense should be allocated to that function (e.g. legal work
in connection with contested claims).
The functional allocation approach could have resulted in allocating expenses
to the different lines of business. There may be others where such allocation
may not have been possible. All such expenses can be spread over the various
functions in the same proportion in which the rest of the allocable expenses
have been allocated.
Once the overhead expenses have been allocated, all the expenses of the insurer would have
been allocated to various cells (viz. combinations of line of business, first year/renewal and
function).
14.
Description of Functions - Other Lines of Business
The above description assumes that the line of business is individual life insurance. Similar
approach can be adopted for other lines business. Following comments on other lines of business
may be relevant:
Group Life and Health
Acquisition expenses will include all efforts by group field sales
representatives.
Policy issue expenses will include plan changes, employer administration
manuals, issuance of certificates, etc.
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The maintenance function will include renewal underwriting, certificate
administration, etc.
The payment of health benefits will need to be handled separately.
Immediate Annuities
Expenses of making periodic payments will have to be identified separately.
15.
Relating Expenses to a Common Measure
Once all the expenses have been allocated, they have to be related to a common measure. A
variety of measures can be used. For this purpose, the relevant data for the year will have to be
obtained. The following measures can be used:
% of Premium
First year and renewal commissions.
Acquisition expenses.
Per New Policy Issued
Selection expenses.
Per Premium Collection
Premium billing and collection, work related to premium paying policies.
Per In Force Policy
Benefit payments, policy loans, policy valuation, general maintenance.
Per Payment
Payments under immediate annuities.
16.
Reflection of Expenses in Pricing and Valuation
The expense analysis would have generated appropriate expense factors for each line of business
and product type. These can then be built into pricing and valuation in the following manner.
Any expenses associated with policy issue will be relevant only for pricing.
First Year
Commissions will be expressed as a percentage of premiums.
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Acquisition expenses will be expressed as a percentage of premiums.
Selection and issue expenses will be expressed as a flat amount per policy.
Renewal
17.
•
Commissions will be expressed as a percentage of premiums.
•
Separate expenses related to billing and collection of premiums will be used.
If a weighted average premium mode is used, a single figure could be used.
•
A flat per policy expense will cover all the maintenance expenses. If a single
weighted average value has been used for premium billing, etc., a single per
policy expense can be used.
Monitoring Actual Expenses
As discussed above, one of the objectives of putting in place a system of analysing expenses is to
be able to monitor the actual expenses.
No insurer can expect to stay in business by selling products that are inadequately priced. As the
insurer’s expected experience changes, it has to be reflected in the pricing of products it is
currently selling. In other words, the current pricing basis should always reflect the current
experience levels. These levels, along with appropriate Margins for Adverse Deviations, will
then be employed in valuation.
After performing the annual valuations, the actuary will be performing an analysis of earnings
by source. One of these sources will relate to expenses. This will compare the provision made
foi expenses in the valuation with the actual level. The expense profit will consist of two
components. The first component will consist of the profit from the actual level being different
from the expected level. The second component will consist of the release of expense MAD’s
over the year. A loss arising in the first component will indicate that the expected level used in
the valuation needs an update.
While the analysis of earnings by source will be informative, it will not be available until after
the annual valuation. A simplified approach can be used for monitoring during the year.
The basis used for current pricing will provide the different expense factors - both for first and
renewal years. These factors can be applied to the business of current year (new and in force).
This will provide a measure of the expense allowances that are available in the current year.
This total can then be compared with the actual expenses. The ratio of the actual expenses to the
available allowances can be called “Total Expense Adequacy Ratio” (TEAR). A ratio of over
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100% will indicate overspending and a need for closer monitoring. If the ratios continue to stay
over 100% year after year, it will indicate a need for repricing of the products currently sold.
18.
Other Approaches for Expense Analysis
The discussion so far focussed on a fairly detailed analysis of expenses. Once the system to
track the expenses in the manner described has been put in place, the actuary will be able to use
the analysis for pricing and valuation.
It is, however, quite likely that the insurer may take some time to design such a system and start
getting the results. In the meantime, some approximate approaches may have to be used. One
such approach is described below. It should be borne in mind that any approximations would
result in some form of averaging between different lines of business or product lines. This may
tend to invalidate the cost factors in the future years. A detailed analysis on the lines described
in the paper will be a desirable approach to be followed.
(a)
Allocation Bases
The insurer’s expenses can be allocated using three ratios indicating the apportionment between
new and renewal:
Ratios specified ahead of time.
Salary ratios (relative proportions of salaries spent for new and renewal
functions).
Premium ratios (relative proportions of new and renewal premiums).
These are discussed below.
(b)
Specified Proportions
There will be some functions where it may be possible to establish ahead of time whether the
function falls under “new” or “renewal”. If a function is not completely “new” or completely
“renewal”, the relative proportions may not be difficult to establish. Following may some
examples:
Certain functions can be treated as 100% “new” - first year commissions,
costs associated with second line sales personnel, medical fees, policy stamp
costs, product development costs, printing of development material, etc.
Certain functions can be treated as 100% “renewal” - renewal commissions,
policy administration, etc.
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For certain functions, relative proportions between “new” and “renewal” can
be specified. For postage, teleprinter and fax costs the proportion could be
35:65. For rent, travelling expenses, staff training, etc. the ratio could be
50:50. For telephone charges, the ratio could be 75:25.
It should be borne in mind that the proportions used will depend on the insurer’s perception of
the related costs, set up of the operations, etc. These relative proportions may need periodic
review.
(c)
Salary Ratios
The salary ratios would be similar to the proportions indicated above. These would depend on
the nature of the function. These salary ratios would be used to allocate salary related costs, such
as, salaries and benefits, staff benefits, printing, stationary, electricity charges, etc. Following
will be some of the examples:
For areas such as marketing, sales, new business, publicity, etc., the salary
costs could be allocated 100% to “new”.
For areas such as policy servicing, claims, building maintenance, etc., the
costs could be allocated 100% to “renewal”.
•
(d)
For other departments, some proportions, such as 20:80, could be specified.
Premium Ratios
These could be used for items such receipt stamps, computer expenses, etc.
19.
Other Considerations
The work relating to analysis of expenses, on the lines described above, could face a number of
practical difficulties. Some of these are discussed below.
For some expenses, the accuracy of allocation depends on the accuracy of time
estimates prepared by the employees. For a large employer with employees spread
across the country, getting accurate time estimates may be difficult. However, it
should be borne in mind that such time estimates would be relevant only for
“corporate” activities. Almost all of the activities associated with functions such
as underwriting, policy issue, premium billing and accounting, policy servicing,
etc. do not have to use time estimates. These allocations can be based on some
statistical data such as number of new policies issued, number of premium
collections, number of policies in force, etc. The question of using time estimates
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will then be required only for those activities that spread across different function
or lines of business. In some situations, the time estimates can be prepared on
group basis (e.g. for a section or a department).
The insurer’s organisational structure will have a definite bearing the method used
for allocation. As one goes up the tiers of the organisational structure, the activities
would tend to become “corporate” in nature. Depending on the role a tier plays,
the method of allocation may have to be modified. Different methods of allocation
may be found appropriate - number of policies, premium income, etc. If the
allocation is made as a percentage of premium income, the manner in which special
business classes are to be handled may need some examination — for example,
single premium business, term insurance, etc.
The cost of setting up the procedures for expense allocation also has to be borne in
mind. It should not be unduly high. The fact that it is a tool and not a master has
to be borne in mind.
20.
Concluding Comments
The paper gives a description of the general approach that can be used in the analysis of expenses.
It may have to be modified to suit the special circumstances of the insurer. Slight modifications
may be needed for different lines of business.
The suggested approach for reflecting expenses in pricing and valuation cannot be used unless
the insurer has systems in place to analyse the expenses in the suggested manner.
The suggested approach will result in ensuring that all products sold by the company are placed
on the books on a self-supporting basis. This will avoid subsidies between different product
lines. Any changes in the product mix will have no effect on the expense allocation.
With the explicit recognition of expenses in valuation, the actuary will be in a position to compare
the provision made in the valuation with the actual expenses. This gives a powerful means for
monitoring expenses.
Once the actuary obtains a good handle on expenses, he/she will be in a much better position to
discharge his/her duties placed by legislation.
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About the Author
Shriram Mulgund
Shriram Mulgund retired in 1999 after working in the insurance
industry for 40 years - eight years in India, four years in England
and 28 years in Canada.
He has a Masters degree in Pure Mathematics from University of
Poona and another one in Computer Science from University of
London. He is a Fellow member of the Institute of Actuaries, the
Canadian Institute of Actuaries and the Actuarial Society of India.
He is an Associate of the Society of Actuaries in the U.S. and a
Member of the American Academy of Actuaries.
Shriram has worked in the areas of valuation, corporate financial
management and pension plan administration.
He has been playing an active role in the Canadian Institute of
Actuaries. He was a member of the Mortality Committee, a
member of the Financial Reporting Committee and the chairman
of the Papers Committee. He has been taking a very active interest
in the changes that have been taking place in the Indian insurance
scene. He has published numerous papers at the Canadian Institute
of Actuaries, International Actuarial Congress and the Actuarial
Society of India. His paper “Practical Aspects of Cash Flow Testing
in Determination of Reserves”, published in 1995, has been
specified by the Canadian Regulators as the paper the Appointed
Actuaries should look at for compliance for the annual valuations.
Shriram plans his annual visits to India to coincide with the annual
conferences of the Actuarial Society of India.
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About the Author
Name
P A Baiasubramanian
Designation
Executive Director (Investment/Actuarial)
Appointed Actuary, Life Insurance
Corporation of India.
Education and Professional Qualifications
B Sc , AIA (London), FASI, AHI
Date of Birth
1st June 1943
Work Experience
>
Since April, 1998, Executive Director (Investment) responsible for Investment
management of LIC of India
>
April 1996 - April 1998 Chief (Investment) with specific responsibilities in the area of
Market Operations, Social Sector investments, foreign investments and Group & Pension
fund investments.
>
May, 1994 - April, 1996, Secretary (Investment) responsible for Project evaluation,
Review and Follow-up of Corporate Sector investments and Social Sector investments,
Supervision of money market operations.
>
May 1991 - May, 1994, Senior Divisional Manager of Madurai Division with
responsibilities to control 24 branch office operations including Marketing, Sales and
Service.
>
May 1990 - May 1991 Regional Manager (Actuarial) responsible for underwriting and
actuarial support to Divisional offices in Maharastra, Goa and Gujarat. The work included
reaserch work in actuarial areas like expenses analysis, bonus earning power investigations,
Special actuarial quotations etc.
>
May 199 - May 1990 Deputy Actuary - Responsibilities included carrying out valuation
of life and annuity business in India.
>
June 1987 - May 1988 Asst. Actuary - Overseas branch business including actuarial
investigations associated with Valuation and compilation of statutory returns. Report of
Valuation of liabilities and assets and financial Position in the nature of support function
to Chief Actuary.
>
Prior to 1987 between 1981 worked in Actuarial Research covering Expenses Analysis
and functional cost analysis and included transfer of business between LIC (Overseas)
and other insurers, Special quotations, reinsurance administration etc.
156
ASI
4th Global Conference of Actuaries
FICCI
Achievements and special positions held presently or previously:
>
Past Secretary, Actuarial Society of India
>
Past Vice President and Member, Executive Committee of Actuarial Society of India
>
Past Examiner of Insu -ance Institute of India (Licentiate/Associateship Exam) and
Actuarial subject for PG Diploma in Actuarial by an autonomous College.
>
Served as Chairman of working group on investments for Insurance Regulatory and
Development Authority during 1996-97.
>
Presented Paper on Functional Cost Analysis at the 3rd Actuarial Conference at Mumbai
1980.
>
Presented Paper on Regulatory Issues of Investment of Insurance Business at a Seminar
sponsored by IIM, Bangalore in May 1999.
>
Visiting Faculty at NIA Pune on actuarial aspects of Pension Business and Investments
of life and Pension Business.
>
Attened CPD programme on Investments by Institute of Actuaries, London at Scotland
in May 1999.
>
Attened Seminar on ‘Life Actuary 2001 at London in March 2001.
157
The Market for Catastrophe Risk:
A Clinical Examination1
Kenneth A. Froot
Harvard Business School
and National Bureau of Economic Research
July 25,1999
Abstract
This paper examines the market for catastrophe event risk - i.e., financial
claims that are linked to losses associated with natural hazards, such as
hurricanes and earthquakes. This market is in transition as new
approaches for transferring risk are being explored. The paper studies
several recent transactions by US AA which use reinsurance capacity from
capital markets, rather than only from reinsurers. We identify two puzzles
concerning the cat protection purchased in these transactions: there is no
coverage for the largest, most severe events; and premiums appear well
above actuarial value. We demonstrate that both features deviate from
what theory would predict, yet are characteristic of many transactions, not
simply those of USAA. We then explore a number of possible
explanations for the facts. The most compelling are combinations of
capital market imperfections and market power on the part of reinsurers.
Conclusions for broader capital market and risk management issues are
discussed.
1 The author would like to thank Josh White for excellent research assistance. Thanks for suggestions and
discussions also go to Ernie Asaff, Clement Dwyer, Peter Diamond, Marty Feldstein, Howard Kunreuthcr,
Chris McGhee, Roberto Mendoza, Paul O’Connell, and Jeremy Stein. Responsibility for any errors and
omissions and for all views lies solely with the author.
1. Introduction
Hurricanes, earthquakes, wind and ice storms, floods, etc. have long been known to cause
large and unexpected losses among owners of physical capital. Recently, it has become
more widely appreciated that a single hurricane or earthquake could result in damages of
well over $50 billion. Given the growth rates in physical asset values and in population in
high-risk zones, distribution of catastrophe event losses continues to grow.
Because households are risk averse, they have a strong incentive to share their risks with
others through the purchase of insurance. Corporations - to the extent they have a wellfoundered concern with risk management — also have an incentive to purchase insurance
and reinsurance. If these groups behave in a risk averse manner, then they treat severe
losses as expectationally more costly than moderate losses. Thus, one would expect
insurance and reinsurance to focus on catastrophic outcomes. Moreover, since cat event
losses are uncorrelated with (and perhaps even independent of) financial wealth, the
premiums for such catastrophic protection should, if markets are perfect, be close to
expected losses.
This paper explores these propositions and the market for cat event risk by examining in
depth several recent reinsurance transactions completed for USAA, one of the largest
insurance companies in the US. These transactions have been widely discussed. They are
among the first to back reinsurance with dedicated collateral supplied by bondholders otherwise known as cat bonds. Traditionally, reinsurance has been backed by the general
credit of reinsurers, who use equity to fund a portfolio of reinsurance liabilities. We
demonstrate that these transactions display the two characteristics above: that very large
losses are not covered; and that premiums are very large compared with expected losses.
We then attempt to analyze these transaction features in two ways. First, we attempt to
show that they do indeed conflict with what equilibrium models would predict about the
profile and price of reinsurance coverage. Second, we provide evidence from a large
sample of reinsurance transactions, in order to put the clinical data points in perspective.
The large-sample evidence demonstrates that the USAA coverage has had very much in
common with other, traditional reinsurance transactions.
The paper then turns to why this is the case: what could explain the widespread tendency
to underinsure (particularly for large events) and to set prices so high. We look at eight
different explanations. The majority of these focus on distortions on the supply side, but
several suggest problems with the demand side as well. The most important explanations
are supply-side stories of capital market imperfections facing reinsurers and the exercise
of market power by reinsurers.
The most interesting implications of the evidence we present go well beyond the cat risk
market itself. After all, cat risk will never be a very large standalone asset class. In the
conclusions, we discuss several lessons drawn from this evidence for the broader
behavior of capital markets and corporate risk management.
1
2. Recent Reinsurance Contracts: Clinical Evidence
2.1. USAA: The company
To understand the developments in the traditional reinsurance market and the associated
risk transfer mechanisms, it is useful to investigate USAA’s recent purchases of
reinsurance. USAA is the fifth largest private passenger automobile insurer and the
fourth largest homeowner insurer in the United States. It sells exclusively to U.S.
military officers and their families and is organized as a mutual insurance company.
Because of its military customer base, USAA has relatively little control over the
geographic pattern of its exposures that come disproportionately from California and
Florida.
The risk of Florida hurricane is a real one for USAA. In August 1992, Hurricane Andrew
swept through Florida and Louisiana, causing losses of $620 million to USAA and
approximately $17.9 billion to the insurance industry overall, of which 67% was
residential.2,3 Hurricane Andrew was by far the most costly insured cat event in the US
over the last 30 years, even when all loss figures are expressed in constant dollars. Small
changes in Andrew’s trajectory would have resulted in major changes in total industry
and USAA losses.
2.1.2. USAA’s 1997 reinsurance program
In many respects, USAA’s catastrophe reinsurance program looked like the programs of
other insurers. USAA purchased reinsurance in “excess-of-loss layers” conforming to
different cat-triggered loss amounts.4 The main parameters of an excess-of-loss layer are
the “retention,” “limit,” “exceedence” and “exhaustion” probabilities, and amount of
“coinsurance.” The retention is just the deductible - the level that losses must exceed
before coverage is triggered. The probability that losses reach this level is the
exceedence probability. The contract limit is the maximum recovery that can be made.
The probability of reaching a loss that exhausts the limit is the exhaustion probability.
Most reinsurance contracts require that the cedent share, or coinsure, a portion of the
layer - usually between 5% and 20%. Coinsurance and positive retention levels help
diminish moral hazard and adverse selection. Essentially, reinsurance layers are call
spreads written on a company’s underlying cat losses: long one call struck at the retention
or exceedence point, short one call struck at the retention plus limit, or exhaustion point.
The risk period for these contracts is typically one year.
USAA began contemplating alternatives to traditional reinsurance beginning in 1993. By
mid-1995, proposals had been requested from bankers on securitized risk transfer ideas.
2 Source: John Major, “A Synthetic History of the Guy Carpenter Catastrophe Index,” Guy Carpenter,
1997.
3 Dollar amounts in the text are in 1996 dollars unless stated otherwise.
Only paid claims associated with event-triggered losses are reimbursable under standard cat reinsurance
contracts.
2
By early 1996 USAA had selected three investment banks for the execution of a cat bond
transaction for the hurricane season beginning in July 1996. However, even though the
bankers had 4 or 5 months to construct the transaction, it could not be completed that
year. Among the most important reasons were that: few investors understood the
securities; rating agencies had no established criteria on which to rate cat bonds;
regulators had to agree that Residential Re’s noteholders were not, in fact, writing
insurance (something that they generally were not licensed to do); and legal, regulatory
and tax complications made finding the right location for the special purpose vehicle
complicated. Because of these problems, the issue did not come to market until mid-1997
for the risk period running from June 1997 to June 1998.
Figure 1 and Table 1 provide a simple depiction of the layers of USAA’s 1997
reinsurance program. In prior years, USAA had purchased reinsurance to cover losses up
to $1 billion only. In 1997 the company decided to extend its coverage up to losses of
$1.5 billion. It hoped to source this capacity directly from the capital markets. The
reasoning for doing so, according to Steve Goldberg, the chief architect of USAA’s
capital market’s effort, was that “traditional reinsurance capacity is necessarily
limited...” and that “what was needed for USAA as well as other intermediaries was a
long term “supplement of additional capacity.”25
2.1.3. Residential Re
As Figure 1 shows, the top-most layer was reinsured through the capital markets using an
independent, special purpose reinsurer called Residential Re. Residential Re’s sole
purpose was to be an efficient provider of reinsurance to USAA; it would do no other
business. For tax and regulatory reasons, the company needed to be run entirely
independently of USAA. Residential Re provided a one-year reinsurance contract to
USAA, covering events which struck between the dates of June 16, 1997 and June 14,
1998. (See Figure 2 for a time-line.)
From USAA’s perspective, the reinsurance contract written by Residential Re differed in
several respects from those commonly written by reinsurers. The first difference was that
the contract covered a single event only - USAA would have the right to choose one and
only one event from the risk period. Typically, reinsurance contracts covered losses for
any number of events that breached the retention, until the limit was exhausted.6 The
second difference concerned credit risk. Residential Re’s sole purpose was to write a
single reinsurance contract for USAA. It would dedicate collateral equal to the contract
limit. As a result, there was virtually no chance of default once a claim against the
contract was made. Traditional reinsurers did not fully collateralize individual contract
limits, and therefore could conceivably default on their obligations in sufficiently dire
states of nature.7
5 See Goldberg (1997).
6 Traditional reinsurance contracts often contain a reinstatement provision specifying that a new premium is
to be paid to extend additional coverage after the initial limit is exhausted. Often the reinstatement would
be mandatory. The Residential Re contract, however, had no reinstatement provisions.
7 For additional details on the Residential Re contract, See Froot and Seasholes (1997).
3
Residential Re agreed to reimburse 80% of USAA’s single-event cat losses between $1
billion and $1.5 billion, making the reinsurance contract limit $400 million (0.8 x ($1.5
billion - $1.0 billion)). To collateralize this limit, Residential Re sold A-l and A-2 notes.
The A-2 notes, totaling $313 million, had all of their principal at risk. Thus, if an event
resulted in USAA losses exceeding $1.5 billion, USAA would receive $313 million from
A-2 noteholders’ principal.
The A-l notes were slightly more complicated, as they blended part of an A-2 note with a
Treasury strip. This latter feature provided the A-Is with principal protection.
Specifically, $164 million in A-l notes were sold. The A-l principal was then divided in
two parts. The first part was $87 million, which effectively went toward the purchase of
A-2 notes. The remaining $77 million went toward the purchase of 10-year US Treasury
strips with a maturity value of $164 million if an event occurred. The strips allowed A-l
holders to receive full principal repayment regardless of what happened. This meant that
the first $87 million would sustain losses pari passu with the A-2 notes. Thus, between
the A-Is and A-2s, reinsurance collateral of $87 million + $313 million = $400 million
was available from Residential Re to pay USAA’s admissible event losses.
In order to have time to process insurance claims for disaster victims and therefore to
determine the extent of USAA losses, Residential Re notes featured a six-month extended
claims period. If no event occurred, the due date of the notes was June 14, 1998 - a 1
year maturity. If an event did occur, however, USAA could elect to extend the notes’
maturity until December 15, 1998. During this time, USAA was to pay Residential Re an
additional half year’s premium. The reinsurance contract, however, was not similarly
extended. Thus, if USAA elected to extend the notes, it would pay 1.5 years premium for
1 year of risk protection.
In return for the reinsurance, USAA agreed to pay Residential Re $24 million, or 6.0% of
the limit.8 After fees, noteholders received LIBOR plus 576 basis points for putting
funds at risk. Thus, A-2 and A-l holders received fractions (313/400 and 87/400,
respectively) of the premium based on capital at risk. For every dollar noteholders put at
risk of a one-year cat-event loss, they took out 5.76 cents in guaranteed premium.
2.1.4. Actuarial probabilities
The risk of loss to the reinsurance contract was modeled by Applied Insurance Research,
Inc. (AIR), one of several independent firms specializing in the probabilistic modeling of
catastrophic events. AIR (along with its main competitors, EQECAT and Risk
Management Solutions) model the climatology of atmospheric disturbances, the
geophysics of earthquakes, and the engineering of building structures, etc. They hire
actuaries, engineers, geophysicists, software specialists, and mathematicians. Using
Monte Carlo methods, AIR developed a probability distribution of losses for USAA’s
specific portfolio on insured homes and autos, shown in Figure 3 below. AIR estimated
that the Residential Re layer had a 97 basis point probability of exceedence and a 39 basis
8 This excludes fees to USAA of approximately 100 basis points.
4
point probability of exhaustion. The expected loss for the layer (i.e., the integral of the
probability of a given loss times the associated loss of principal) was estimated to be 63
basis points.
These actuarial estimates of expected loss stand in striking contrast to the size of the
premium. In equilibrium we would expect a zero-beta risk to have an expected return
equal to the riskfree rate. This implies that the theoretical spread over LIBOR for the cat
event risk in the Residential Re layer is 63 basis points.9 In return for putting capital at
risk, investors received 576 / 63 = 9.1 times the actuarially fair premium!
When the issue came to market, it attracted considerable interest. The notes were
approximately 3 times oversubscribed. In the days following the issue, the yield fell from
576 basis points to the mid-400s, suggesting that there was indeed excess demand.
It also appeared that investors were not the only ones interested in providing this
reinsurance capacity. There were unconfirmed rumors that a major cat reinsurer had
attempted to undercut the bond offering by promising to write the full reinsurance
contract for a lower premium, without the additional expenses or complications created
by these bonds.10
2.2. CEA 1996
Such undercutting by a traditional reinsurer of a proposed cat bond offering had
happened before. In 1996 the State of California had decided to assemble a fund - the
California Earthquake Authority (CEA) - to help insurance companies finance potential
earthquake losses. In November 1996 the CEA announced that it had decided to purchase
reinsurance from National Indemnity, a subsidiary of Berkshire Hathaway. National
Indemnity is one of the world’s largest reinsurers and easily the biggest single reinsurer
of “super-cats” (high incidence, low probability cat layers).
A purchase of traditional reinsurance was, however, not the expected outcome. Over the
prior year, California’s insurance commissioner had solicited detailed proposals from
investment banks for a CEA cat bond. During the year the commissioner had chosen a
lead bank for the bond’s issuance. This proposed CEA offering was similar to the USAA
transaction, though it was more than double its size. A CEA bond would have attracted
considerable attention as a watershed transaction. However, it was not to be. Just as the
investment bank s underwriting mandate was to be signed, National Indemnity
intervened, offering a lower premium than the bond would have required.11 The offer
Of course, LIBOR itself is not risk free and on average exceeds the US Treasury bill rate by on average
40bp. There is, however, also some amount of credit risk associated with the special purpose vehicle.
Assuming that this credit risk charge is lower than that applied to major money-center banks, all our
computations are conservative by using LIBOR as the corresponding “risk-free” benchmark.
10 Based on a private communication with Christopher McGhee, Managing Director, Marsh McLennan
Securities Corp.
The bonds would have incurred considerable incremental legal and modeling expenses as well as
transactional uncertainty due to the unprecedented nature of the transaction. This latter feature, in
5
was particularly unusual given that the limit exceeded $1 billion, well in excess of the
limit a typical reinsurer would assume in a single transaction.
Why did National Indemnity attempt to undercut this transaction? Under the structure of
CEA’s four-year reinsurance contract with National Indemnity the actuarially expected
loss was 1.7% and the limit $1.05 billion. In return for bearing the earthquake risk,
National Indemnity would receive an annual premium of $113 million - or 6.3 times
actuarially expected losses of $1.8 million.12 In fact, the terms were slightly better, as the
contract called for Berkshire Hathaway to receive all four annual premiums in the first
two years. Since the $1.05 billion limit aggregates over the 4 year period, the gamble
effectively amounted to Berkshire putting up about $600 million in downside exposure
for a 93.4% chance to make about $400 million in premium.13
Berkshire Hathaway shareholders seemed to agree that the CEA contract was a windfall
for their firm. The contract announcement appears to have increased Berkshire’s stock
market valuation by almost $300 million, or 75 basis points in excess of the broad stock
market change.14 Figure 4 demonstrates. This suggests that shareholders saw the CEA
reinsurance contract (and those that might follow) as being priced well above “fair”
value.
While information on Berkshire Hathaway’s bidding tactics is understandably sketchy,
market participants acknowledge repeated interventions by the firm in undercutting
potential capital market transactions. As a very recent example, rumors are that, in early
July 1999, Berkshire Hathaway again underbid a potential $250 million cat bond issue,
by XL, a major Bermudan reinsurer. The bond issue was quite far along, but Berkshire
Hathaway made an eleventh-hour offer to provide all of the capacity in return for a
premium that was below the total cat bond costs to XL.15
These tactics are now strongly associated with Berkshire Hathaway, and they have fueled
speculation among reinsurance specialists that Buffett attempted, but failed, to undercut
the 1997 Residential Re offering as well. Indeed, Buffett’s annual letter to Berkshire
Hathaway shareholders has done little to dampen this speculation. In several of these
letters around the time of the offering, he alludes to the size of Berkshire’s balance sheet
particular, may have influenced CEA’s decision, given the insurance commissioner’s status as a publicly
elected official.
12 The average annual premium for the 4 year aggregate cover was 10.75% of the annual limit, whereas the
likelihood that the reinsurance is triggered was 1.7%, according to EQE International, a catastrophe risk
modeling firm. This yields 10.75 / 1.7 = 6.3 premium times expected loss.
13 Based on a probability of 1.7% per year, the chance of no event over the four years is (98.3%)4 = 93.4%.
Data in this paragraph are from IBNR Insurance Weekly (Volume III, #46), Dowling & Partners Securities,
LLC.
14 The contract announcement by Berkshire Hathaway occurred on Friday 11/15/96, after market close. On
Monday, 11/18/96, Berkshire’s class A shares closed at $33,200, up from Friday’s close of $33,000 (total
equivalent class A shares outstanding were 1,210,762). Over the same period, the S&P 500 fell from
737.62 to 737.02.
15 Private communications with reinsurance brokers and investment bankers from Guy Carpenter, Goldman
Sachs, and Marsh McLennan Securities. Thanks to Christopher McGhee for bringing this to my attention.
6
as being an important competitive advantage in reinsurance, allowing it to “move quickly
to seize investment opportunities. ”
2.3. Residential Re 1998 and 1999
In 1998 and 1999, Residential Re purchased reinsurance contracts from incarnations of
Residential Re that were nearly identical. The terms of the reinsurance have evolved
slightly over time, with important differences summarized in Table 2. All of the 1998 and
1999 notes were like the 1997 A-2s, in that all principal was at risk. There was therefore
no need for a Treasury strip or defeasance mechanism in the 1998 or 1999 programs.
The exposures covered by the policy were essentially the same, as USAA’s underwriting
profile changed only marginally during this time.
Perhaps the most important difference in the notes was the premium received by
investors. It fell from 5.76% in 1997 to 4.12% in 1998 and to 3.66% in 1999. Although
not as well publicized, there was a decline in expected loss as well. As Table 2 shows,
the expected loss rate stood at 63 basis points in 1997; this fell to 52 basis points in 1998
and 44 basis points in 1999. Because expected losses declined, the ratio of premium to
expected loss fell by less than premiums - from 9.1 in 1997 to 7.7 in 1998 and 8.3 in
1999.
The decline in expected loss appears surprising at the outset. During this period, property
values and construction prices rose somewhat, and there was a slight increase in the
number of units USAA insured. Thus, based on exposures alone, there was an increase of
approximately 5% in the expected loss for a 1%-likely event from 1997 to 1999. The
main reason for the decline was therefore not a change in exposure, but a set of
incremental changes made to the AIR model. The overall effect of these is shown in
Table 3. Changes were made in the way the model generates events, event paths, and
geographic windfield speeds. Changes were also made in the way the model estimates
damageability from high winds and storm surge, and estimates the demand surge (i.e., the
additional costs due to relative scarcity of contractors, materials, etc. in the aftermath of a
storm). These changes were important in that use of the 1997 AIR model for all years
would show an increase (rather than a decrease) in exposure and expected loss.16
It is also interesting to note that the 1999 Residential Re contract limit is smaller - $200
million versus $400 million and $450 million for the 1997 and 1998 programs,
respectively. For the 1999 renewal, USAA is supplementing the Residential Re contract
by purchasing a nearly identical reinsurance contract for $250 million from traditional
reinsurers. Thus, between these two contracts USAA will in 1999 again be covering $450
million (i.e., 90%) of its single-event losses between $1.0 billion and $1.5 billion.
It is likely that USAA has bifurcated its 1999 coverage for several reasons. First, by
splitting the program, USAA may succeed in stimulating greater competition between the
See Residential Reinsurance (1999) for more details. It is unclear which version of the model should be
used to evaluate each year’s expected losses. We apply the version of the model that was current for each
year of the program. This assumes that the market thought the expectation of future revisions was zero.
7
traditional reinsurance and cat securitization markets. Overall program costs would
therefore fall further by instituting such a split. Given the extent to which premiums for
traditional reinsurance have fallen over time (see the discussion below), there is a concern
that capital markets premiums would not otherwise decline as quickly.
There is some evidence to support the competition argument. The premium paid by
USAA for the $200 million 1999 Residential Re program was 3.66% received by
investors, plus 0.21% for a swap to deliver LIBOR and for minor day-count adjustments
(excluding fees). At the same time, USAA locked in a nearly-equal premium rate on the
$250 million traditional reinsurance portion of the 1999 program. This experience
differed from that of earlier years. In both 1997 and 1998, it was rumored that USAA
paid more for the Residential Re program than it would have for traditional reinsurance.
(Note this comparison does not take into account the differences in credit quality between
a collateralized special purpose vehicle and a standard reinsurance company, nor does it
take into account the additional fees required for the bond-financed program.) While
paying more may have been justified as an investment in developing the capacity of the
capital markets, the returns on further investments of this kind are likely to be low.
Second, while the 1997 and 1998 Residential Re notes were oversubscribed, there was
some concern about whether the same would be true in 1999. Large portions of the 1997
and 1998 programs were purchased by 2 large institutions. One of those dropped out in
1998, but the other, a single large hedge fund, reportedly increased its purchase
substantially that year.
However, this hedge fund experienced severe financial
difficulties in the late summer and fall of 1998 and was unlikely to participate in 1999.
These developments, coupled with the lower reinsurance market premiums, may have led
to concerns about the success of a full $450 million issue of 1999 Residential Re notes.
3. Puzzles
The USAA transactions discussed above raise two basic puzzles for financial economists:
1) What explains USAA’s purchase profile of reinsurance, with it buying protection for
relatively minor cats while remaining exposed for large cats?
<
2) Why do USAA’s premiums appear to be so high?
We try to explain these puzzles in Section 3 below. However, before doing so, it is
useful first to gain some perspective. To do so we attempt to show that these features of
USAA’s reinsurance are representative of the broader cat risk market.
3.1. The profile of reinsurance purchases
The first puzzle concerns the profile of protection purchased by USAA. It is clear from
Figure 1 that USAA purchases protection above a relatively small deductible. However,
8
USAA has little protection for the largest and most severe catastrophes. (For rough
magnitudes, note from Figure 3 that the AIR model shows USAA looses $242 million
with probability 10% and $1 billion losses with probability 1% from hurricanes alone.)
Indeed, it was not until 1997 that USAA purchased reinsurance beyond the 1% level. Is
this what financial economists would expect as a risk management profile? What
determines the loss level beyond which such hedging is no longer economical?
3.1.1. The optimal reinsurance profile
The first question to ask is whether USAA’s purchase profile in Figure 1 differs from an
optimal purchase profile, and if so, how. To do this, we derive the optimal reinsurance
purchase profile in a standard model of corporate hedging. Specifically, we apply the
framework of Froot, Scharfstein and Stein (1993). The basic FSS approach is that value
maximizing corporations face financing imperfections that make external capital more
expensive than internal capital. Corporate hedging can raise value to the extent that it
ensures that a corporation has sufficient internal funds available to take advantage of
attractive investment opportunities.
Following FSS, consider a value-maximizing firm that faces financing imperfections that
add to the cost of raising external funds. The future-period value of the firm is given by
P = P(w), where w measures the availability of internal capital. In the first period,
internal capital is a random variable, in that it depends on the future realization of cat
events.
The model has two time periods, present and future. In the present period, the insurer
makes a reinsurance (i.e., hedging) decision regarding its catastrophic exposures by
maximizing the expected value of the firm, £'[F>(w)]. The future period serves to close the
model: insurers realize cat event shocks and maximize shareholder value subject to the
financing imperfections they face going forward.
In the future period, a shock to the internal capital of the insurer is realized. Before
hedging, the future-period internal funds are w=w0£, where w0 is initial level of
internal capital, and £ is the random negative shock from a cat event, with
N(l, o2),
Vf g (-©o, 1], To keep things simple, we choose units such that w0 = 1. Thus, if there is
no cat event, internal funds remain at 1.
In the first period, the insurer can purchase reinsurance against some range of event
losses. Specifically, we let the insurer choose a retention, r, and a limit, /, which together
define a layer of insured £ shocks, [r - /, r] c (-©c, 1], for simplicity, we assume the
insurer buys complete reinsurance on this interval and that the reinsurance is fairly
priced. We also subject the insurer to a spending constraint, B, for premiums spent on the
layer.
Under these assumptions, next-period wealth is given by the shock, £, less fair premiums,
plus reinsurance claims:
9
w(r) = s -
(r ~ £)dF(s) + J ldF(£)\ + [(r - r)(r -1 < s < r) + 1(e < r - /)],
(1)
where r-E is the payment under the reinsurance contract when £ falls in the region [r - /,
r], and I is the payment when £ is in the range [-<*>, r - /].
As stated above, the future-period value of the firm is given by P = P(yv). Following
FSS, P is assumed to satisfy Pww <^Pw>\. FSS prove that these conditions can be
derived from a costly-state verification model of external financing, provided that the
hazard rate of the distribution of £, g(£)/(l-F(£)), is strictly increasing.
In the first period, the insurer chooses the reinsurance it wishes to buy by maximizing
future value subject to the premium constraint:
max
r,l
s.t.
(2)
(r - £)dF(£) + J 'ldF{£)"l < B
Without the budget constraint, the unconstrained insurer would set [r - /, r] = (-oo, 1], In
other words, the limit would be infinite and the retention would be set at a loss of zero
(with no cat event, we have s = r = 1). The insurer would therefore be fully hedged
against the cat shock. Clearly, the premium constraint is not binding unless B is strictly
less than the required premium for the unconstrained contract:
B<
(3)
The first-order conditions with respect to r and I are therefore:
- (-_dF{£) lPwdF^ I PwdF(£) = A
and
- ldF^ l^dF^+ 2'pb,^(£) = A r'jF(e).
(4)
Combining these gives:
[PwdF(£) TdF(E)= JPwdF(£)Jr dF(£)
(5)
Note that with the firm completely insured over the interval [r - /, r], w becomes a
constant over the corresponding range of £. Thus, w(r*) = w(r* - /*), Vfe [r* - /*, r*],
so Pw(yv(r -/)) can be taken out of the integral on the left-hand side. Thus,
f PMr-WF(£)= j Pw(^(Ey)dF(£) .
(6)
10
Since Pww is negative, FJv(w(r-Z))<Pw,(w(f)), ^£<r-l. In other words, the greatest
need to hedge, as measured by the marginal value of external funds, is greatest for the
most severe risks. The only way to satisfy the equality in equation (6) is to set I to -oo.
The spending constraint, because it is binding, then determines re (-oo, 1].
Thus:
Proposition: When reinsurance is priced fairly, the optimal reinsurance profile protects
against unboundedly large events first; the benefit of hedging higher probability layers is
less. The retention is then set at lower loss levels as the spending constraint, B is
relaxed. The optimal layer satisfies [r* - /*, r*] = (-^, z], where z < 1.
Figure 5 demonstrates the intuition for this result graphically. The shaded region shows
the optimal interval over which E is fully hedged. Larger risks are hedged first, and the
retention, r, moves up continuously as the spending limit is relaxed.
3.1.2. The aggregate profile of reinsurance purchases
USAA’s profile of reinsurance purchases is clearly not what one gets out of a model of
corporate risk management. Is this profile common among insurance companies for their
purchases of cat reinsurance? In this subsection we examine insurer hedging of
catastrophe risk in the aggregate.
To determine the pattern of reinsurance purchases for a broad group of insurance
companies we apply actual reinsurance transaction data obtained from Guy Carpenter &
Co., the reinsurance brokerage subsidiary of Marsh McLennan Inc and by far the largest
US cat risk intermediary. These data include over 4,000 cat reinsurance layers for 22
nationwide insurers and a large number of regional insurers for the years 1970 to 1998,
all of which were brokered by Guy Carpenter & Co.17
We use these data to calculate the fraction of aggregate insurer exposure that is reinsured
for different sized aggregate events. To do this, we must relate the losses on individual
contracts to aggregate cat event losses. For each contract, we link individual firm
retention and exhaustion loss amounts to a level of industry-wide losses. This is done
using data on US regional market shares for each firm and year from A.M. Best. So, for
example, a nationwide firm that has a 10% market share of cat-sensitive premiums is
calculated to incur 10% of the aggregate industry losses. For such a firm, a reinsurance
layer of $100 million (limit) in excess $150 million (retention) is calculated to provide
protection for industry-wide losses of between $1.5 billion and 2.5 billion.18
The CEA reinsurance is not included in this data. Furthermore, only traditional reinsurance contracts are
used, so that USAA’s reinsurance from Residential Re is not included.
This procedure was developed in Froot and O’Connell (1997) and is discussed in detail there.
11
(
Figure 6 shows the relationship in these data between the fraction of pooled insurer
exposure covered by reinsurance and the size of industry-wide events.19 The fraction of
coverage is based on marginal (not total) losses. So, for example, 50% coverage for a $3
billion national event implies that one half of an additional dollar of loss at the $3 billion
level is covered by reinsurance.
There are two main points to be made from Figure 6. First, there is in the aggregate a
clear resemblance to USAA’s individual purchase profile. Reinsurance coverage as a
fraction of exposure is high at first (after some small initial retention) and then declines
markedly with the size of the event, falling to a level of less than 30% for events of only
about $8 billion. Such events are not very large - aggregate statistics suggest that an $8
billion event occurs annually with probability of about 9%. So only a small fraction of
large event exposures are covered, and if anything, Figure 6 overstates that fraction. That
is because the only insurers included in the data are those that actually purchase
reinsurance. The implication is that insurance companies overwhelmingly retain, rather
than share, their large-event risks.
This point needs to be expanded in an important way. Insurers themselves intermediate
only a small fraction of cat exposures. Many exposures faced by the corporate and
household sectors are retained. Corporations, for example, tend to self-insure, and
particularly so against large losses — even while purchasing insurance against small
losses. Doherty and Smith (1993) document that insurance coverage is extremely limited
for corporate cat losses of between $10 million and $500 million (for a single
corporation) and virtually nonexistent for losses above $500 million. This suggests that
the hedging profile of USAA is typical not just of the insurance industry, but of corporate
insurance purchases as well. The vast majority of primitive cat risk in the economy is
being retained. This suggests that lack of complete risk sharing - and the failure of the
insurance and reinsurance sector to help accomplish it - is on a scale even greater than
that shown in Figure 6.
There is a second point to take from Figure 6. A comparison of the reinsurance profiles
at different points in time suggests that retentions increase after a large event. To see this,
recall that between 1990 and 1994, Hurricane Andrew struck Florida and the Northridge
earthquake occurred in California. These were by some margin the two most costly
events since the 1960s. During this time period, Figure 6 shows that the fraction of
exposures reinsured for medium events (between $2 billion and $8 billion) increases,
while the fraction of exposures reinsured for small events (under $2 billion) actually falls.
This is unlike the changes that occurred in previous periods. One explanation is that
reinsurance contract retentions shifted upward. In other words, when coverage for large
events increases after an event, it appears to do so at least partly at the expense of small
event coverage. We will provide further evidence on this point below.
3.2. Comparison with market-wide reinsurance prices
19 Event losses are in 1994 dollars.
12
Next we turn to the prices paid by USAA and CEA for reinsurance. Strikingly high
though the premiums may be, it is useful to be clear about the appropriate benchmark. In
this section we consider two premium benchmarks: actuarially expected losses and
average premiums on other reinsurance contracts.
3.2.1. Actuarially expected losses as fair-value premiums
Our use of actuarially expected losses as the fair-value benchmark hinges on two
important assumptions. First, this benchmark clearly assumes that cat risk is diversifiable
in equilibrium. A sufficient condition would be that the cat risk returns are independent
of total wealth. Not surprisingly, the data on cat returns provide no evidence to reject this
independence assumption. It should be noted, however, that existing tests examine only
correlations (i.e., second and not higher moments) with other financial assets, finding
them to be zero. In addition, cat events have a clear and direct effect on nonfmancial
assets (e.g., housing), so correlations with financial assets may not tell the whole
story.20’21
The second assumption we make in using actuarially expected loss as a benchmark is that
our estimate of loss is unbiased. While there is uncertainty about the true probabilities,
the presence of uncertainty, per se, should not matter under expected utility theory.
Agents should care only about gamble outcomes provided they have unbiased estimates
of outcome probabilities.22 However, given the paucity of rich cat event data, there may
be a common bias in the estimated event probabilities made by the cat models. Even if
such a bias exists, it is hard understand why the capital market would think it knows more
about unbiased cat-event loss probabilities than do specialized cat modeling firms. As
long as the capital markets take the model expected losses to be unbiased based on
currently available information, our unbiasedness assumption is satisfied.
3.2.2. The aggregate pricing of cat reinsurance
The next question is whether these individual premiums are also representative of the cat
risk market. The quick answer is that they seem to fit well with historical data based on a
wide cross section of cat reinsurance contracts. To demonstrate this, we again apply
reinsurance contract data from Guy Carpenter and Company. As in the section above, we
link these individual contracts to industry-wide losses. To calculate each contract’s
expected losses, however, we need an additional step. In order to assign probabilities of
loss we must estimate the frequency and severity distributions of cat events. Once we
20 See Froot, Murphy, Stem, and Usher (1995) and Litzenberger, Beaglehole, and Reynolds (1996). It is
worth noting that, because of low power, there is little to be gained from investigating higher-order
moments. Yet, because cat risk is highly non-normal even in continuous time, cat risk can easily alter the
higher-order moments of wealth. Fortunately, for risk exposures that are small in comparison with the risk
of total wealth, the effects of higher-order moments are small.
In addition to the destruction of nonfmancial wealth, cat events also result in subsequent wealth transfers,
and even in wealth increases for some. For example, building contractors may work longer hours as a result
of a cat event.
See Bantwal and Kunreuther (1999) for a discussion of departures from expected utility and its
implications for cat pricing.
13
have estimated probabilities, it is straightforward to derive the estimated expected loss for
each contract.
Figure 7 depicts the ratio of premium to estimated expected loss across reinsurance
contracts. For comparison, we also graph an index of premiums relative to limit, a ratio
that, in reinsurance parlance, is known as “rate on line.” Here rate on line is calculated as
the average across contracts of the ratio of premium to limit, and (for comparison
purposes only) is set equal to the premium-to-expected-loss curve in 1989. Note that rate
on line contains no calculation of expected loss, so it is immune to any measurement
errors in our methodology. Of course, rate on line is also unable to provide information
about shifts in retentions.
>
Figure 8 breaks down each treaty by layer, in order to measure premium to expected loss
by exceedence probability. Higher deciles represent lower exceedence probabilities.
Although not included in this database, the Residential Re and CEA layers discussed
above would fall into deciles 9 or 10.
Several points emerge from Figures 6 and 7. First, reinsurance became considerably
more expensive during the 1990s, with premiums rising by 3 times expected losses
between 1992 and 1993 alone (contract terms for each year are set in January). This
largest price increase coincides precisely with the occurrence of Hurricane Andrew in
August 1992.
Because there were so few large storms (and none near the size of
Andrew) between 1970 and 1992, it is hard to find a historical analogue to this magnitude
of price increase. The next costliest US natural disaster since 1970 was the 1994
Northridge earthquake. Since that time only relatively minor insured cat losses have
occurred.
Second, note that industry-wide prices on reinsurance contracts seem to match almost
exactly the pricing of the 1996 CEA contract (at 6.3 times expected loss). And, if
anything, they appear somewhat low in comparison with Residential Re in all years.
Figure 8 offers an explanation for this. It shows that much of the high premium-toexpected-loss ratio (which is an average across all layers) comes from the lowerprobability layers. Thus, as low-probability layers, USAA and CEA could be expected to
have somewhat higher premium-to-expected-loss ratios than the average contracts
graphed in Figure 7.
Third, note that prices have declined in 1998 by a factor of two from the post-AndrewNorthridge level. The decline has occurred smoothly since 1994 when measured in terms
of rate on line. However, premium-to-expected-loss fell strongly only in 1998. The
reason for this disparity is that the premium-to-expected-loss curve picks up changes in
retention levels. As mentioned above, retention levels rose in the post-Andrew period,
1992 to 1994. From 1994 to 1997, it appears that retentions continued to rise, insofar as
23 Hurricane Andrew and the Northridge earthquake resulted in roughly $20 billion and $13 billion,
respectively, in industry-wide damages.
14
the rate on line curve declines while the premium-to-expected-loss curve does not. Only
in 1998 do retentions begin to fall.24
Fourth, Figure 7 suggests a cyclical price path triggered by large events. It is argued that
similar price cycles are observed in other insurance markets.25 So even though there are
not many comparable cat events in the US record, there is a strong presumption in the
catastrophe marketplace that these price fluctuations are part of a kind of price “cycle.”
Fifth, given the paucity of event data, one should naturally be skeptical of our (or any)
estimates expected loss. After all, there is by definition little empirical information on
rare catastrophic events. Even though our estimates agree broadly with those of the
disaster-modeling firms, which employ different methodologies, it is possible that —
across methodologies - there is a systematic underestimation of true expected losses.26 If
true, this would lead us to overstate the cost of cat reinsurance.
However, one might argue that even if the level of our estimates is in error, it is unlikely
that the price changes in Figure 7 are prone to large errors. It seems hard to argue that
rationally-estimated expected losses increased and then decreased so substantially over
such a short period of time. If an event occurred that was thought to be of low
probability, a good Bayesian with little prior information might indeed update the
probability of reoccurrence. However, nonoccurrence of such an event would give such
a Bayesian little new information since the event was unlikely to occur in the first place.
Thus, it is hard to understand how any rational scheme for estimating probabilities would
yield a precipitous decline as a result of a non-event. We discuss a number of hypotheses
that might explain the behavior of prices in the next section.
Before leaving this point, it is interesting to note that revisions of the AIR model for
constant USAA exposures downwardly adjust expected losses during this time period.
Table 3 shows the decline in the event-loss distribution between the 1997 and 1999 AIR
models. Even though exposure sizes increased, expected losses from the 100 basis point
to 40 basis point levels of likelihood fell by between 10% and 14% due to model revision.
While the timing of this decline may be coincidental, it is interesting to introspect on
whether these same model revisions would have been implemented were a major cat
event to have taken place during this period.27
There is preliminary evidence from the January 1999 cat reinsurance renewals that premiums and
retentions have both continued to fall.
For evidence of price cycles in insurance, see for example, Gron (1994).
Cat modeling firms use complex Monte Carlo simulations with many sources of uncertainty and many
parameterized distributions. Nevertheless they also can work only with historical data which is highly
limited. For investigations of the uncertainty in cat event model estimates, see Bantwal and Kunreuther
(1999), Maj or (1999), and Moore (1998).
27
There is no suggestion by AIR that these changes are correlated at all with recent cat-event activity.
Model refinements are a continuing process. During this two-year period, changes in the windfield
generation module of the model accounted for much of the decline in expected loss. This module “was
enhanced to provide for smoother transitions between the filling rates from one region to another and to
update surface friction factors.... In addition, an updated coastline [data] file was implemented...”
(Residential Re 1999 offering circular, p. 47). Both changes reduced expected losses, but neither is
explicitly motivated by recent event occurrence.
15
(
Even with the model changes, the USAA ratio of premium-to-expected-loss ratio
declines. However, it does so only slightly, falling from 9.1 in 1997 to 8.3 in 1999.
Thus, recent premiums do appear to decline when changes in expected losses are taken
into account. But the changes in the AIR model leave one suspicious about how much
weight the modeling process places on very recent (non) events. Much of what appears
to be a change in premium-to-expected-loss ratios in Figure 7 may instead be a change in
perceived event probabilities.
3.3. Summary
To conclude, the agreement between different measures of expected loss in Figure 7, and
the CEA and USAA contracts is strong. It seems clear that the two puzzling aspects of
these layers - the relatively small amount of reinsurance for large events and high prices
- have been pervasive across the catastrophe risk market. In the next section, we
consider a number of different explanations that may help explain these puzzles. The
goal here is not to provide comprehensive evidence on each of these possible
explanations, but to identify and clarify hypotheses.
4. Explanations and Interpretations28
Our explanations are of two types: those that affect supply and those that affect demand.
Taking the two findings above as given - that reinsurance quantities are low and prices
high - naturally suggests some form of supply restriction. However, there is unlikely to
be a single explanation, and several demand-related explanations appear to be supported
by some of the evidence as well. Thus, we consider factors that affect both demand and
supply.
4.1. Explanation 1: Insufficient capital in reinsurance
Perhaps the supply of reinsurance is low because catastrophic risk-taking capital is
somehow inhibited. In other words, there may be financing imperfections similar to that
in the model above. Such capacity shortfalls, even if relatively temporary, might exist for
a number of structural reasons: it may be costly for existing reinsurers to raise additional
funds in the capital markets; it may be hard to find investors who expect appropriate
“equilibrium” rewards for bearing catastrophic risks; it may also be that it is costly for
reinsurers to hold large amounts of collateral on their balance sheets. What is the
evidence that reinsurance capital is in short supply?
First, judging from Warren Buffett’s writings, shortages of capital appear to be an
important rationale for Berkshire Hathaway’s reinsurance strategy. In his 1996 letter to
shareholders, Buffett observes,
“Our ... competitive advantage [in writing “supercat” risks] is that we can provide
dollar coverages of a size neither matched nor approached elsewhere in the
28 Parts of this section draw upon Froot (1999a).
16
industry. Insurers looking for huge covers know that a single call to Berkshire
will produce a firm and immediate offering.”
Perfect access to capital by new and existing reinsurers would remove this “competitive
advantage.” So it seems Buffett believes in - and pursues a strategy of exploiting capital shortfalls.
Buffett’s strategy is also predicated on a perception that a capacity shortage may become
temporarily worse, for example, if reinsurer capital is depleted by a large event. A
temporary shortage would be consistent with the post-event cycle suggested by Figure 7,
wherein prices rise and then fall while quantities fall and then rise. Again from Berkshire
Hathaway’s 1996 annual report, Buffett writes:
“After a mega-catastrophe, insurers might well find it difficult to obtain
reinsurance even though their need for coverage would then be particularly
great. At such a time ... it will naturally be [Berkshire’s] long-standing
clients that have first call on it. That business reality has made major
insurers and reinsurers throughout the world realize the desirability of
doing business with us. Indeed, we are currently getting sizable ‘stand
by fees from reinsurers that are simply nailing down their ability to get
coverage from us should the market tighten.”
Buffett seems to be saying that the prospect of a capital shortage in the aftermath of a
major cat event motivates insurers to purchase ‘capacity’ protection. Note that this is not
protection against an increase in prices - presumably National Indemnity’s clients would
pay the going market rate - but protection against being excluded from the marketplace.
The price of a guarantee to participate in a well-functioning marketplace should be zero.
In both of these quotes, and in other discussions of “supercat” risks in Berkshire
Hathaway annual reports from 1995, 1996, and 1997, Buffett emphasizes the value to
Berkshire’s shareholders of the company’s substantial balance sheet. In a world of
costless access to external finance, a balance sheet earns no rents by virtue of its size. It
therefore ought to bestow no competitive advantage on those who control them.
Buffett s emphasis on quantity shortages, and not price increases, is important for making
an argument on financial imperfections. It is consistent with the low level of risk transfer
and post-event decline in quantities - both shown in Figure 6. It also avoids reliance on
the price evidence we have seen so far (e.g., Figures 6 and 7). As we mentioned above,
this price evidence can be distorted by unobserved variation in subjective event
probabilities (such as those driving the updates in the AIR model). It is the weakest link
in the argument. So isn’t there a way to test whether prices comove inversely with
quantities, in a way that is not subject to the probability-updating critique? If so, we
would have more decisive evidence that capacity shifts lie behind price movements and
levels.
17
It turns out the answer to this question is yes. Suppose we were to observe a large
hurricane that subsequently increased reinsurance premiums. The probability updating
hypothesis would say that the change is due to learning about the future damages
associated with hurricanes (fully rational or not). We would therefore expect the
premiums on hurricane risk to change, and probably to rise. At the same time, would we
have learned nothing about the probabilities of loss on independent perils, such as
earthquakes. Thus, under the probability updating hypothesis, the premiums on
earthquake risk in California should remain constant. Alternatively if the post-hurricane
price increase is a result of capital market imperfections, we would expect an increase in
both hurricane and earthquake premiums. Thus, if we can divide up the post-event
cross-section into different peril combinations, we can perform a kind of event study to
better test the comovement of prices and quantities.
Table 3 provides the results of such an event study. The table shows both price and
quantity responses in reinsurance purchased during the year following hurricane Andrew.
As before, reinsurance quantity is measured as actuarially expected loss. We already
know that in aftermath of Hurricane Andrew, reinsurance purchases fell, and that this
occurred primarily through an increase in retentions. Table 3 adds the fact that the
quantity purchased/e// by more - and the premium paid rose by more - for those insurers
that had greater exposure to the Southeastern US and to hurricanes wherever they occur.
Thus, across contracts, prices rise most where quantities decline most. It seems hard to
explain this fact by a subjective increase in probabilities, provided that the probability
increases retain some bearing to the information revealed in the event. Thus, while there
may be some probability updating that we cannot capture in our unconditional estimates
of expected loss, there also appears to be a strong element of true price increase. This can
only be explained by a temporary, shift backward in the supply of capital.
Of course, it is not surprising that the supply of cat risk bearing capital is momentarily
restricted immediately following an event. Large-event losses deplete reinsurer capital
and surplus and, realistically, require at least a short amount time to replenish. However,
6 years elapsed between Andrew and the first declines in the premium-to-expected-loss
ratios in Figure 7. The timing therefore also seems consistent with the hypothesis that
frictions retard capital flows into the reinsurance sector.29
The final point in this section is that there is a kind of irony in the financing
imperfections story as applied to insurance and reinsurance: much primitive cat risk could
be reduced through investments in mitigation, investments that would appear to pay high
actuarial returns. However, many of these investments are not made because they require
individuals and corporations, who have scarce capital themselves, to raise (or deplete
internal) capital. Thus, capital market shortages may in part be responsible for the large
It is common in the industry for reinsurers to require “paybacks” for event losses and to do so through
higher premiums and retentions. Note that there is nothing in this practice, to the extent it explains the
data, to contradict explanation #1. However, an important question remains as to why this kind of
contracting prevails and what it tells us about reinsurance markets. See explanation #5 below for one
potential answer.
18
and growing risk pool needing insurance and reinsurance. Without capital shortages,
reinsurance capacity could costlessly be greater, but there would also be fewer risks to
reinsure in the first place.30
To conclude, the post-Andrew decline in premiums has not altogether escaped Warren
Buffett’s attention. He offers his own explanation in his 1997 annual letter:
“Many investors who are ‘innocents’ - meaning that they rely on representations
of salespeople rather than on underwriting knowledge of their own - have come
into the reinsurance business by means of purchasing pieces of paper that are
called ‘catastrophe bonds.’ ...The influx of ‘investor’ money into catastrophe
bonds — which may well live up to their name — has caused super-cat prices to
deteriorate materially.”
Clearly, Buffett believes that a capacity expansion, not a change in true probabilities, is
the cause for the decline in premiums. Understandable, but less than fully credible, is his
claim that this expansion is the result of misinformation rather than better risk sharing
and greater competition.
4.2. Explanation 2: Reinsurers have market power
A number of observers have suggested that the evidence on prices and quantities above
might be explained by market power rather than by a capital shortage per se. Under this
explanation, prices rise and quantities decline not because reinsurance capital is
impossible or costly to obtain, but because existing reinsurers have no incentive to
increase their capital. By putting less money at risk and preventing new entry, incumbent
reinsurers keep prices high. Some observers, such as James M. Stone of Plymouth Rock
Company (a former Harvard Professor of Economics and Massachusetts Insurance
Commissioner), argue that market power among reinsurers is the main reason that
catastrophe reinsurance has proved a more attractive business than insurance.
Of course, it is very hard to provide evidence that market power among reinsurers has
increased secularly over time or cyclically in the aftermath of events. There is a general
view that the reinsurance industry has been consolidating. There has been a distinct drop,
for example, in the number of Lloyd’s syndicates since the 1960s and 1970s. There has
also been an increase over time in the capital and market share of large reinsurers.
However, these facts aren’t necessarily associated with increased market power in setting
prices or restricting supply. For example, even though there are fewer Lloyd’s
syndicates, catastrophic risk pricing is not typically determined by individual syndicates.
Furthermore, while consolidation has occurred in the industry, greater market power need
not be the driving force. Consolidation may result from economies of scale. The
information-intensity of reinsurance is one possible source of scale economies. For
30 See Howard Kunreuther and Paul Kleindorfer, “Challenges facing the insurance industry in managing
catastrophe risks,” NBER conference on The Financing of Property/Casualty Risks.
19
example, there may be high fixed costs of developing analytic capabilities and systems.31
Once these systems are in place, optimal reinsurer size grows as the required investment
in fixed-cost systems increases. Consolidation may also be an efficient industry response
to costs of obtaining outside capital. If those costs are partially fixed, or proportionately
decline with size, the amount of outside capital may also be a source of increasing
returns.
Barriers to entry are another place to look for market power. Clearly, the barriers to
buying a cat bond are lower than the barriers to underwriting reinsurance. This is not
surprising, given that the cedent does not bear the bondholder’s credit risk, but is forced
to bear the reinsurance underwriter’s credit risk. Even so, there is considerable evidence
of entry into reinsurance in the 1990s. For example, beginning in 1993 at least 6 major
reinsurance companies were formed in Bermuda, representing over $7 billion in new
reinsurance capital. (The first of these companies, Ace, XL, and Mid Ocean Re, were
organized prior to Hurricane Andrew, and so cannot be construed as a response to that
event, per se.) While the barriers to entry may be high for some agents (e.g., individual
or institutional investors), Bermuda is evidence that the barriers are not uniformly high
for all groups.
Still, it is interesting to speculate about the role of market power in the steep 1998 price
decline shown in Figure 7. After all, not much new capital was injected into traditional
reinsurers in 1997 or 1998. It’s true that during this time, reinsurer balance sheets grew
marginally with premiums and interest, while experiencing trivial event losses. But the
same was true for each year since 1994. Similarly, the cat bonds issued in 1997 and 1998
may have been innovative, but they accounted at most for only a few percent of total cat
reinsurance treaties (based on limit). Thus, there has been surprisingly little change in
reinsurance capacity since 1995.
Probably the best explanation for the magnitude and timing of the recent price decline is
a change not in capacity, but in contestability. While a large amount of new capacity
may be needed to drive down prices in a competitive market, the same is not true when
producers are perceived to have market power. In that case, all that is required is to
increase the perceived level of competition. This fits with the cat bond experience. While
cat bond issuance has been quite small, it began to seem intensely interesting and
important beginning in mid 1997 with Residential Re I. Furthermore, Warren Buffett’s
final remark in the previous subsection seems to assign disproportionate importance to
cat bonds; it is hard to imagine Buffett going out of his way to acknowledge (and
discredit) other traditional sources of cat capacity at all, never mind a source of such tiny
size. The conclusion we draw is that cat bonds have affected markets well beyond the
size of the actual issues. It seems market power stories can explain a few of the facts we
have identified, and therefore ought to be taken seriously.
4.3. Explanation 3: The corporate form for reinsurance is inefficient
31 Comments by Stewart Myers, in Froot (1999b), pp. 434-437.
20
Under this explanation, the corporate organizational form of reinsurers is unnecessarily
costly. Observers of corporate governance often point out that there are costs associated
with discretion given to managers to run a business. In principal, managers could pursue
objectives other than value maximization. It may be difficult for shareholders to identify
and discipline this behavior. Even if most managers are benevolent, the prospect that a
bad manager might use his agency relationship against shareholders reduces stock prices
and drives up the cost of capital.
This generic corporate finance argument of “agency costs” has application in a number of
arenas. First, it clearly can be applied to insurers and reinsurers. Many of the details of
the reinsurance business and the specific contracts are not transparent to arm’s-length
capital providers. And, given the occasional-big-loss nature of reinsurance, it takes many
years to evaluate management efficacy and true business profitability. In reinsurance,
managers may have an unusually large incentive to gain market share (and increase their
size) by cutting premiums beyond that called for by shareholder value maximization.
How costly is it to delegate discretion to managers? This is generally a difficult question
to answer. However, for some narrowly-defined businesses it is possible to get a partial
answer. Closed-end funds are one such business. Closed-end funds invest in publicly
traded securities and then sell stakes in their portfolio to shareholders, much like mutual
funds do. However, unlike “open-ended” funds, closed-end-fund portfolios are not
affected by fund purchases or redemptions; shareholders buy and sell shares among one
another, without the fund involved. Thus, the price of the closed-end-fund shares, like
the price of most traded stocks, must find its own value in the marketplace in accord with
supply and demand.
As is well known, there is a puzzle associated with closed-end fund shares: their prices
are, on average, considerably below their net asset values.32 This cannot happen with
open-ended fund shares. Closed-end share discounts average about 10%-20%, and are
fairly pervasive across funds and over time. It is often argued that agency costs account
for these discounts.33 The agency story is that closed-end funds must pay an average
return in excess of what would be required for holding the underlying net assets. The
reason is that shareholders can’t directly observe or discipline managers. Thus there is a
bias toward managerial decisions that put the managers’ interests above those of
shareholders.
The agency cost argument may explain why the costs of reinsurance capital, and by
inference, reinsurance prices, are high. The argument is buttressed by two regularities.
The first is that reinsurance managers regard their capital costs as “equity-like” - i.e., as
requiring a return considerably above US Treasury rates. An actuarially fair premium is
viewed as beneath the hurdle rate imposed by shareholders. Yet, given that catastrophe
risks are uncorrelated with those of other financial assets, shareholders’ required returns
on cat risk should, as argued above, be low. Agency costs may be one factor forcing up
required returns. The agency cost explanation may therefore help understand the view in
See Lee, Shleifer, and Thaler (1991) for a general discussion of the closed-end fund puzzle
33 Citation?
21
the industry that, for many risks, there is “too much” capital and that prices are “too low.”
Indeed, some public reinsurers have recently been repurchasing stock on the argument
that premiums are too low, and therefore do not meet shareholders hurdle rate.
There is a second regularity behind the view that reinsurers are an inefficient corporate
form. This is that, even without agency costs, there is evidence that shareholders expect
reinsurer equity returns to be well above US Treasury rates. Evidence for this comes from
the behavior of stock prices of public Bermudan reinsurers, such as Mid-Ocean Ltd.
(recently purchased by XL), Renaissance Re, and Partner Re. These firms hold large
property/catastrophe liabilities, and historically have held assets in the form of short-term
notes and bills. Neither their assets nor liabilities are correlated with the stock market,
yet their share prices comove positively with the stock market. Specifically, a 10%
increase in the level of the S&P 500 is associated with an increase in the average value of
these firms of about 6.5%.34 We cannot identify a source of this comovement that
emanates from the companies themselves.
While it is interesting to speculate on the source of this distortion (e.g., noise, liquidity,
etc.?), the point here is to ask how reinsurance managers ought to respond. Clearly,
investors should require a higher return on these stocks if their prices will move with the
market. And, as a result, value maximizing reinsurance managers should inherit higher
hurdle rates, setting premiums above actuarial value.35 This argument suggests that
equity-financed reinsurance may be inefficient even in the absence of agency costs. If
equity capital requires a high return and reinsurer assets and liabilities contain no broad
equity market risks, then equity is an expensive form of capital, pure and simple. And if
reinsurance is financed in an expensive manner, reinsurance prices will be high.
Note the relationship between this argument and explanation 1 above. Reinsurance
companies may experience financial distress and other deadweight costs of raising
outside capital. Such costs clearly add to the cost of capital, thereby driving up
reinsurance premiums. This story is really a version of explanation 1, but it can also be
construed as an inefficiency in reinsurers’ corporate form. What we have added to this
under explanation 3 is that an inefficiency in equity markets may be responsible for the
added costs.
Offsetting our arguments about inefficiency, however, is a view articulated by Roberto
Mendoza of J.P. Morgan. The view is, first, that Bermuda’s zero rate of corporate income
tax reduces reinsurers’ costs of equity. With no income tax, reinsurers would gain little
by substituting debt for equity finance, since there are no interest tax deductions available
to them in the first place. Furthermore, Bermudan reinsurers provide shareholders with an
34 Data on unadjusted stock betas from Bloomberg.
35 Of course, if it were feasible, the first-best response would be to remove the underlying distortion
altogether. If, for example, the market exposures of the stock prices were immutable and fixed, then it
would be best for managers to increase the equity exposure of their assets, so that the firms’ true asset betas
corresponded with the fixed betas assigned by the market. Then there would be no need to increase the
hurdle rate on cat reinsurance. Alternatively, managers could potentially substitute debt finance for equity
to avoid the “high” costs of equity.
22
opportunity to achieve tax-free compounding on invested capital. This tends to lower the
cost of equity relative to what it would otherwise be.
Second, Mendoza argues that managerial discretion may provide an “agency benefit” in
the case of cat reinsurance. In a highly inefficient and specialized market, shareholders
need an experienced agent to cherry picking risk-writing opportunities.36 In this case, the
present value of the managerial discretion is positive, since it allows shareholders to
exploit reinsurance market inefficiencies.
If true, Mendoza’s arguments suggest that the corporate form of reinsurers, particularly
those in Bermuda, is actually a highly efficient delivery mechanism for reinsurance risk.
4.4. Explanation 4: The frictional costs of reinsurance are high
This explanation says that prices are high because, as financial instruments, reinsurance
contracts are illiquid, have high transactions costs, brokerage, etc. These sources of
friction imply that there are important costs in getting capital and reinsurance contracts
together in a repository called a reinsurer.
There is abundant evidence that illiquid assets trade at significant discounts. Letter stock,
as one example, typically trades at discounts of 25% versus publicly-traded stock; on-therun bonds trade at significant premiums versus less liquid off-the-run bonds; and so on.
However, illiquidity of one-year reinsurance contracts is not enough to drive up
premiums. Part of the reason for capitalizing reinsurers who hold short-term notes for
assets is to enable reinsurers to provide liquidity to insurers’ risk exposures. In order to
raise reinsurers cost of capital, their own placements would need to be discounted for
illiquidity. This may arguably have been the case for Lloyd’s commitments from
individual names; it is far less compelling for publicly traded reinsurers in Europe, the
US, and Bermuda.
Other frictions such as brokerage costs and servicing expenses can legitimately raise the
cost of procuring reinsurance. However, these costs are not out of line with other
financing charges. For example, in the National Indemnity transaction described above,
annual brokerage fees were less than 1% of premium, and therefore, were about 11 bp of
limit. If the reinsurance had been issued as a capital market instrument, as had been
anticipated by some, these costs would have amounted to about 5% of annual premium,
or approximately 55bp of limit. In fact, the fees associated with 1997 Residential Re
bond offerings came to approximately lOObp of limit.37 Thus, if anything, the traditional
reinsurance brokerage and issuance expenses are lower than standard capital-market fees.
Furthermore, the high level of prices seems well above anything that can be explained by
brokerage and underwriting costs. Even if brokerage and underwriting expenses had
come to a high of 10% of premium in the National Indemnity deal, complete elimination
Of course, the same argument is often made in defense of closed-end fund managers
37 See Moore (1998).
23
of these expenses would have driven down the multiple of premium relative to actuarially
expected losses by about 0.6 from 5.3 to 4.7. Brokerage and underwriting expenses
cannot explain observed price levels.
Another kind of frictional inefficiency is the means by which reinsurers manage risk.
Reinsurers manage their risk by aggregate (notional) limits, rather than exposures. For
example, a reinsurer might decide it will risk up to $100 million on Florida, but without
specifying the distribution of Florida losses on contracts written, or the covariance of
Florida losses with potential losses on its North Carolina contracts. Removing such
portfolio inefficiencies could have a substantial impact on the cost of risk transfer.
Better reinsurer risk allocation can reduce the cost of capital if reinsurers face financing
imperfections, as in explanation 1. A poorly diversified portfolio of reinsurance adds
needlessly to risk, and risk to internal capital is costly if there are financing
imperfections. As a result, there is a kind of interaction effect between this explanation
and explanation 1 above: costs of external finance can magnify the impact of poor
diversification on reinsurer capital costs. This might be a more promising place to look
for frictional inefficiencies in reinsurance intermediation, but only if one accepts the
notion of financing imperfections in the first place.
4.5. Explanation 5: Markets are degraded by moral hazard and adverse selection
Moral hazard and adverse selection are often singled out as distortions that prevent
markets from functioning efficiently. In general these distortions suggest that risks
should be disproportionately borne by those who control them and/or know them best.
Clearly, these effects restrict reinsurance supply. So they may help explain some of the
facts we observe.38
Market participants also claim that there is evidence for the presence of moral hazard and
adverse selection in reinsurance market conventions. Often an explicit reinsurance
contract contains an implicit agreement that reinsurers will charge more in the aftermath
of a claim and that the cedent will continue to buy reinsurance from the same
underwriter. Under this interpretation, property / catastrophe reinsurance is an implicit
form of “finite” reinsurance. Finite reinsurance does not so much transfer risk from the
cedent, as it finances the cedent. During an event, the reinsurer makes funds available,
expecting to be paid back later through higher subsequent premiums. In its purist form,
the arrangement is just event-contingent borrowing.39
This interpretation of our evidence of cat reinsurance is interesting and far-reaching.
First, it suggests that there may be even less risk transfer than we thought. The numbers
in Figure 6, for example, are overstated, since they do not account for the present value of
38 In some circumstances, higher prices may actually exacerbate the problem, making it impossible for the
market to function. For a discussion of the implications of adverse selection on reinsurance contracts, see
David Cutler and Richard Zeckhauser (1999).
39 The contingent credit arranged for the Nationwide by J.P. Morgan has many of these features.
24
claim repayment. Second, the price and retention cycle we have seen subsequent to
Hurricane Andrew are not evidence of explanations 1, 2, 3 or 4. Instead, they become
evidence of a kind of “repayment cycle,” where post-event periods are characterized by
more rapid repayment for past claims.
While it has a number of virtues in explaining the evidence, this explanation has two
basic flaws. First, there is the question of time-consistency. What disciplines a cedent
from switching reinsurers after making a claim? Since there is no contractual obligation
to the original underwriter(s), the only way reinsurers could enforce repayment is through
implicit collusion and barriers to entry into reinsurance. And, as we have already seen,
market power by itself (even in the absence of moral hazard and adverse selection) can
go a long way toward explaining the facts. This does not rule out explanation 5, it only
says that believers have to acknowledge support for explanation 2 as well.
Second, moral hazard and adverse selection seem relatively harmless for cat reinsurance
as compared with other forms of insurance and reinsurance. Product liability protection,
for example, can be understandably plagued with asymmetric information and moral
hazard. Given the disclosure requirements, the large number of small risk units (i.e.,
houses, autos, etc.), and the presence of third-party modeling expertise for cat risk, it is
hard to see how these distortions could be important.
Finally, the high deductible and coinsurance in virtually all of these contracts reduces the
scope for moral hazard and adverse selection. Indeed, the evidence in Figure 8 suggests
that the pricing is most elevated at high layers where exceedence probabilities are low.
Moral hazard and adverse selection problems would not predict this. Indeed, retentions
and lows layers ought to be the most affected by moral hazard and adverse selection, so
these effects imply that lower layers should less efficient.
4.6. Explanation 6: Insurance regulation discourages the purchase of reinsurance
This explanation begins with the observation that many states use regulatory barriers to
keep insurance prices down. In some states, lines of business, and specific geographic
areas, insurers must underwrite the cat component of risk at prices that are well below
those that are actuarially and financially profitable. This is perhaps not a surprising state
of affairs given that insurance commissioners are publicly elected officials in 12 states,
including California and Florida.
Clearly this story cannot explain a high level of prices in the reinsurance market.
However, it can explain why there is so little reinsurance purchased, even if prices are
actuarially fair. The basic reasoning is that if insurers are unable to earn a profitable
return by underwriting risk, they need to cut costs. One way of cutting costs is to avoid
purchasing reinsurance in a way that is consistent with profit maximization.
The mechanism here is similar to that of rent control. Rent control makes housing
cheaper in the short run. But in the longer run, it cannot affect the equilibrium rental rate.
25
Thus, if rents can’t adjust upward, the value of the housing stock adjusts downward
through depreciation in quality.
In response to price controls, value-maximizing insurers will necessarily produce a
product that has lower quality and higher risk. Price controls reduce going-concern value
and increase insurer leverage considerably.40 Insurer equity becomes more like an out-ofthe-money option. As a result, the demand to hedge risk with reinsurance is reduced. The
result is that state guarantee funds must bear considerably greater risks that a large
catastrophe will become their responsibility or the responsibility of policyholders,
taxpayers, and/or remaining insurers. In short, everyone suffers if regulation makes it
unprofitable for insurers to provide high quality insurance contracts.
This explanation fits the cyclical behavior of quantities in addition to their low average
level. After a big event, there is political pressure to expand the scope of insurance
without raising its cost. If prices are cut through the regulatory process, insurers will cut
back on reinsurance purchases, even if the reinsurance is offered at a fair price.
The major weakness of this explanation is that it cannot explain high reinsurance
premiums. However, it does explain why insurers may perceive reinsurance prices as
“high,” i.e., in excess of what they can profitably afford to pay.
A.l. Explanation 7: Ex-post intervention by third-parties substitutes for insurance
Ex-post financing of catastrophes occurs when other parties step in to transfer funds to
those who experienced event losses. Chief among these entities is, of course, the US
government. As is well known, the government has a major role in funding disasters at
both state and federal levels, through a number of agencies, and through both the
executive and legislative branches. Since the late 1970s, the Federal government has
spent annually an average of $8 billion (current) dollars on disaster assistance. This is far
greater than the average annual loss borne by reinsurers on US catastrophe coverage. In
some forms of disasters, notably floods, the federal government has effectively
eliminated the incentive for private insurance contracts. Indeed, before the Federal
government stepped in to provide disaster relief, private insurers did offer flood
•
41
insurance.
The federal government is not the only entity involved in ex-post financing of
catastrophes. State guarantee funds are often the next line of defense if an insurer is
unable to meet its policy liabilities. And if the state fund is exhausted, then solvent
insurance companies are often required to make up the difference. This creates two types
of bad incentives. First, companies have an incentive to shift the burden onto the fund or
other insurers before the fund is exhausted. Second, companies who do not act to shift
high layer losses onto the pool are themselves likely to have to pay for others. Wellbehaved insurers will wish to avoid doing business in states with guarantees funds and
40 Even without debt capital, insurers have plenty of financial leverage because of policyholder liabilities
41 See Moss (1996).
26
pools. This strengthens the need for regulation and can create a kind of vicious cycle in
market vs. regulatory incentives.
From an economist’s perspective, such ex-post financing should be viewed as a form of
market failure. The federal government cannot credibly commit not to fund disasters
after the fact: even if it says it will not provide disaster relief ex ante, the political
incentives to do so ex post are overwhelming. Given this, the demand for purchasing an
insurance contract is reduced.
It is therefore clear how ex-post financing affects the price and quantity of reinsurance.
The effect on quantity is strongly negative, for both insurance and reinsurance. As with
explanation 6, ex-post intervention by third parties cannot explain why prices are high. It
can, however, explain why insurers perceive that reinsurance prices are high. It can also
explain low quantities of high-layer reinsurance and the cyclical downturns in quantities
after major events.
4.8. Explanation 8: Behavioral factors dampen demand
A commonly cited reason for the low quantity of high-layer reinsurance is that the
perceived likelihood that reinsurance will pay is too low to matter. For those who use
expected utility-based or profit-maximization approaches - such as that in section 2.1
above - insurance against severe, low-probability events is most valuable. But
behavioralists have suggested that expected utility approaches fail to describe decision
making.
One important failure is that people discount too heavily events they cannot readily
perceive. For example, a famous study from the 1970s shows that the rate of smoking is
higher among the general populace than among doctors (general practitioners), higher
among general practitioners than among internists, and higher among internists than
among specialists who work directly with lung cancer patients. Even when the
consequences and probabilities of bad outcomes are well known, it takes repeated
hammering home of bad outcomes to affect behavior.42
A second behavioral effect is that individuals often seem “ambiguity” averse. A lack of
clarity about the risks and events being insured may lead insurers and reinsurers to set
premiums high.
Behaviorally, people seem to distinguish between risk (where
probabilities are known) and uncertainty (where they are not). Uncertainty is inherently
more ambiguous, and surveys suggest that individuals charge more to bear it.
42 See Tamerin and Resnik (1972) and Kunreuther et al (1978).
See Howard Kunreuther, Robin Hogarth, and Jacqueline Meszaros, “Insurer ambiguity and market
failure,” Journal ofRisk and Uncertainty, 7:71-87(1993).
27
c
5. Conclusions
This paper has shown that reinsurance premiums are coming down and that the market is
becoming more competitive, while capacity is increasingly available since the time of
Hurricane Andrew. With time, USAA and other firms have begun purchasing more
coverage for the largest events. So the movement is in the direction predicted by our
model. Indeed, it is interesting to ask what, in equilibrium, determines the probability
level beyond which reinsurance becomes uneconomic. All of the explanations we explore
would seem to have a role in this.
What important lessons can we take from the evidence? After all, the cat risk market is
small - traded notional exposures probably are in the (low) hundreds of billions, not the
trillions as in major credit, mortgage prepayment, and straight debt markets.
First, we learn something about capital markets and intermediary structure. It is clear
from what we have seen that securitization is not automatically the lowest-cost way to
transfer risk. Why is this? Principals with wealth often hire dedicated agents to manage
their portfolio. If there are corporate taxes then it makes sense to install the agent as the
manager of a mutual fund pass-through that buys securities but pays no taxes. However,
if there are no corporate income taxes, then there is little difference between a mutual
fund buying securities and a corporate reinsurer underwriting reinsurance. Thus, it isn’t
so wrong to think of reinsurers in tax havens as investment advisors for infinitely-lived
closed-end mutual funds. From a capital markets perspective, there is nothing
dramatically inefficient with this, provided that the principals care little about the
liquidity of this small part of their portfolio, and therefore are indifferent to the liquidity
of reinsurance contracts versus cat bonds. From a corporate perspective, the closed-end
fund version avoids costs of financial distress, but it must distribute its income, and
therefore cannot legally achieve the tax-free compounding available to Bermudan
reinsurers.
Second, we learn something about corporate risk management. Because managers of
insurance companies purchase reinsurance at far above the fair price, they clearly must
believe that risk management adds value. This statement is not easy to make in other
markets, since it is so hard to measure the value of corporate risk management, and since
Modigliani Miller can accommodate any risk management policy when prices are fair.
Of course, these conclusions follow from the assertion that fair prices can be more
credibly measured for cat events than for other, less object!vely-modeled exposures.
Finally, the facts support the idea that there are capital market imperfections or barriers to
capital entering into reinsurance. Cat bonds tend to lower, but not eliminate, these
barriers. This may be because of friction capital-raising costs, but also because it is
difficult to remove transparency in new products without an investment of time and
energy on the part of investors. As a result, cat premiums may continue to decline, but it
is unlikely they will permanently reach the level of expected loss.
28
6. References
Cutler, David, and Richard Zeckhauser, “Reinsurance for catastrophes and cataclysms,”
in K. Froot, ed., The Financing of Catastrophe Risk, University of Chicago Press,
1999.
Doherty, Neil, and Clifford Smith, “Corporate insurance strategy: the case of British
Petroleum,” Journal ofApplied Corporate Finance, Fall 1993,4-15.
Froot, Kenneth, “Introduction” to K. Froot, ed., The financing of catastrophe risk,
University of Chicago Press, 1999a.
Froot, Kenneth, ed., The financing of catastrophe risk, University of Chicago Press,
1999b.
Froot, Kenneth, and Paul O’Connell, “On the pricing of intermediated risks: theory and
application to catastrophe reinsurance,” NBER Working Paper no. 6011, April
1997.
Froot, Kenneth, and Mark Seasholes, “USAA: Catastrophe risk financing,” case no. 9298-007, Harvard Business School Press, 1997.
Froot, Kenneth, Scharfstein, David, and Jeremy Stein, “Risk management: coordinating
corporate Investment and financing decisions,” Journal of Finance, 48, December
1993, 1629-1658.
l
Froot, K., B. Murphy, A. Stem, and S. Usher, “The emerging asset class: insurance risk,”
July 1995, White Paper, Guy Carpenter and Co.
Goldberg, Steven F., “Securitization Of Catastrophe Risk,” Presentation To PPP 2000
Forum, December 11, 1997.
Gron, Anne, “Capacity constraints and cycles in property-casualty insurance markets,”
RAND Journal ofEconomics, Spring 1994, 110-127.
Jaffee, Dwight, and Thomas Russell “Catastrophe insurance, capital markets, and
uninsurable risks," Journal ofRisk and Insurance, Vol 64, No 2, 205-230, 1997.
Kunreuther, Howard, et al, Disaster insurance protection, Wiley, New York, 1972.
Lee, Charles, Andrei Shleifer, and Richard Thaler, “Investor sentiment and the closedend fund puzzle,” The Journal ofFinance, 46, March 1991.
Litzenberger, Robert, David Beaglehole, and Craig Reynolds, “Assessing catastrophe
reinsurance-linked securities as a new asset class,” Journal of Portfolio
Management, December 1996, 76-86.
29
r
Moore, James, “Tail estimation and catastrophe security pricing - Can we tell what target
we hit if we are shooting in the dark?” Wharton Financial Institutions Center,
1998.
Moss, David, “Government, markets, and uncertainty: An historical approach to public
risk management in the United States,” working paper, Harvard Business School,
1996.
Residential Reinsurance, Offering Circulars, May 1999, 1998, 1997.
Tamerin, J.S., and H.L.P. Resnik, “Risk taking by individual option: case study cigarette smoking,” in P. Diamond and M. Rothschild, ed., Perspectives on
benefit-risk decision making, National Academy of Engineering, Washington,
D.C., 1972.
30
Figure 1
USAA's 1997 Reinsurance Program (contracts in force from July 1997 to June 1998)'.<14
$1,500mm
Layer #
Annual
Premium
Illustrative
ROL
5
$24.0mm*
6.0%'
4
$6.6mm
5.5%
3
$15.0mm
10.0%
Excludes
Autos
2
$16.9mm
12.5%
Excludes
Comments
80%
Reinsured through
Residential Re
securitized by
Residential Re
1,000mm
' ,-s- *.«.
60.0%
800mm
75.0%
600mm
Excludes
California
and Autos
90.0%
450mm
Autos
90.0%
1
$24.4mm
7.5%
125mm
FHCF
Hurricanes
in FL Only
0mm
= Reinsured
=Retained
Calculation of ROL for Layer 2
Calculation of premium to expected loss
for Layer 2
Premium Paid:
$16.9mm
ROL of Layer 2:
12.5%
Limit:
90%*(600-450)
Actuarial Prob, of Loss > $450mm:
4.5%
= 90%*(150)
o.
12.5%
Price: =-------4.5%
= 2.8
= $135.0mm
ROL:
Premium / Limit
= $16.9mm / $135.0mm
= 12.5%
♦
Rumors in the market were that Layer 5 would cost approximately 5% ROL for traditional reinsurance
(private communication with Guy Carpenter, Inc. brokers.)
44 With the exception of the top layer reinsured by Residential Re, the premiums and illustrative ROLs
shown in this exhibit are not the prices and rates paid by USAA. Due to the sensitive nature of the
information, only illustrative rates have been provided.
31
<
Table 1
Residential Reinsurance, Cat Bond Contract Specifications
Obligor:
Residential Reinsurance Limited, a Cayman Island reinsurance company, whose
sole purpose is to provide reinsurance for USAA
Amount:
Class A-l:
$ 164mm
$87mm principal variable
$77mm principal protected
Class A-2:
$313mm
100% principal variable
Yield:
LIBOR + 576 basis points
Loss Occurrence:
One Category 3,4, or 5 hurricane
Reinsurance
Agreement:
Residential Reinsurance Limited will enter into a reinsurance agreement with
USAA to cover approximately 80% of the $500mm layer of risk in the excess of
the first $ 1,000mm of USAA’s Ultimate Net Loss
Ultimate Net Loss:
Ultimate Net Loss = amount calculated in Step 6 (below)
Step 1
All losses under existing policies and renewals
Step 2
All losses under new policies
Step 3
9% of the amount calculated in Step 1
Step 4
Add the amount from Step 1 with the lesser of Step 2 & 3
Step 5
Multiply Step 4 by 1.02 for boat and marine policies
Step 6
Multiply Step 5 by 1.02 to represent loss adjustments
Coverage Type:
Single occurrence
Coverage Period:
June 16, 1997 to June 14, 1998 (see Figure 2b)
Ratings:
Class A-l:
Rated AAAr/Aaa/AAA/AAA
by S&P, Moody’s, Fitch, and D&P, respectively
Class A-2:
Principal variable notes are rated BB/Ba/BB/BB
by S&P, Moody’s, Fitch, and D&P, respectively
Covered States:
Alabama, Connecticut, Delaware, District of Columbia, Florida, Georgia,
Louisiana, Maine, Maryland, Massachusetts, Mississippi, New Hampshire, New
Jersey, New York, North Carolina, Pennsylvania, Rhode Island, South Carolina,
Texas, Vermont, and Virginia
32
Figure 2a Structure of the 1997 Residential Re Transaction
Highly Rated
Short-term
Inv estments
(Reg. 114 Trust)
$400mm
LIBOR
Reinsurance Premiums
USAA
■---------------------------------- ►
4—---------------------
$40Qnm Reinsurance
Remaining
Funds
SPV
Residential Re
Cayman Islands
$77nn
at
Maturity
$477mm at Maturity and
Liqiidation
-------------------------- ►
Class A-1 $164mm
Interest Payments *
4-
Class A-2 $313mm
$477mm
UBOR
$164mmat
Maturity
$77mm
Collateral
Account
$77mm Contingent
on an Event
Defeasance
Securities
Counterparty
Source: Goldman Sachs.
Figure 2b Time Line for Residential Re Contracts
June 16, 1997 - June 14.1998
June 15,1998 - Dec 15.1998
Risk Period
Extended Claims
Period
Dec 16,1998 - Dec 15,2008
—//—
June 1
Dec 1
June 1
Class A-1 Principal
Extension Period
Dec 1
-//Typical Hurricane Seasons
Source: Residential Re offering memorandum.
33
Figure 3 Estimated Probabilities of Hurricane Losses for USAA ($mm - from simulations)45'46
p
Annual Probability
that USAA Losses
are Greater Than
Amounts in Column 3
1-P
________ [1]_________ (2)
10.00%
90.00%
5.00%
2.00%
1.00%
0.96%
0.40%
0.39%
0.20%
0.10%
Total Losses
(not additive)
(3)
$ 242
400
674
986
1,004
1,464
1,496
1,845
2,507
95.00%
98.00%
99.00%
99.04%
99.60%
99.61%
99.80%
99.90%
Home
Owners
(4)
$ 200
332
552
820
831
1,180
1,216
1,555
1,962
Dwelling
(5)
$ 20
32
50
66
68
92
93
119
157
Condos
(6)
$ 8
16
Renters
(7)
$ 6
10
18
29
29
43
43
61
90
33
55
58
95
95
138
184
Graph of Above Data ($mm)
102.00%
100.00%
I
I
JZ LI IE C
I
c
IZ
Zl ZI
J
ZZIZIZIZIZC
z"’?! Z I z!zc E
_____ J.
98.00%
■■ ■ -Total
96.00%
'—
5
—1 jA*
zx-c z z/j
Z Z I Z I
E I I E L
I
--------- Homeowners
Z Zi Zi Zi
94.00%
■Zi
z!
iTF
—4c—Dwelling
92.00% - EIIE E
90.00%
E
—X - Condos
E Z C J J Zi
—G—Renters
88.00%
Ci:
'Z1'
Cl
86.00%
~|.7 ~ T ~ T
JUZiZi.
~ :r ~ ~r -| i-u-uq
4-
s
S
I
Losses ( $mm - Log Scale )
45
Source: USAA
46 “]-P” in column two and on the graph’s y-axis represents the annual probability that a catastrophic loss
suffered by USAA will be less than the corresponding amount shown in column three and on the x-axis.
34
|
Figure 4 Changes in Berkshire Hathaway’s Market Value (in excess of the market)
300-
I
200-
100-
«•
o
o-
v>
w
a -100-|
□>
O
3 -200 -1
ra
Hi i
date
w
8 -300-I
i
.a
iailSl.
-400 -
-500-
-600-
i
11/13/96
11/14/96
11/15/96
11/18/96
11/19/96
11/20/96
11/21/96
Notes: Graph shows the value of the percentage excess return of Berkshire Hathaway’s market
capitalization in excess of the S&P 500. Announcement date is the first day on which news of
National Indemnity’s reinsurance contract with the California Earthquake Authority is reflected in
the closing stock price.
35
Table 2 Residential Reinsurance Transaction Comparison
Issue
1999
1998
1997
Exceedence Loss
Exhaustion Loss
Risk Capital
Premium
Expected Loss
Premium / Expected Loss
Attachment Probability
Exhaustion Probability
US AA Coinsurance
Coverage Period
Extended Claims Period
Defeasance Period
Interest Payments
S&P Rating
$1.0 billion
$1.5 billion
$200 million
3.66%
0.44%
8.3
0.76%
0.26%
10%
52 weeks
6 months
not applicable
Quarterly
BB
$1.0 billion
$1.5 billion
$450 million
4.13%
0.52%
7.9
0.87%
0.32%
10%
50 weeks
6 months
not applicable
Quarterly
BB
$1.0 billion
$1.5 billion
$400 million
5.76%
0.63%
Source: Residential Re Offering Memoranda.
36
9.1
0.96%
0.42%
20%
52 weeks
6 months
10 years
Monthly
BB
Table 3 Effect of AIR Model Updates on US AA Expected Losses
(a)
Estimated Annual Occurrence Losses ($ millions)
(12/31/98 exposure, no demand surge included)
Estimated Probability
Of Occurrence
1997
Model
1999
Model
% Change
in Losses
200 basis points
100 basis points
40 basis points
20 basis points
10 basis points
$600
$831
1,239
1,431
1,776
$564
$751
1,066
1,377
1,603
-5.9%
-9.7%
-14.0%
-3.8%
-9.8%
(b)
Effect of Demand Surge Changes
Estimated Annual Occurrence Losses ($millions)
(12/31/98 exposures, 1999 models)
Estimated Probability
Of Occurrence
200 basis points
100 basis points
40 basis points
20 basis points
10 basis points
Using 1997
Demand Surge
Function
Using 1999
Demand Surge
Function
% Change in Losses
Due to Changes
in Demand Surge
654
868
1,283
1,689
2,039
641
849
1,240
1,633
1,962
-2.0%
-2.2%
-3.4%
-3.3%
-3.7%
Source: Residential Re Offering Memorandum, May 1999.
37
Figure 5 Optimal Constrained Hedging Program Under The Froot, Scharfstein, And Stein (1993) Model
PM
r-l
P(^))
i
P(w(e)), insured
1
£
Note: Shaded region indicates the area in which a company would hedge, if given the choice of
range over which it could fully insure against losses at fair value.
38
Figure 6 Percentage of Exposure that Insurance Companies Reinsure (by various event sizes)
80.0
11
70.0 -
-------- 1994
60.0 -
—X— -690
■B80
50.0 - 40.0 - - -
r
30.0 20.0 t).0
■t-
4-
-4-
0.0
0.0
0.5
10
15
-42.0
2.5
3.0
-43.5
4.0
4.5
5.0
5.5
6.0
Industry-wide Insured Losses from an Event ($bn)
39
6.5
f
-4-
4-
7.0
7.5
8.0
Figure 7 Price level of reinsurance contracts relative to actuarial value, 1989-1998
weed
RSX
40
i
Figure 8 Premium To Expected Loss, By Exceedence Probability And Year
n^“r30
25
I
Pr
em
20 iu
? [i
in
■
'-
■ I'h
I
HpJf
WH®j
19941993
'
to
15 Ex
pe
cte
B-10 d
Lo
■ tar . _
■
SHTla
1992
19901989
1987
1986
1985
1983
41
1982
I
1981
I
'
10
7 8 9
2 3 4 5
Exceedence decile
(l=highest
Table 4 Changes In Reinsurance Premiums And Quantities Purchased Subsequent To Hurricane
Andrew
(a) Southeast exposure
Mean
exposure
5 most-exposed insurers
5 least-exposed insurers
Mean
Aln(py,z)
0.141
0.000
Mean
Alnfe,)
(b) Hurricane exposure
Mean
exposure
Mean
Mean
Alnfe,)
Alnfe,)
0.415
-0.021
0.184
0.583
-0.082
0.335
-0.013
0.112
0.336
-0.047
Comparison of price responses in the year after Hurricane Andrew (8/20/92-8/19/93) for different insurers.
Panel (a) contrasts insurers that have high and low exposure to the Southeast (as measured by market
share). Panel (b) contrasts insurers that have high and low exposure to hurricanes. The table shows the
mean exposure and the mean price change of the 5 most extreme contracts in each case. The mean price
change for the insurers with lesser exposure to the Southeast is calculated using all 14 of the insurers that
have zero market share in that region.
42
CHAPTER
8
Risk Management
Strategy: Duality
and Globality
In the previous chapter we examined why risk was important to
firms. If a firm is publicly owned then its shareholders can diver
sify risk in their choice of portfolio. Even if risk is not diversifiable
within the capital market, its sale will command an appropriate
risk premium. Therefore, hedging the risk at this price will not
add value but will merely change the risk-return combination
available to investors. This reasoning suggests that, if risk is costly,
it is not because that risk causes a problem for the firm's investors
directly. Rather, it is because it gives rise to a set of transaction
costs that lower the expected value of the firm's cash flows. These
transaction costs include increased tax burden from risky cash
flows, increased expected costs of bankruptcy, agency costs that
arise from potential financial distress and lead to inefficient in
vestment decisions, crowding out of new investment by unhedged
losses, and inefficiencies that arise from managerial risk aversion.
In this chapter the task is to lay out generic risk management
strategies. In deriving risk management strategy, we must start by
understanding why risk management is a problem, in order to
know how to address it. Consider a medical analogy. Suppose you
have an allergy which is triggered each time you are exposed to
common dust. You can, of course, manage that allergy by remov
ing yourself from dust. So you vacuum your home with great
frequency and refurbish it with surfaces that do not retain dust.
234
CHAPTER 8
Risk Management Strategy: Duality and Globality
235
This may be an effective solution, depending on your degree of
sensitivity. But it may not be an ideal solution, since it can be very
time-consuming and costly. Moreover, some people may respond
to trace amounts that cannot be removed practically. But there is
another way of dealing with the problem. If one understands why
dust triggers the allergic reaction, then it may be possible to break
the link between the exposure to dust and the allergic reaction.
Thus, to manage the condition, one can either remove the expo
sure or one can accommodate the dust but break the link between
the exposure and the reaction with a treatment such as an anti
histamine. This accommodation strategy is an important part of
the treatment menu. Indeed, for many with allergies it is imprac
tical to remove every environmental stimulus, and the only prac
tical treatment is an antihistamine or similar drug.
Consider the parallel between the allergy problem and the
corporate risk management problem. To manage the allergy, one
can remove the dust or one can accommodate the dust and re
move the cost caused by the dust. One can address the cause or
one can address the effect. Thus, the physician must have a good
understanding of the physiology and chemistry of the body. Sim
ilarly with risk. If risk causes costs to firms, one can either remove
the risk or one can accommodate the risk and arrange the affairs
of the firm so that the risk does not cause a problem. But to do
this, one must understand exactly why risk is a problem. This is
the principle of duality, which asserts that for every type of cost
that risk imposes on the firm, there are two generic risk manage
ment strategies: either remove the risk or accommodate the risk
but reduce its cost.
This chapter will begin by exploring duality and using this
concept to derive a basic risk management menu. We will then
establish some general principles for assembling a risk manage
ment strategy from this menu. In particular, we will examine to
what extent the strategy should be integrated or holistic.
DUALITY IN RISK MANAGEMENT STRATEGY
The essence of duality is that one can address the cause or the
effect. One can remove the risk or one can adapt the firm so that
the risk is not a problem. Table 8-1 lists the various reasons why
risk is costly to publicly owned firms. The table also shows that
PART 2
236
TABLE
Risk Management Strategies
_____________
8-1
Duality of Risk Management Strategies
Strategy .hWA.W-
Type of Risk Cost
tax arbitrage . •.<
nonlinear taxes
expected bankruptcy costs
hedge
hedge
change leverage^#;.; * it'Ws
contingent leverage
,
agency cost:
dysfunctional investment
crowding out new investment
hedge
aSSSle„,age'“" k' ■
;
managerial risk aversion
stakeholder risk aversion
contingen financing
hedge
.
■.
IO
hedge
change compensation scheme^ ,
hedge
change stakeholder contracts ■
J
for each type of risk cost there are two potential strategies. First,
the cause of the problem can be removed; risk can be hedged.
Second, the risk can be retained but the firm or its activities can
be structured so that the risk causes less of a problem; this strategy
is labeled "accommodate." This dual principle is important for
identifying the menu of strategies available for dealing with risk.
The task now is to take each risk cost in turn and flesh out the
types of hedging and accommodation strategies that are available.
Duality and Nonlinear Taxes
To explore the principle of duality, consider the following simple
example. A firm purchases a capital asset at a cost of $1 billion,
which will generate an income stream over a five-year period. The
annual income stream is risky, with:
0.5 chance of $132 million
0.5 chance of $532 million
expected annual earnings = $332m
The firm is allowed to depreciate the asset in equal installments
over its five-year life. Thus, the firm can shield $200m from tax
each year. The tax rate is 34%. The expected tax liability (in $m),
and, if we note that if earnings are $132m no tax will be paid, is:
CHAPTER 8
Risk Management Strategy: Duality and Globality
237
0.5 X 0.34(532 - 200) + 0.5 times (0) = $56.44
And the expected value of this investment opportunity (at a zero
discount rate for simplicity) is:
expected net present value = — $lz000m + 5($332m — $56.44m)
= $377.8m
The example is depicted in Figure 8-1. If earnings turn out to be
$532m, the tax liability is $112.88m, as shown. If earnings are only
$132m, then taxes will be zero. If we bear in mind the 50-50
chances of the two earnings levels, expected taxes are $56.44m.
Notice that the firm gets the full benefit of depreciation if
earnings are $532m (i.e., taxes fall by 0.34 X $200m). But if earn
ings are only $132m, then the depreciation has no effect on taxes.
Thus, the depreciation allowance can be wasted (this lost deduc
tion can sometimes be partly recovered with carryforwards, but
this is uncertain and does not accrue interest).
Hedge Strategy
Suppose the firm can hedge its earnings to fix earnings at the
expected value of $332m. Expected tax is now reduced to:
FIGURE
8-1
Tax due $m
112.88 •56.44 •
44.88 •
Earnings
------ $m
0 L
132
200
332
532
238
PART 2 Risk Management Strategies
0.34(332 - 200) = $44.88
And the expected net present value of the investment opportunity
is now increased to:
expected net present value = —$1000m + 5($332m — $44.88m)
— $435.6m
compared with the unhedged value of $377.8m. Note that ex
pected taxes have changed even though expected earnings have
not. How this hedge strategy would be achieved would depend
on the source of the risk. For example, if the risk were insurable,
then an insurance policy might be purchased. If the risk stemmed
from the effects of interest rate fluctuations on demand for the
product (as is common for consumer products that are financed,
such as cars), an interest cap or future might hedge the risk. Sim
ilarly, if the risk stemmed from exchange rate fluctuations, an ap
propriate forward or future contract could hedge the risk.
I
!
i
Tax Arbitrage Strategy
Consider that there is another firm, whose expected earnings are
either $1 billion or $2 billion. The precise amounts do not matter;
the point is that this other firm can always expect to earn more
than $200 million. Therefore, if the second firm were to buy the
same asset and receive an annual $200m depreciation allowance,
it would always have more than enough income to receive the full
benefit of the deduction (0.34 times $200m — $68m). Ignoring the
time value of money (simply to make the issues transparent), the
annual cost (after tax) of buying this machine is ($200m — $68m
= $132m). Consequently, the second firm could buy the machine
and lease it back to the first firm at an annual charge of $132m
without losing any money. Suppose firm 2 did just that. Let us
now reexamine firm Ts expected after-tax income with this lease
instead of the purchase of the asset. Expected pre-tax income is
$332m. Expected taxable income is now:
0.5($532m - $132m) + 0.5($132m - $132m) = $200m
If the firm is able to deduct the cost of the lease ($132m) as an
ordinary expense, expected taxes are now:
0.5($532m - $132m)0.34 + 0.5($132m - $132m)0.34 = $68m.
CHAPTER 8 Risk Management Strategy: Duality and Globality
239
The expected net present value of the investment (bearing in mind
there is no upfront capital cost) is now:
5($200m - $68m) = $660m
which is even higher than when the firm hedges (compare with
$435.6m above). The reason for the extra gain is that the depre
ciation has been given a double tax advantage in this treatment
(firm 2 deducts the full $200m annually, then firm 1 deducts the
lease cost, which here is the after-tax cost to firm 1). Note that if
firm 1 were unable to deduct the lease cost, its annual after tax
income would be:
0.5($532m
$132m) + 0.5($132m - $132m)
- 0.34{0.5($532m) + 0.5($132m)} = $87.12m
and the expected net present value project would be 5 X $87.12m
= $435.6m, which is identical to that in which firm 1 buys the
asset and hedges the earnings risk. Thus, the lease and the hedge
are equivalent ways of securing the full tax advantage of depre
ciation.
This example is naturally oversimplified. The tax code is
more complex than shown here. For example, there are carryfor
wards to consider, and the example should also consider the time
value of money. I have also not allowed any profit for the leasing
company but assumed that all tax advantage for depreciation is
passed to the lessee. These effects will modify the numbers, but
they will not destroy the main concept illustrated. Differences in
marginal tax rates between firms do present arbitrage opportuni
ties, and these can be used as a substitute for more conventional
risk management strategies. One firm needs to purchase equip
ment but faces a large probability that its potential tax shield will
go unused. Another firm does not need to make such a capital
investment for production purposes, but its earnings profile is
such that it could nearly always fully use any depreciation. This
configuration yields opportunities for the latter to take full tax
advantage of capital expenditures and then lease the equipment
to the firm that needs to use it. The tax advantage afforded to the
leasing company can be shared with the lessee in the price of the
lease.
PART 2 Risk Management Strategies
240
Other forms of tax arbitrage might be used in conjunction
with risk management. A particularly interesting one is reinsur
ance. Insurers routinely purchase reinsurance as a means of limi
ting their portfolio exposure on the book of insurance poUcies they
have sold to their clients. Thus, reinsurance is clearly used as a
hedging strategy. However, there is some evidence suggesting that
reinsurance is also used as a form of tax arbitrage. Insurers can
deduct additions to loss reserves from taxable income. The value
of this deduction to an insurer depends upon how much taxable
income that insurer has that determines its marginal tax rate. Work
by Keun-Ock Lew (1991) sought to explain patterns of reinsurance
between firms. If firms were using reinsurance to hedge, then one
would expect the patterns of trade to be explained by differences
in risk between insurers and differences in the financial capa
city bear risk. This indeed was found, but these factors did not
fully explain reinsurance activity; there was considerable "unex
plained" variadon. It was found that differences in marginal tax
rates between insurers explained much of the remaining variation.
Insurers with low marginal tax rates (and who therefore gained
little from more deductions) were transferring business to insurers
with higher marginal rates. This suggests that reinsurance is being
used for both hedging and tax arbitrage.
Duality and Bankruptcy Costs
We can also use an example to show the effect of hedging on
expected bankruptcy costs and how a dual strategy can achieve
the same effect. A firm has an expected value (the discounted
value of future earnings) of $500m, but this is not certain. The
effect of risk can be picked up by considering the following dis
tribution (all figures are in $ million)
Value
Probability
100
0.1
0.2
0.4
0.2
0.1
300
500
700
900
CHAPTER 8
Risk Management Strategy: Duality and Globality
241
Now we add that the firm has debt with a face value of 200. Let
us now consider the value of this firm simply as its expected
value. Since the firm owes 200, but there is a 10% chance firm
value could fall to 100, there is a distinct chance of bankruptcy.
Moreover, bankruptcy costs are assumed to be 50, which will fall
upon the bondholders because equity will be worthless in this
situation. If the firm does go bankrupt, bondholders receive only
50 (i.e., 100 - 50), but in all other situations they receive the full
face value of 200.
value of debt
0.1(100 - 50) + 0.2(200) + 0.4(200) + 0.2(200) + 0.1(200) = 185
value of equity
0.1(0) + 0.2(300 - 200) + 0.4(500 - 200)
+ 0.2(700 - 200) + 0.1(900 - 200) = 310
total value of firm1 = 495
Hedge Strategy
Suppose the firm is now able to hedge and compress the firm
value to its expected value 500 — T, where T is the transaction
cost associated with the hedge. This transaction cost could be the
loading required by the insurer on the purchase of a policy or a
similar cost from another hedge.2 Unless T is very large (over 300),
the firm will always have enough to pay off its debt and the prob
ability of bankruptcy falls to zero. Consequently, the expected
bankruptcy cost is also zero. Let us suppose T = 2. The value of
1. Notice that the total value of the firm, 495, falls short of the expected value of the cash
flows in the table, 500, by 5, which is the expected value of the bankruptcy costs
(0.1 X 50).
2. For example, the firm might have a value of 900 if no insurable loss occurs. But there
is a 0.2 chance of an insurable loss of 200, leaving firm value of 700; a 0.4 chance
of a loss of 400, leaving firm value of 500; a 0.2 chance of a loss of 600, leaving
firm value of 300; and a 0.1 chance of loss of 800, leaving firm value of 100. These
would explain the numbers in the table. Notice the no-loss value is 900 and the
expected value of insurable loss is 400, giving an expected firm value of 500. One
would expect an insurer to charge at least 400 to insure this loss. But the insurer
would also charge a loading above the expected loss, explaining the value T.
Thus, if the premium is 410, then T = 10.
242
PART 2 Risk Management Strategies
the firm with the hedge is thus 498, divided between 200 value of
debt and 298 value of equity. On these numbers, there is a overall
gain from hedging; the firm values has risen from 495 to 498, the
value of debt has risen from 185 to 200; but the value of equity
has fallen from 310 to 298.
It seems as though we have something of a problem. mShareholders seem to be better off if the firm does not hedge. To sort
this out we must look at the issues from two different time perspectives.
Post Analysis First, imagine that bondholders had already purchased bonds at a price of 200. In this case the share
holders would prefer not to hedge, since equity is worth 310 with
out the hedge and only 298 with the hedge. The reason for the
extra value in the unhedged situation is that risk is attractive to
the shareholders. Without a hedge, if things go well, shareholders
reap all the benefit. If things turn out poorly, shareholders can
simply default on the debt. Thus, shareholders keep the upside
risk and pass the downside on to the bondholders. This is a
"heads I win, tails you lose" strategy.3
Ex Ante Analysis Rationally, bondholders will recognize
that they will be taken for a ride; they recognize that once share
holders have their money, the latter will be tempted to adopt the
unhedged strategy. Anticipating this choice, bondholders believe
that there is a real chance of default and that the bonds are only
worth the unhedged value of 185. Now consider the situation
from the shareholders' perspective. If shareholders can commit to
a hedge strategy and convince bondholders that they will not de
viate from this strategy, then bondholders would be willing to pay
200 for the bonds. Thus, shareholders benefit by receiving an ad
ditional 15 in proceeds of the bond issue, whereas the share price
is 298 compared with 310. The additional proceeds of the bond
issue more than outweigh the fall in share price. There are various
devices the shareholders could use to reap this value. For example,
they could distribute the additional 15 of proceeds from the bond
issue as a dividend or use it to fund new investment without
3. Notice the operation of the default put option considered in Chapter 6.
U9b3G
CHAPTER 8 Risk Management Strategy: Duality and Globality
243
having to dilute equity. Thus, shareholders gain if they can send
a credible commitment to bondholders that they will hedge risk.4
Leverage Strategy
Another simple strategy- can achieve the same ends. Suppose that
the firm simply funded its operations at a lower level of leverage.
In this case imagine that debt has a face of value of only 100. Now
the lowest value of the firm is sufficient to pay off debt in full and
there is no possibility of default. In this case, the value of the firm
is divided as follows:
value of debt
0.1(100) + 0.2(100) + 0.4(100) + 0.2(100) + 0.1(100) = 100
value of equity
0.1(100 - 100) + 0.2(300 - 100) + 0.4(500 - 100) + 0.2(700 - 100)
+ 0.1(900 - 100) = 400
value of the firm = 500
Now the firm has avoided expected bankruptcy costs alto
gether. In practice this might be a little fanciful since one can never
really reduce the probability of bankruptcy to zero. But one can
reduce the expected value of bankruptcy costs effectively by low
ering the level of debt in the capital structure.
Contingent Leverage Strategy and
Post-loss Financing
There are other, more subtle strategies that do not change current
leverage but entail a plan that will change leverage in the future
should some specified event arise. I will mention such ideas now
simply to complete the portfolio of risk management strategies.
4. In the example given, the value of the firm is higher with a hedge (if credibly signaled
to bondholders) only if the transaction cost of the hedge (T = 2) is lower than the
expected value of the bankruptcy costs (here 5). An unhedged strategy would ap
pear to be better were the transaction costs reversed. However, remember that this
is only a partial analysis. We have listed several potential efficiency gains that can
arise from risk reduction, not only reduction in expected bankruptcy’ costs. So,
even if T = 10, it may still be preferable to hedge if other efficiency gains from
hedging (reduced taxes, reduced agency costs, etc.), together with the reduction in
expected bankruptcy costs, exceed 10.
PART 2 Risk Management Strategies
244
Some of these ideas may seem a little opaque (indeed, they in
clude some rather exotic financial instruments), so you may sim
ply note their presence and wait till later chapters where they will
be explained more completely.
One of the problems with changing leverage to reduce ex
pected bankrupt costs is that leverage is chosen to balance out a
number of costs and benefits. The costs of debt and equity differ.
As we will see in the next section, leverage influences agency costs
between various stakeholders. Also, there are tax effects arising
from the differential tax treatment of debt and equity. The CFO
will normally choose the firm's leverage to balance these costs and
benefits. Thus, it is unlikely that the firm's risk manager could
steal control of the firm's capital structure from the CFO simply
by arguing that leverage is an important risk management tool.
Another approach is to keep the firm's current capital structure
but put in place some facility or plan so that the capital structure
changes should some predetermined event occur (an uninsured
liability or property loss, a foreign exchange hit, etc.). Some simple
examples are:
An insurance policy or other hedge. Here, somebody else
funds the loss so that the post-loss capital structure will
revert to its pre-loss value.
♦ The firm may simply plan to issue new stock should a
loss occur. These would be issued at whatever price the
market would bear after the loss.
♦ The firm could issue put options on its own stock that
could be exercised only after the defined event. Such
options have been issued by insurers as a method of
recapitalizing the firm after a major loss.
♦ Tire firm could issue current debt, with the provision that
it be forgiven or that it convert to equity should a major
loss occur.
♦
Duality: Agency Cost: Asset Substitution
Consider a firm which has an existing product line that exposes
the firm to some risk. Future earnings have an expected present
value (PV) of either 100 or 200, each with a 0.5 probability. This
risk could reflect different possible scenarios about consumer de
mand, commodity price risk, or the prospect of some uninsured
CHAPTER 8
Risk Management Strategy: Duality and Globality
245
property or casualty loss. Tire value of the firm is the expected
value of 150. The firm has existing senior debt with a face value
of 100. Since the debt is covered even under the worst-case sce
nario (firm value is 100), its value is 100 and the value of equity
is the residual value of 50 (i.e., firm value of 150 minus the value
of debt of 100). We assume all risk is diversifiable.
The firm now faces this choice; it can select one of the fol
lowing new investments:
Capital cost
PV of earnings
E(NPV)
Project A
200
220
'20; probability 0.5
20
Project B
200
’ or
-35
,310; probability 0.5
The capital cost of each project is 200. Project A generates an
earnings stream with a certain present value of 220, which leaves
a net present value of 20. Project B generates a risky earnings
stream that has a present value either 20 or 310, each with a 0.5
probability, resulting in an expected value of 165. The expected
NPV of project B is therefore —200 + 165 = —35. The earnings
from the projects are independent of those from existing opera
tions.
The firm issues new (junior) debt with a face value of 200
prior to making its project selection with a (dubious) hope of fi
nancing the project, which has a capital cost of 200. Finally, we
assume that the transaction cost in the event of bankruptcy is 100.
We now value the firm's claims, bearing in mind the permutations
of earnings that can arise from existing operations and from
whichever new project is chosen. We also net out bankruptcy cost
where total value of earnings is insufficient to pay both senior and
junior debt. If we note that the value of the firm will be the sum
of the PV of existing operations and the PV of value generated by
the project (less bankruptcy costs of 100 if firm value falls short
of the total debt obligation of 300), the various claims can be val
ued under the alternative assumptions that A is chosen and that
B is chosen.
The following tables show the overall cash flows to the firm
from the original operations and from each new project. The left
table shows overall value when project A is chosen, and the right
PART 2 Risk Management Strategies
246
table shows value if B is chosen. In each table the rows show the
possible value of the existing operation (either 100 or 200) and the
columns show the value from the project (200 for project A and
either 20 or 310 for project Bj. The terms in parentheses are probabUities. The cells that are starred show bankruptcy situations. In
each of these cells the total value is lower than the amount owed
of 300. Accordingly, the firm must pay the bankruptcy cost of 100.
We can use these values and probabilities to value the firm and
its constituent claims.
B
New Project =:
A
Original
Operations U
220
(1.0)
20
(0-5)
310
(0.5)
100
320
120
-100
410
(0.5)
(0-5)
200
420
= 20*
(0.25)
510
220
-100
= 120*
(0.25)
(0.5)
(0.5)
(0.25)
(0.25)
Value of the firm if project A is chosen:
Value of the firm
Old debt
New debt
Equity
0.5(320 + 420)
0.5(100 + 100)
0.5(200 + 200)
0.5(20 + 120)
= 370
= 100
= 200
= 70
Value of the firm if project B is chosen:
Value of the firm
Old debt
New debt
Equity
0.25(20 + 120 + 410 + 510)
0.25(20 + 100 + 100 + 100)
0.25(0
0.25(0 ++ 20
20 + 200 + 200)
0.25(0
0.25(0 +0
+ 0 + 110 + 210)
= 265
= 80
= 105
= 80
This illustrates the classic asset substitution problem. Since
project selection is made after debt has been issued, shareholders
CHAPTER 8
Risk Management Strategy: Duality and Globality
247
favor project B, which offers an equity value of 80 compared with
70 for A. If bondholders anticipate this choice, they would only
be willing to pay 105 for the new debt issue even though the face
is 200. Since the capital cost of project B is 200, the amount raised
from the debt issue would be insufficient to fund the project. In
this example, there is insufficient gain to shareholders to make
good the shortfall of 95 (i.e., 200 — 105) required to fund project
B, since the value of equity is 50 with neither project and is only
80 if B is undertaken. Thus, the firm is simply unable to finance
project B. Does that mean that A will be chosen? Suppose indeed
that the firm announced its intention to choose A. Unfortunately,
investors buying the new debt issue would still rationally assume
that if they subscribed 200 for the issue, the shareholders would
have an incentive to change the minds and use the 200 to fund
project B. Thus, investors would still only subscribe 105 for the
new bond issue. The firm is snookered. It is unable to accept either
project. Because bondholders anticipate the firm's retroactive
temptation to choose the risky negative NPV project, the firm is
unable to fund either project. It is forced to sacrifice not only the
expropriatory project B but also a project with a genuine positive
NPV.
Hedge Strategy
Suppose that the firm can commit itself in some credible way to
hedge any risk that arises from new projects. Since there is no risk
in A, the commitment to hedge the project risk is meaningless and
the values of debt and equity are exactly the same as shown
above. But project B is risky and, with a costless hedge, the firm
could replace a lottery of 10 and 310 with a certain value of 165.
It is straightforward to show that the shareholders would never
select a project with cost 200 and certain PV of 165 over an alter
native with cost 200 and certain PV of 220. The various calcula
tions to support this conclusion are now shown.
Value of the firm if project A is chosen:
Value of the firm
Old debt
New debt
Equity
0.5(320 + 420)
0.5(100 + 100)
0.5(200 + 200)
0.5(20 + 120)
= 370
= 100
= 200
=
70
248
PART 2
Risk Management Strategies
Value of the firm if project B is
r. chosen:
0.5(165 •+ 365)
Value of the firm
0.5(100 + 100)
Old debt
0.5(65 + 200)
New debt
0.5(0 + 65)
Equity
= 265
= 100
= 132.5
= 32.5
Since the project yields a certain 165, the firm will be unable to
pay off all debt if existing operations yield only 100. Thus, there
is still a potential for bankruptcy despite the hedge of the new
project risk. With the hedge, equity will be worth 70 if A is chosen
against only 32.5 if B is chosen. Thus, if a credible hedge is in
place, bondholders will find it rational to anticipate that share
holders will choose project A and will be willing to pay the full
200 for the debt. Now the firm can pay for the new project since
the proceeds of the bond issue are sufficient to meet the capital
cost of the new project A.
Notice that the gain in value, and the ability to finance and
undertake the positive NPV project A, do not come from the hedge
per se. Rather, the value added comes from convincing bondhold
ers that the project risk will be hedged. This creates an interesting
issue as to how to give such a credible signal. This was exactly
the same issue that was raised above when the hedging of firm
risk as a method of reducing expected bankruptcy costs was con
sidered. A commitment can be made to hedge risk in the bond
indenture agreement. Suppose that the firm binds itself to insure
all risk that may arise from any project chosen. Insofar as this
agreement is effective and binding, it should serve the present
purpose. The effectiveness of such a commitment is enhanced by
the prospect of ex post sanctions on directors and managers who
violate it. The pervasiveness of directors' and officers' lawsuits,
not only by shareholders but by other corporate stakeholders,
speaks to this issue. On the other hand, effective hedges may not
always exist. For example, it is possible, and indeed common, for
a bond agreement to require insurance against fire and hability,
but hedges for the risk of variations in the demand for the product
are not easily constructed and it would be impractical to require
such hedges.
Leverage Strategy
The asset substitution problem can be solved in another way. If
the new project were to be financed with equity, project A would
CHAPTER 8 Risk Management Strategy: Duality and G1 obality
249
be chosen. This follows because the total debt is now only 100 (old
debt) and there is no chance that firm value would fall below 100
whatever project is chosen. Since the probability of bankruptcy is
zero, shareholders bear all risk with either project and will select
the project with the higher NPV In fact, it is not necessary to fund
the whole project with equity. Suppose that the firm chooses to
raise 100 in new equity and 100 in new debt. The following cal
culations will show that the incentive conflict will be solved and
the shareholders will opt for project A, which yields an equity
value of 170 compared with 135 for B. Moreover, bondholders will
anticipate the choice of A and will subscribe the full 100 for the
new debt. Thus, there is no problem in funding the project and
capturing its NPV of 20:
Value of the firm if project A is chosen:
Value of the firm 0.5(320 + 420)
Old debt
0.5(100 + 100)
New debt
0.5(100 + 100)
Equity
0.5(120 + 220)
= 370
= 100
= 100
= 170
Value of the firm if project B is chosen:
Value of the firm
Old debt
New debt
Equity
0.25(20 + 220 + 410 + 510)
0.25(20 + 100 + 100 + 100)
0.25(0 + 100 + 100 + 100)
0.25(0 + 20 + 210 + 310)
= 290
= 80
=
75
= 135
Contingent Leverage Strategy and
Post-loss Financing
In the discussion of duality and bankruptcy costs, the idea of con
tingent leverage strategies was introduced. Such strategies also
can be useful in addressing agency costs. These will be discussed
in more detail later; the present purpose is simply to stake a claim.
However, the idea is simple enough. Increased leverage will lead
to incentive conflicts between bondholders and shareholders.
These problems become especially severe when the firm loses
value and approaches financial insolvency. If the firm's stock value
PART 2 Risk Management Strategies
250
is very low and bankruptcy is imminent, shareholders are much
more likely to engage in high-risk activities that could hurt bond
holders. When the firm is on the verge of failing, the shareholders
have little more to lose but everything to gain. If the high-risk
investment fails, it was the creditor's money at stake; but if the
high-risk investment succeeds, the upside goes to the sharehold
ers. Accordingly, one can imagine that a device that automatically
unlevers the firm or refinances after a major fall in share value
would remove this temptation to "bet the firm" on such high-risk
investments.
Duality: Agency Cost: Underinvestment
Asset substitution can lead to the failure of the firm to undertake
a positive NPV project, as shown in the previous example. Because
bondholders anticipate the substitution of an asset with greater
default risk, the amount they subscribe for the debt is insufficient
to enable the firm to fund its desired investment. In this sense
there is an underinvestment issue; the firm has failed to invest,
even though faced with at least one positive NPV project. And
even if the desired (by shareholders) project, B in this case, could
be funded, this will not maximize firm value, since A has a higher
NPV. We now address a more direct underinvestment problem
that arises because the riskiness of existing operations causes the
firm to pass over new positive NPV investment opportumties.
Ex Post Analysis
The underinvestment problem arises from the same conditions as
asset substitution; the fact that the shareholders can default on
their obligation to pay debt in full if the firm is bankrupt. The
remedies are similar to those for asset substitution. Consider a
banking firm with operations that generate a value of either 50 or
200, each with a 50% probability. The variation depends on inter
est rates. The firm has debt of 140. A new investment opportunity
exists that will cost 100 to shareholders and will generate a cash
flow with a present value of 120; thus, the NPV is 20. Let us sup
pose first that the firm will make its decision on the new project
after it knows what the interest rate will be.
CHAPTER 8 Risk Management Strategy: Duality and Globality
251
Existing
Value
Potential
Decision
Value of
Firm
Value of
Debt
Value of
Equity
Decision
200
accept
220
80 ‘
accept
reject
200
140
140
accept
70*
50
140*
50
-70*
50
reject
60
reject
It is clear that the firm would accept the project if the original
value turns out to be 200 as shown by the first two rows. The new
project increases the firm value by the NPV of the project, that is,
20, and all the increase goes to shareholders because the firm is
not in default on its debt.
To see what happens when the original firm value is 50, con
sider the starred items in the third row. There is little point to the
shareholders putting up an additional 100 when the firm is al
ready insolvent. Recall that the investment decision is made after
the firm value is revealed, and shareholders invest 100 such that
the firm then receives 120. The firm therefore has this 120 plus the
original value of 50, but owes 140 to bondholders. This leaves only
30 shareholders who have just paid 100 to invest in the new pro
ject. Shareholders are down a net of 70. Clearly, shareholders
would not undertake the investment when the original value was
only 50.
Hedge Strategy
The following table shows what happens if the interest rate risk
is hedged, thereby fixing the firm value at 125. Clearly, the firm
will undertake the project since the absence of downside risk does
away with the bankruptcy problem that was causing the distortion
of investment incentives.
Existing
Value
Potential
Decision
Value of
Firm
Value of
Debt
Value of
Equity
Decision
125
accept
reject
145
125
140
125
5
accept
0
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PART 2 Risk Management Strategies
Another interesting point here is how the hedge affects the value
of debt. In the original, unhedged, situation the potential for de
fault on debt would be anticipated into the price of the debt. When
debt is issued, bondholders can anticipate the uncertainty in in
terest rates and the likely investment decision. Therefore they es
timate that the firm will be worth 1/2(200) + 1/2(50) — 135 and that
their debt will be worth 1/2(140) + 1/2(50) = 95. Thus, the firm will
receive only 95 for debt issued with a face value of 140. After
hedging of the risk, the debt will be worth its full face value of
140. There is a definite gain to the shareholders from hedging. Not
only does the hedge lead to the full capture of the NPV of the
new project, but it also yields a higher price for the issue of debt.
Leverage Strategy
The following table shows that a reduction of leverage also will
lead to the correct investment decision. The example shows the
same investment choice for the firm with no debt.
Existing
Value
Potential
Decision
Value of
Firm
Value of
Debt
Value of
Equity
Decision
200
accept
220
0
220
accept
reject
200
0
200
accept
70
50
0
0
70
reject
50
accept
50
Ex Ante Analysis
The underinvestment problem can also be examined in a different
time sequence. Suppose that the details are the same as given
above when debt was 140, with the exception that the investment
decision is made before interest rates are known. This can be done
by reconfiguring the numbers in the original table above to get
the following (these values are prospective based on the anticipated
investment decision and using the probabilities of 0.5 that interest
rates will be low and 0.5 that they will be high).
Undertake project:
Value of firm
^(200 + 20) + ^(SO + 20) = 145
Value of debt
^(140) + ^(MO)
= 140
Value of equity ^(80) + !/2(-70)
= 5
CHAPTER 8 Risk Management Strategy: Duality and Globality
253
Do not undertake project:
Value of firm
72(200) + 7z(50) = 125
Value of debt
^(140) + 7z(50) = 95
Value of equity ^(bO) 4- ^(O) = 30
Again the positive NPV investment is lost since, should the firm
go bankrupt, a very large portion of the 120 cash flow generated
by the new project would go towards reducing the degree to
which the firm defaults on its debt. You can also work through
yourself to see whether the firm does in fact undertake the project
when the original risk is hedged or when the firm unlevers.
Duality and the Crowding Out of
New Investments
Recall that firms typically prefer to finance new investments from
retained earnings because this is cheaper than external financing.
If a sudden loss absorbs internal funds, then new investment can
only be funded by more expensive external capital. Accordingly,
unhedged losses tend to crowd out some new investment.
We will examine alternative generic strategies with a simple
example. The firm identifies five investment opportunities, each
having a capital cost of 10 but having different net present values
as shown in order in the following table. We will suppose that the
firm has available liquid funds of 50 and can therefore undertake
all five projects. Clearly, all five projects will add value to the firm
and should be undertaken.
Project
Capital Cost
NPV
3
2
1
10
2
3
10
4
10
5
10
10
1
1
1
NPV less
Cost External
Capital
0.5
0.5
-0.5
-0.5
-0.5
Now suppose that the firm takes a sudden hit to liquidity
from an unhedged loss of 30, reducing cash from 50 to 20. The
254
PART 2
Risk Management Strategies
firm can now only fund two of the projects from internal sources
and must go to the external capital market to fund the remaining
three. If the transaction cost associated with external capital is 1.5
for each 10 raised, then the adjusted NPV shown in the final col
umn reveals that projects 3, 4, and 5 will be lost.
Hedge Strategy
Had the risk been hedged, there would be no loss of internal cap
ital; the sudden loss of 30 would have been paid for by an insurer
(or other counter-party); the 50 in liquid funds would have been
available to pay for all five new projects; and the total NPV of 3
from projects, 3, 4, and 5 would have been secured. Thus, the
expected value of hedging is a gain of 3 multiplied by the prob
ability that the loss will occur.
While hedging can create value, it too has transaction costs.
For example, insurance encounters direct costs, moral hazard
costs, and adverse selection costs. These transaction costs must be
balanced against the costs of ex post financing that give rise to the
crowding out idea. In the above illustration, suppose that there is
a 0.1 chance that a liquidity loss of 30 will occur. We know that
the loss of NPV will be 3 if such a liquidity loss actually occurs,
so the expected loss of NPV from an unhedged position is 0.3. Sup
pose now that an insurance (or other) hedge can be purchased but
the transaction cost of the hedge is 0.5 (note that the hedge cost
arises whether or not the loss occurs). In this case the hedge will
not add value prospectively. The optimal hedging policy involves
a balance between the actual (i.e., certain) transaction cost incurred
with the hedge and the expected loss of NPV from the displacement
of investment opportunities.
Leverage and Contingent Leverage Strategies
The cost of external funding is not constant; it can vary according
to the leverage of the firm and its financial strength. The relation
ship between leverage and cost of capital is considered in more
detail in later chapters. For the moment, we can simply accept
that leverage is material. Accordingly, by changing leverage, one
can manipulate the conditional cost of external capital. For ex
ample, suppose that the firm lowered its leverage before any loss
occurred. Lowering fixed obligations from earnings will raise re
tained earnings to, say, 80. Now the firm can absorb a loss of 30
CHAPTER 8 Risk Management Strategy: Duality and Globality
255
and still have available the 50 internal funds needed to finance all
five investment projects.
More radically, the firm may set in place some contingent
financing facility that is triggered by the unhedged loss. Above,
we discussed the idea that a firm may issue put options on its
own stock that are exercised at a given price, but only when a
defined loss occurs. In such a scheme the firm is effectively low
ering the cost of external capital should an unhedged loss occur.
Of course, there will be an upfront price for this facility, and this
needs to be compared with the expected loss of value from pro
jects that otherwise would be sacrificed.
Duality and Managerial Utility Maximization
In keeping with earlier discussions of duality, the issues will be
developed with an example. You own a small firm. The profita
bility of this firm depends jointly upon the level and quality of
work supplied by the manager and upon the state of demand for
your product, which is related to general economic conditions.
This second determinant of profit introduces risk. You must decide
whether to pay the manager a flat salary or incentive (profitrelated) compensation. If you pay a flat salary of 100, the man
ager's productivity will be such that the firm's profit is either 500
or 1500, each with a 0.5 probability. Call the profit before deduc
tion of compensation V. Alternatively, you can pay the manager
performance-related compensation at a level x X V, in which case
productivity is expected to improve by 60% such that V is either
800 or 1800, each with 0.5 probability. The manager, being riskaverse and undiversified, is interested in the expected utility of
her wealth, which includes only her employment compensation.
The manager's utility function is LI = W05, where W is wealth.
However, utility also reflects the effort provided, and we assume
that high effort lowers utility. To capture this, the utility function
is:
utility with low effort
—
U = W05
utility with high effort
=
LI = W0 5 — 1
The
1" is the monetary equivalent of the loss of utility of high
effort, since people usually do not like to work hard, other things
PART 2 Risk Management Strategies
256
being equal. You, as owner, are more diversified and are interested
in the expected value of the profit (after deduction of the man
ager's compensation). Some questions will need answering:
1. If you pay performance-related compensation, what
must the value of x be to compensate the manager for
risk and effort?
2. Given that performance-related compensation must
include a risk premium, which compensation schedule
(flat salary or x X V) would you choose to pay the
manager?
3. Suppose that you can insure or hedge the riskiness of V
(i.e., replace 0.5(500) + 0.5(1500) by 1000 and replace
0.5(800) + 0.5(1800) by 1300). What is the gain from the
hedge to you as the owner?
Consider question 1. If the manager is paid a flat salary of 100,
her expected utility5 is 1OO0-5 = 10. For the manager to be com
pensated for the risk and hard work inherent in performancerelated compensation, x must be set such that her expected utility
is no lower than under a flat salary (1000-5 = 10). I will use an
equals sign in the calculation to derive the minimum level of x:
ELI(flat salary) = ELI(compensation at x X V
and assuming high effort)
(1OO)05 = (0.5)(800x)°-5 + (O.5)(18OOx)0-5 - 1
11 = (0.5)(800t)-5 + 18OOo-5)x0-5
x = 0.0968
The expected earnings of the manager under performance pay
are 0.0968(1300) - 125.84, compared with 100 under flat pay. The
difference, 25.84, reflects two things. First, incentive compensa
tion is risky (compensation will either be 0.0968 X 800 = 77.44 or
0.0968 X 1800 = 174.24), so the manager requires a risk premium.
5. Notice that this utility is calculated anticipating that the manager will choose high ef
fort. This should be clear. Expected utility with low effort is 1OO0,5 = 10, whereas
the expected utility with high effort is lOO05 -1 = 9. Consequently, low effort
offers higher utility and would be chosen.
CHAPTER 8
Risk Management Strategy: Duality and Globality
257
Second, if the manager is providing high effort, this also requires
compensation.6
As owner, you face a tradeoff. You can pay on a performance
basis, which will mean that you pay more on average to managers,
but the incentive effects will improve profitability. Which schedule
is better? Compare expected profit (you are risk-neutral in this
example) net of compensation.
flat pay
performance pay
0.5(500 + 1500) - 100
= 900
0.5(800 + 1800) - 125.84
= 1174.16
Clearly, the improvement in productivity far outweighs any additional payment to the manager to compensate her for risk and
for disutility of high effort in this example. Performance pay is
better.
Hedge Strategy
Can you alleviate the tradeoff (i.e., avoid paying managers risk
premium but still keep them motivated) by hedging the risk? Sup
pose you hedge the risk but can still manage to motivate managers
by paying some fraction y of V. With such motivation, expected
profit will be 0.5(800) + 0.5(1800) = 1300 (ignoring transaction
costs). What does y have to be so that compensation is competitive
and motivates the manager to high effort? You can pay managers
some amount y V, where, to make this acceptable to managers, yV
must satisfy (remember to deduct 1 for the disutility of high effort
and recall that the competitive level of utility is 10005 = 10):
(yV)0.5 _ T = (^300)0.5 _ 2 = 10
y = 0.09308
Because of the hedge, managers will not face risk and will end up
6. It is important to verify that if the manager is paid a portion 0.0968 of value, she will
indeed supply high effort. To verify this, recall that with low effort value will be
either 500 or 1500. Therefore the expected utility of the manager will be
EU = (0.5)(500 X O.O968)0'5 + (0.5)(1500 X O.O968)0-5 = 9.503
which is less than the utility from high effort of 10. Thus, the manager will choose
high effort with this compensation schedule.
258
PART 2 Risk Management Strategies
with certain compensation of 121.004 (i.e.z 0.09308 X 1300). With
out the hedge, the expected compensation was 125.84; the savings
of 4.836 is the risk premium, which is no longer necessary. How
ever, here the manager does not contract for 121.004 flat salary.
Rather, the contract is to pay 0.09308 of value V, which will turn
out to be 121.004 only if she works hard. If the manager were to
slacken her effort such that production fell to 500/1500 (which is
hedged at 1000), her income would fall to 0.09308(1000) = 93.087
Thus, hedging and paying by performance maintains managerial
effort but enables the firm to avoid the risk premium to the man
ager.
Alternative Compensation Strategy
0
The generic alternative to the hedge strategy is a risk accommo
dation strategy. The task here is to find some way the firm can
live with risk while still motivating managers to high effort and
avoiding paying the risk premium. To see one way this can be
tackled, look back on the hedging example we have just consid
ered. By hedging risk and paying the manager 0.09308 of value,
the firm avoided paying a risk premium of 4.836 but still managed
to keep the manager motivated to supply high effort. What drove
the gain in value was not the hedge per se, but that the compen
sation was based on a hedged value. So can we create a "phantom
hedge?" This can be achieved by defining an accounting definition
of profit or value that is purged of risk and basing compensation
on this accounting number.
AN ILLUSTRATION OF HEDGING AND
LEVERAGE STRATEGIES
To see some of these strategies (hedging, simple and contingent
leverage) set in a single context, imagine a firm that is developing and
producing new drugs. The current earnings are $300m, from which
$100m interest (8% interest on debt of $1250m) must be paid, leaving
7. Just verify here that the manager will work hard if paid 0.09308 of earnings when
earnings are hedged. Thus, check that (0.09308 X 1300)°5 - 1 > (0.09308 X
1OOO)05.
CHAPTER 8
Risk Management Strategy: Duality and Globality
259
$200m. Of the remaining $200m, half is reinvested in research and de
velopment (R&D), and this continues to generate a stream of new in
vestment opportunities. Because of these opportunities, earnings remain
ing to shareholders (i.e., the $100m) are expected to grow at an average
of 5% per year.
Total earnings (current year)
$300m
Interest
$100m
R&D
$100m
Residual (dividend) forshareholders $100m
but expected to grow at 5% annually
The firm's cost of equity capital is 10%, and it has 200 million shares
outstanding. How much would an income stream starting at $100m but
growing at 5% per year be worth? To anticipate some analysis which
will be developed later, a simple formula for finding the market value of
the equity, MVE, of a firm is to divided the current earnings. E0/ by the
difference between the cost of equity capital, kE/ and the expected growth
rate, g:
MVE =
Eo
$100m
— $2 billion
kE- g ~ 0.1 - 0.05
Each share would be worth $2 billion 4- 200 million = $10.
Let us pause and take a look at some of the risk management issues
facing this firm.
♦ The firm faces some probability of bankruptcy. If some set of
events occurred that reduced annual earnings below $100m per
year, it would be unable to pay its debt.
♦ The firm has investment opportunities that are generated from
prior investments in R&D. Investing in R&D is risky. Much
R&D does not result in any product that can be brought to
market; some results in marginal and high-risk project
opportunities; some results in much more solid project
opportunities. The willingness of the firm to undertake
marginal high-risk projects will be increased by the presence of
debt because the shareholders get to keep the upside risk and
pass much of the downside to bondholders. We have the sort of
agency problems discussed above.
9
260
PART 2
Risk Management Strategies
♦ Suppose some unhedged loss occurs that causes a continuing
loss of earnings. This firm must still service its debt. The firm
would have less in retained earnings to pay for its R&D. To
some extent the firm can continue to fund new projects by
cutting down on dividends (i.e., from retained earnings). There
is the prospect that it would be forced to:
Raise new equity and/or debt capital to continue to fund its new
projects, and/or
Cut down on its new investment projects.
Now consider what would happen if the earnings were reducedfrom
$300m to $150m by some sudden event {fall in currency value, an un
insured property loss, a loss of a government contract, etc.). Tire firm
still has the $l,250m in debt, on which interest still has to be paid. There
is correspondingly less left, only $150m, to invest in R&D and to pay
shareholder dividends, and the firm must decide how much it can con
tinue to invest in R&D when shareholders still demand dividends. Thus,
there will be:
Less money to pay dividends.
Less money to invest in R&D.
Less money to invest in new projects generated from R&D.
Increased cost of external financing; the loss will have increased
financial leverage, which in turn will increase the cost of raising
new debt or equity.
In terms of the above formula (MVE = E0/(kE - g)), all three terms
will deteriorate, Eo will be smaller, kE will be larger, and g will be smaller.
The loss will cause a fall in the stock price. For example, if only $75m
were now paid to shareholders (Eo = 75), kE increased from 10% to
11 /o, and growth fell from 5% to 3%, then the market value of equity
would be reduced to:
75
MVE =------ —------ = $937.5m
0.11 - 0.03
and each of the 200 million shares would be worth only $4.69.
One can now think of the risk management issues as protecting the
interests of the shareholders in preserving the share value. Think of how
the share value can fall:
CHAPTER 8
Risk Management Strategy: Duality and Globality
261
A direct loss {through Eo) can occur simply because the ability
to continue to earn revenues has been reduced.
♦ A set of indirect losses {through kE and g) can arise because
the firm could lose its ability to secure future growth:
♦ Because the earnings are lozver
♦ Because of the prior claim of debt on those reduced earnings.
♦ Indirect losses will arise because debt and risk give rise to
agency costs and bankruptcy costs.
♦
Thus, risk management can potentially create value by:
Protecting the earnings from sudden loss
♦ Relieving the burden of debt so that reduced post-loss earnings
can be allocated to R&D and new investments rather than to
paying off debt
♦ Relieving the burden of debt so that the probability of financial
distress is reduced and with it the expected bankruptcy costs
and agency costs
♦
These can be accomplished by:
<
Avoiding the earnings loss; i.e., hedging the loss.
♦ Reducing the amount that has to be paid from post-loss
earnings to service debt. This in turn can be accompanied by:
♦ Reducing current leverage so that there will be less debt in
place if and when a loss occurs
♦ Having an automatic arrangement for debt to be forgiven
should a loss occur
♦ Having an arrangement for debt to be converted to equity
should a loss occur.
♦ Having an arrangement for
new equity to be issued to fund
R&D and investments after loss.
♦
CLASSIFYING RISK
MANAGEMENT STRATEGIES
From the discussion of duality, it should be clear that the same
risk management strategy can address several different types of
PART 2
262
Risk Management Strategies
risk cost. The riskiness of a potential product liability imposes
costs in the form of additional taxes, additional bankruptcy costs,
additional agency costs, loss of value from crowded out invest
ments, and loss from inefficiencies in compensating and motivat
ing managers. The purchase of an insurance policy will provide
relief from all these costs; the relief is not specific. Reducing lev
erage will provide relief from the agency costs, bankruptcy costs,
and crowding out losses. On the other hand, redesigning com
pensation relieves only the specific risk costs of efficient motiva
tion of managers. Tax arbitrage is another specific risk manage
ment strategy in that it focuses on only one type of risk cost. Table
8-2 shows the various strategies and their domain.
It is clear from looking at the various risk management strat
egies that there is an issue of boundaries. Some of the strategies
clearly wander into other areas of management, including finan
cial management, corporate governance, and tax management. For
example, determining the capital structure is a central issue in
financial management, and this function is usually assumed by
TABLE
8-2
Risk Management Strategies
;t Addressed
_____________ r
I9
.J ,..
T '•
ft-'
bjtrage
v
'
jihg leverage
Contingent
leverage and post-loss .
c-
Rejc
■'''■■cc
ign executive
Sensation
Desi
-<c
___________
Lion and undennves
jf new-inyestmenS
< aversion
isk aversion
CHAPTER 8 Risk Management Strategy: Duality and Globality
263
the firm's chief financial officer or treasurer. But risk management
is becoming an increasingly important part of financial manage
ment. Contrarily, leverage management is becoming an increas
ingly important part of the risk manager's function. In short, risk
management and financial management are becoming increas
ingly hard to keep apart. Consequently, in the remainder of this
work, capital structure strategies will be considered in some detail.
Other strategies will receive less emphasis. Compensation design
for managers is a highly specialized area and will be given some
limited attention because it is managers who formulate risk man
agement policy and any principal-agent conflicts here are of great
practical concern. Nevertheless, compensation design is complex
and specialized and we will do little more than scratch the surface.
Tax management and tax arbitrage is an even more highly spe
cialized area of study and gives rise to very focused strategies that
exploit the detailed structure of the tax code. Here the coverage
will be limited to very general issues. Thus, in what follows, hedg
ing, leverage, and contingent leverage strategies will be the prime
focus, with coverage of compensation and tax issues somewhat
secondary.
Hedging Strategies
A hedge is a focused risk management tool in that it addresses a
specific form of risk. Hedge instruments usually are paired with
specific forms of risk. Consider the following types of risk that
face many firms: risk of liability suits, risk of damage to property;
changes in demand over the business cycle, and the effects of in
terest rate changes and foreign exchange rate changes on firm prof
its. For each source of risk there may or may not exist a specific
hedge instrument. For the liability risk there is a liability insurance
policy, for the property risk a property insurance policy, and there
are interest rate and foreign exchange futures that can hedge these
risks. For some risks, finding an appropriate hedge instrument is
difficult. For example, inflation can be difficult to hedge.
An important distinction as we proceed is that between asset
hedges and liability hedges. Think of a hedge instrument as the pair
ing of two cash flows with offsetting risk. It is useful to start with
some preexisting asset owned by a firm or individual; for exam
ple, a home. The value of this asset is risky because it can be
264
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damaged or bum down. The risk to this asset can be hedged on
both sides of the balance sheet.
Asset Hedge
An asset hedge can be defined as an asset that provides a hedge
against the risk in some other asset. A portfolio including the basic
asset and the hedging asset has little or no risk. The asset hedge
can be represented in a portfolio F in which an amount $ is in
vested in two assets. The first basic asset has a payoff of AB for
each dollar invested. The second asset, the hedging asset, has a
per dollar payoff of AH. The capital $ is allocated over the two
assets in the ratio {l:/z}, and the correlation coefficient rBH is neg
ative (in the limit approaching negative unity).
asset hedge
F = $(AB + /zAH)
where 0 > rBH > — 1
If rBH = “1/ then some hedge ratio h* can be chosen such that the
portfolio is riskless; that is, the variance, VAR, is zero:
VAR {$(Ah + /AAh)} = 0
The obvious asset hedge for a home is a homeowner's insurance
policy. The policy is purchased at a price, the premium, and yields
a potential payoff if your house bums down. Other examples are
the purchase of a future contract by a farmer to hedge the risk of
grain price movements; a reinsurance policy is a traditional form
of asset hedge for the insurer who wishes to control risk in its
direct insurance portfolio. A newer instrument used by insurers is
the catastrophe option, which is an option written on the value of
an index of insurance company claims that yields a payoff when
the index triggers a pre-set value (the striking price).
Liability Hedge
A hedge can be achieved on the opposite side of the balance sheet.
Instead of the hedging asset, the portfolio includes a liability LH
as follows:
liability hedge F - $(AB - hLH)
where 0 < rBH < 1
If rBH = 1/ then some hedge ratio h* can be chosen such that the
portfolio is riskless; i.e.,
VAR {$(Ab - h*LH)} = 0
Instead of owning an asset that pays off when you have a loss of
CHAPTER 8 Risk Management Strategy: Duality and Globality
265
the basic asset, you now have a liability that will be reduced when
you have a loss on that basic asset. Consider the ownership of a
home again. A liability hedge would exist if the bank holding the
mortgage agreed to forgive the debt if the house were destroyed
by fire, storm, or earthquake. An investor could hedge a long po
sition in a stock by a short position in a call option on that stock.
Some insurers have recently issued debt with the provision that
it be forgiven if the issuing insurer suffers catastrophic losses on
its direct insurance portfolio.
Leverage and Financing Strategies
Leverage Management
We will use terms such as "simple leverage management" and
"leverage" to describe a reduction in leverage in anticipation of a
possible future loss. This reduces the agency cost between credi
tors and residual claimants and reduces the expected value of
bankruptcy costs. Moreover, if a sudden loss arises, the firm will
find itself in a stronger position to approach capital markets for
new funding (either to reconstruct destroyed assets or to fund new
investment projects). Alternatively, dividend policy may be used
to address directly the crowding out problem. Lower dividend
payouts will enhance the ability of the firm to fund future projects
from internal funds and reduce the probability that projects will
be lost for lack of access to low cost capital.
Post-loss Financing
Tn several of the above examples, it was shown that issuing new
equity after some event such as an insurable loss can partly ad
dress some of the costs of risk. This action enables the firm to
finance and undertake investment opportunities that still exist de
spite the sudden event or loss. We refer to the raising of funds
after a loss, on terms that are available after loss, as "post-loss
financing" or "post-event financing." It is recognized that some
times the event may have such a seriously depressing effect on
the firm's value that it will be unable to raise sufficient money for
its needs, or the terms will be penalistic. For example, the chemical
discharge at Bhopal depressed Union Carbide's share price and
made it more expensive to raise new money. Whatever money can
be raised, and at what terms, depends on the severity of the event,
the franchise value of the firm, and how the circumstances are
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PART 2 Risk Management Strategies
received by financial markets. There may be two issues here: one
concerning having money available for investment needs, the sec
ond concerning the post-loss leverage. Equity financing addresses
the need for new funds without increasing post-loss leverage.
Debt addresses the need for funds but increases leverage.
A particular situation in which post-loss financing can be
very valuable is if the firm has significant franchise value but faces
a liquidity crunch as a result of the loss. For example, an insurer
may suffer a catastrophic loss that drains liquid assets. It may have
considerable long-term assets that can only be liquidated in a fire
sale. Recapitalization is essentially a tool to release illiquid assets
and permits the firm to continue operating and preserve its fran
chise value.
Contingent Financing
If it is recognized that post-loss financing can add value, then
contingent refinancing takes the idea one step further. The terms
under which new money is raised can be agreed upon in advance
of any possible loss. A simple example is a line of credit that can
be drawn down on some prespecified event. There could be a
simple commitment fee or, in addition, the interest rate could be
fixed in advance so that the borrower is hedged from market fluc
tuations.
A more radical form of contingent refinancing is for the firm
to issue put options for a new issue of its own stock. One can
imagine two forms of this strategy. First, simple put options are
issued to a counter-party at an agreed striking price. Since a major
adverse event, such as a product liability suit, is likely to depress
the share price, there is a potential for the option to be "in the
money" and to be exercised as a result of the event. If so, the firm
will refinance at a price above the post-event market equity price.
The difference between the exercise price and the post-event share
price amounts to a partial hedge of the loss. Of course, there is a
consideration in the form of the price of the put option, which is,
in effect, an insurance premium for that part of the cost of refi
nancing that is borne by the counter-party.
A variation on this theme is a device that has been used by
insurance firms to provide contingent capital in the event of suf
fering catastrophic claims experience on its insurance portfolio.
Here, the firm issues put options on its own stocks, as before at a
CHAPTER 8
Risk Management Strategy: Duality and Globality
267
stated exercise price. But now there is an added trigger. In addi
tion to the stock price falling below the exercise price, a certain
predefined event must occur. In this case the insurer's own claims
must lie within a range of values. These new instruments have
recently been assembled for insurance firms under the trade name
"CatEPuts."
Other Contingent Leverage Strategies
The same general objective of unlevering the firm after an event
and partly offsetting the cost of the event can be achieved by con
verting the debt into equity. There is always a market option of
buying back equity and issuing new stock. Insofar as this trans
action takes place at market values, there is no direct value added.
An alternative is to embed a conversion option in the debt and to
make this option exercisable at the discretion of the firm. The firm
will exercise the option only if it benefits shareholders, that is, if
the equity has fallen below some critical value such that the shares
offered have a lower value than the debt they replace. This has
two effects. First, the firm unlevers (by exercise of the option)
whenever the value falls sufficiently. Second, insofar as the firm
exchanges less valuable shares to retire more valuable debt, there
is a partial hedge. This instrument is known as “reverse convert
ible debt," and it differs from normal convertible debt in that the
option to convert into equity is given to the firm rather than to
the bondholders.
Other Strategies
Compensation Management
As seen above, risk management decisions can be made to further
the self-interest of managers. This raises the issue of designing
compensation systems to align the interests of owners and man
agers. A risk management formula for compensation design can
be envisioned that balances the need to incentivize managers with
performance-related pay and the risk premia needed in such com
pensation schedules.
Tax Management
Given a nonlinear tax schedule, we have seen that expected tax
liabilities increase as the risk of the firm's earnings increases. Tax
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Risk Management Strategies
management strategies to reduce this cost can be derived that in
effect linearize the tax schedule; these strategies include leasing
and reinsurance. In addition to these general tax features, other
very specific tax features may influence risk management deci
sions. For example, at times the tax code has contained features
that encourage the formation of captive insurance firms. More
over, this tax benefit has changed over time with legal challenges
by taxpayers to broaden its scope and by the Internal Revenue
Service to narrow it. Thus, many captives were located in offshore
domiciles (notably Bermuda), and to distinguish them from self
insurance plans (which were less tax favored), captives often sold
insurance to outside policyholders in addition to their parents.
Tax issues call for a particular skill set and detailed knowl
edge of the tax code. Accordingly, they will not be afforded a
treatment in this book that is proportional to their financial im
portance.
INTEGRATED/HOLISTIC RISK MANAGEMENT
In this chapter there has been extensive discussion of the cost of
risk but little discussion of the source of the risk. Risk has simply
been considered to be a mathematical phenomenon: the variability
of some basic economic number such as corporate earnings or
corporate value. Variability causes problems that were identified
without saying much about the cause of that variability. Earnings
could vary because demand for the product was uncertain, the
income from foreign sales was subject to the effects of currency
fluctuation, there was variability in the annual cost of self insured
worker's compensation liability, and so on.
Various attempts have been made to classify corporate risk.
For example, Babbel and Santomero (1997) classify the risks facing
insurers as:
Actuarial risk, which arises from the estimating and pricing
of insurance products, including the risk that it will receive
an inadequate rate of return on the policies sold or it pay
too much for the funds it receives.
Systematic risk or market risk, which cannot be effectively
eliminated by the owner holding a diversified investment
portfolio. This may arise because either assets or liabilities
CHAPTER 8 Risk Management Strategy: Duality and Globality
269
are correlated with the market portfolio. This risk includes
interest rate risk and inflation risk.
Credit risk because borrowers can default on obligations.
Liquidity risk, which relates to the prospect that the insurer
will be unable to meet short-term obligations for lack of
liquid assets.
Operational risks, which arise from the systems and
processes that are necessary to run an insurance business.
Examples would include the cost of a computer system
failure or the cost of resolving regulatory conflicts.
Legal risk, which can arise because the legal system in
which insurers operate is subject to change as new court
precedents, legislation, and regulation can amend the rules
under which insurers operate and liabilities are established.
While this classification is obviously designed for insurance
firms, similar categories can be derived for noninsurance firms.
For example, a manufacturing firm encounters:
Operating risk, which arises from failures in the basic
processes that are the core of its business, such as plant
breakdown or power supply failure
Financial risk from changes in the cost of capital that affect
the firm's value directly, and indirectly if product demand
is sensitive to capital market rates
Economic or market risk as changes in the level of economic
activity or structural economic changes affect product
demand or the cost of doing business
Pure or insurable risk, which is the downside risk from loss
or damage to corporate assets or sudden claims on those
assets
Classifications such as these are a little arbitrary and often
have overlaps or gaps, but they are useful for several purposes.
First, they are helpful in conducting a risk survey; the structure
helps identify where to look for risk so that no stones can be left
unturned. Clearly, such an exercise is an essential early step in the
risk management process. Second, classification can be useful in
designing an organization structure to manage risk. Different pro
fessional skills are needed for dealing with different types of risk.
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PART 2 Risk Management Strategies
For example, handling insurable risk calls for skills in understand
ing the liability system, settling claims with third parties, and in
vesting in loss control. Handling risk caused by fluctuations in
interest rates and other financial market numbers calls for skill in
financial economics.
However, these are not our main concerns here. Risk is by
nature largely indivisible. The whole process of diversification
tells us that one risk cannot be separated from others; their impact
is communal. And even if risks were separable, is there any reason
to think that the corporate tolerance for risk would differ accord
ing to the source of the risk? If not, then risks presumably should
be handled in a coordinated fashion. This lead us to an issue that
has become an article of faith for many concerned with risk man
agement: should risk management be holistic or global? Should
one grand strategy encompass all corporate risk?
To set the stage for the discussion of integrated risk management, con
sider Commonwealth Petroleum Co. To simplify as far as possible, CPC
has annual earnings as set out in the attached matrix:
Oil Price Low
chance 0.5
Oil Price High
chance 0.5
No Liability Loss
chance 0.5
500
1000
Liability
chance 0.5
250
750
One can interpret this in the following way. CPC faces two types of risk:
1. Earnings can be impacted by a potential liability suit for
environmental damage. Such a loss could cost the firm 250.
There is a 0.5 chance that such a liability will arise.
2. There is an additional risk that earnings can vary through
changes in oil prices—this accounts for a plus/minus
fluctuation of 250. Thus, without environmental liability,
earnings can be 750 + 250 = 1000 or 750 - 250 = 500.
With liability, the values are either 500 + 250 — 750 or 500
— 250 = 250. There is an equal probability of each price
CHAPTER 8 Risk Management Strategy: Duality and Globality
271
regime. The liability risk is assumed to be independent of the
oil price risk.
First, let us calculate the stand alone standard deviation for each source
of risk.
Oil price risk: Expected earnings are either 750 or 500
(depending on liability'), but in either case the standard deviation
is 250. The calculations are:
VO.5(500 - 750)2 + 0.5(1000 - 750)2 = 250
V0.5(250 - 500)2 + 0.5(750 - 500)2 = 250
Liability risk: Expected earnings are 0.5(500) + 0.5(250) = 375
or 0.5(1000) + 0.5(750) = 875. Either way, the standard
deviation is 125, calculated as follows:
VO.5(500 - 375)2 + 0.5(250 - 375)2 = 125
V0.5(1000 - 875)2 + 0.5(750 - 875)2 = 125
Nozo that the expected earnings and standard deviation for the firm as
a whole are:
E{earnings) = 0.25(500) + 0.25(1000) + 0.2(250) + 0.2(750) = 625
(T^earnings')
0.25(500 - 625)2 + 0.25(1000 - 625)2
2 = 279.5
+ 0.25(250 - 625)2 + 0.25(750 - 625)
Clearly, the overall risk of the firm, 279.5, is not the sum of the two
standard deviations for each risk type, 125 + 250, because of the inde
pendence of the two sources of risk.
A nonintegrated approach. A simple illustration of a noninte
grated approach would be that the manager in charge of oil hedges is
told that the firm cannot tolerate a standard deviation above 125, and
the manager in charge of insurance is told the same tolerance level. The
oil hedge manager then purchases oil futures such that half the fluctu
ation is hedged. Assuming no transaction cost, this ensures that earnings
can only fluctuate downwards by 125 and upwards by 125 (instead of
the up and down fluctuation of 25(T).8 The insurance manager buys no
8. You can recalculate the standard deviations for the effect of oil price changes, given
each liability outcome, to verify that the standard deviations are 125, i.e.,
(0.5(625 - 750)2 + 0.5(875 - 750)2|°5 and (0.5(375 - 500)2 + 0.5(625 - 5OO)2)0 5
PART 2 Risk Management Strategies
272
inswrancc, since the standai'd deviation is ali'eady 125. The earnings
matrix now looks as follows:
Oil Price Low
chance 0.5
Oil Price High
chance 0.5
No Liability Loss
chance 0.5
625
875
Liability
chance 0.5
375
625
Now the overall return and risk are:
E(earnirigs)
0.25(375) + 0.5(625) + 0.25(875)
= 625
/o.25(375) - 625)2 + 0.5(625 - 625) 2 = 176.8
(learnings) = y + 0.25(875 - 625)2
The dangers of this approach are:
1. The firm is not controlling the overall level of risk and does
not pay attention to the interaction of risk. Focusing on each
source of risk on a standalone basis means that the possibility
of accumulation is not given attention, i.e., it ignores the
possibility of a low oil price and a liability loss both occurring.
Notice that despite informing both managers to achieve a risk
level of 125, this risk is not attained at the firm level.
2. It does not help the firm achieve overall risk reduction in the
most economical way. For example, here corporate risk falls
from 279.5 to 176.8 and all the burden of reducing falls on
the oil hedge manager. This may be desirable if the transaction
costs of oil hedging is less than that of insurance. But if the
reverse were true, might it not make sense to make marginal
risk reduction through insurance?
A simple integrated approach. Suppose instead that the firm focuses
on its overall level of risk and fixes this at a standard deviation of 150.
There are still two ways of hedging risk available^ oil hedges and insur
ance. An oil hedge can be bought that will reduce the price risk. Without
the hedge, the risk is ± 250. We use the term h to denote the hedge ratio,
which is the proportion of the oil price risk that is transferred to an
CHAPTER 8 Risk Management Strategy: Duality and Globality
273
outsider (the seller of the hedge instrument). Thus, the retained variation
can be reduced to:
expected income 750 ± (1 - h) X 250 = 750 - (250(1 - /?))
Thus, if h = 0, no oil hedge is purchased; if h = 0.5 then half the
variation is hedged; h = 1, then all risk is hedged. With insurance some
portion (hedge ratio') i of the risk will be insured for a premium of 0.5
X 250 X i (that is, the probability of loss X the size of the loss X the
proportion of the loss insured). Notice that this premium is actuarially
fair insofar as it does not include any transaction costs. If a loss happens,
the firm loses 250 but is repaid i X 250, which results in net loss of
(1 — i)250. With these two hedges in place, the earnings of the firm are
now
Oil Price Low
chance 0.5
Oil Price High
chance 0.5
No Liability Loss
chance 0.5
750 - 250(1 - h) - 0.5(250)7
= 750 - 250(1 - h) - 125/
750 + 250(1 - h) - 0.5(250)/
= 750 + 250(1 - h) - 125/
Liability
chance 0.5
750 - 250(1 - h) - 0.5(250)i
- 250 + 250/
= 500 - 250(1 - h) + 125/
750 + 250(1 - h) - 0.5(250)/
- 250 + 250/
= 500 + 250(1 - h) + 125/
The problem now becomes to select two hedge ratios h and i so that the
overall standard deviation of the firm's earnings is 150. It is easier to
work with the variance, which is the square of standard deviation; i.e.,
VAR = 1502 = 22,500. You may also note that since there are no trans
action costs, expected earnings are still 625. Considering that each of the
four cells in the matrix has a 25% probability, the problem is now to
choose h and i to satisfy:
0.25(750 + 0.25(750 +
+ 0.25(500 + 0.25(500 +
250(1- h) - 125z
250(1- /z) - 125z
250(1- /z) + 125z
250(1- h) + 125?
- 625)2
- 625)2
- 625)2
- 625)2 = 22,500
Solving this needs a little trial and error. However, with some checking
v
e
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PART 2
Risk Management Strategies
you can verify that any of the following combinations of h and i will
result in the firm having its target level of overall risk:
h = 0.668
h = 0.6
h = 0.5
h = 0.45
h = 0.4
and
and
and
and
and
I = 0
i = 0.104
i = 0.3365
i = 0.437
i = 1.0
This example shows the interdependence of the hedging policies in
achieving an overall risk target. In this simple example the hedges had
no transaction costs. This is unrealistic; those selling oil futures would
do so at some spread, and insurance premiums would include some
markup over expected costs to cover expenses and a risk premium. Flex
ibility in achieving this target is particularly useful if the availability or
prices of hedges differ. For example, suppose that insurance encounters
very high transaction costs relative to oil hedges. It may be preferable to
select a combination in which no insurance is purchased but oil hedges
are used intensively (h = 0.668 and i = 0). In this way the firm can
choose to achieve its risk target at the lowest possible cost.
Integrated risk management can now be considered in the
light of the reasons given why risk was costly. Certainly none of
the reasons given suggests that risk from one source (oil price
changes) has any different cost to the firm than risk from another
source (product liability). Each source of uncertainty creates var
iation in the bottom line, and this variability gives rise to a set of
costs (higher expected taxes, higher expected bankruptcy costs,
higher agency costs, etc.). A dollar of additional expected tax lia
bility has the same depressing effect on net income whatever the
risk source that spawned it. Moreover, shareholders will be just
as willing to exploit creditors, whether the downside risk stems
from interest rate fluctuation or from currency fluctuation. In
short, the basic rationale for why risk imposed cost on the cor
poration did not differentiate according to the source of that risk.
Accordingly, there is no apparent reason to differentiate in the
treatment of risk. The various sources of risk have a combined
and inseparable effect on overall corporate risk, and this calls for
a combined risk management approach. As the example shows,
CHAPTER 8 Risk Management Strategy: Duality and Globality
275
this means not that the hedge ratios need to be identical, but that
the effect of risk on corporate value should be determined jointly
and the strategies for dealing with each of the risks’ formulated
jointly. The solution could be choosing an intensive hedge of one
risk, h - 0.668, and not hedging the other, i = 0; or the solution
could be a lower hedge on the first risk, h = 0.4, and a full insur
ance on the second, i = 1. The point is not that the hedge levels
are the same, but that they are determined jointly for their com
bined effect on corporate risk.
Commonwealth has two divisions: Products and Refining. The products
division produces and sells oil and oil products. The refining division
does as the name suggests, refining oil, including oil of the products
division, for which it charges a fee. However, the bulk of the refining is
for oil owned by others, and again there is a fee. These external contracts
account for the bulk of refining income. The profit of the product division,
IID, is related to oil prices, p, but there also is a random fluctuation, q,
which is simply noise. Note also that profits are denoted in $ millions
whereas the oil price is denoted in $ per barrel. The noise term has an
expected value of 0 and a standard deviation of 25. Note that the price
term has a positive sign indicating that as prices change by $1, profits
will increase on average by 30 million dollars.
IID = 100 + 30p + 7
E(^) = 0;
cfif) = 25
Refinery profits, IIR, also are determined by two factors. These profits
also are influenced by oil prices, p. But here the sign is negative, showing
that for every dollar rise in oil prices, refinery profits will fall by $25m.9
The second influence on refinery profits is the random noise term, f,
zohich has an expected value of 0 and a standard deviation of 10.10
IIR = 300 — 25p + f
E(f) = 0;
cr(f) = 10
The firm's total profit, II, is simply the sum of the profits of the two
divisions:
9. The story here is that the refining becomes highly competitive when oil prices rise.
The elasticity of refining fees to oil prices is sufficiently high (in absolute terms)
that refining profits fall as oil prices rise.
10. The noise terms q and r are uncorrelated with each other and with the oil price p.
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PART 2 Risk Management Strategies
IID = 100 + 30p + q
+ IIK = 300 - 25p + f
II = 400 + 5p + q 4- f
The risk facing the firm arises partly from the two noise terms that affect
each division's profit, and partly from the fact that oil prices, which affect
both divisions' profits, are also risky. The expected value of the oil price
is $20, but this is surrounded by a standard deviation of $10.
E(p) = 20;
o-(p) = 10
Now suppose that each division decides to buy oil futures and
thereby hedge oil price risk. An oil hedge is an instrument that pays the
amount h = -{p - E(p)}. Notice that the expected payment under each
unit of the hedge is:
E(h) = E(p - E(p)) = E(20 - 20) = 0
Without transaction costs, the price of the hedge would be the expected
value of zero. However, we assume a transaction cost of 2 for each unit
of h bought or sold. The standard deviation is:
a{li) = a(p - E(<p')') = o-(p) = $10
and, since we are discussing the hedge instrument, the correlation coef
ficient between h and p is:
rh,P = "I
Integrated risk management solution. To lay the ground for
what can go wrong, first consider that the firm coordinates its hedging
strategy. Overall profits are:
II = 400 + 5p + q + r
which has an expected value of
E(II) = 400 + 5(20) + 0 + 0
= $500m
and the risk level is (recall zero correlations between p, q, and r):
o'(II) - {(5)2 o-2(~p) + a2(q) + a2(f)}2/2
= {(5)2 102 + 252 + 102)1/2 = $56.79m
If this risk is hedged by the purchase of 5 units of the hedge h (each unit
CHAPTER 8
Risk Management Strategy: Duality and Globality
277
of h has an expected payment of 0 and a price of 2), then the expected
profit is:
E(II) = 400 + 5(20) - 5(2) + 0 + 0
= $490m
The reduction on $10m in expected profit reflects the price of buying 5
units of the hedge each at a price of 2. The risk level is:
cr(II) = {(5)2 cr2(p) + (5)2 cr\h') +
- 2(5)(5)r„,p a(pMh)}^
+ cr2(r)
= {(5)2 102 + (5)2 1 02 + 252 + 102 + 2(5)(5)(—1)(10)10))1/2
= (252 + 102)1/2
= $26.93m
Because the oil price risk is completely hedged, the remaining risk,
$26.93m, arises solely from the noise terms q and r.
Nonintegrated snafu #1 (undoing a natural hedge). Suppose
risk management decisions are made separately by the divisions and the
product division decides to hedge but the refinery division does not. The
profits of the respective divisions are respectively:
IID = 100 + 30p + 30/7 - 30(2) + q
which shows the hedge in place, and
IIR = 300 - 25p + f
which shows no hedge. Total profits are thus:
II = 400 + 5p + 30h - 30(2) + q + r
which has an expected value of
= 400 + 5(20) + 30(0) - 30(2) + 0 + 0
— $440m
and the standard deviation is
<r(II) = {(5)2 cr2(?) + (30)2 a■2(/z) + cr2(^)
+ cr2(f) - 2(5)(30)r„,p
= {(5)2 102+ + (30)2 102+ + 252 + 102 + 2(5)(30)(—1)(10)10))1/2
= $251.45m
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Risk Management Strategies
Look what a disaster this strategy has turned out to be. With no hedging,
expected profit is 490 and risk is $56.79m. With the products division
hedging, expected profit falls to 440 and risk increases to 251.45. What
went wrong? The problem was that, even if no hedge is purchased, a
natural hedge exists. Price affects the two divisions in the opposite di
rection. Price rises benefit the product division but hurt the refinery
division, and vice versa. When the product division went off and bought
30 units of the hedge to insure its divisional risk, it not only spent 60
but disassembled the natural hedge across the divisions. Essentially this
strategy reintroduces risk that was already hedged. Lufthansa has been
reported as making this mistake.11 Ordering jets from Boeing under a
contract denominated in dollars, it was concerned that an increase in the
value of the dollar would increase the Deutschmark cost of the planes.
Accordingly, it hedged this currency risk. What went wrong was that
its overall demand was closely related to the value of the dollar and that
a natural hedge already existed. The currency hedge simply undid the
natural hedge.
Nonintegrated snafu #2 (overkill). The second blunder is that a
nonholistic approach can lead to overkill. Suppose that both divisions
independently decide to hedge their risk. The product division buys 30
units of the hedge and the refinery division sells 25 units. Because each
unit is fully hedged against price risk, it will only have the noise term
left. Thus, the overall risk level is the same as with the previous complete
hedge, $26.93m. However, to achieve this overall level of risk reduction,
the firm trades a total 55 units of the hedge (30 buys and 25 sells') for
a cost of 110. Thus, expected profit is reduced to 390. This is simply a
waste. Since there was a natural hedge, it was unnecessary to buy so
many units. All that was necessary was to hedge the net exposure to
price risk shown in the total profit equation (i.e., buy only 5 units of the
hedge').
Focused and Global StrategiesRifles and Blunderbusses
The various strategies identified turn out to have interesting do
mains. Some strategies are inherently holistic, whereas others are
specific to a type of risk. Consider an insurance policy covering
11. This is reported in The Economist, February 10, 1996, Corporate Risk Management
Survey, p. 16.
■ - .-
CHAPTER 8 Risk Management Strategy: Duality and Globality
279
product liability risk. This is a hedge instrument targeted at a very
specific source of risk: it covers only product liability risk. Simi
larly, a currency hedge achieved by buying pounds sterling for
ward covers only the risk that the exchange rate between dollars
and pounds will change in a way that affects the firm's value. The
forward contract covers only this risk. Similarly, one can think of
focused hedges of property risk, interest rate risk, and risk from
changes in other macroeconomic indicators that affect the firm's
profitability. These hedges are "rifle shots;" each hedge targets
only a single risk.
One can certainly imagine a holistic risk management strat
egy making use of rifle shots. Each source of risk is identified and
matched with a particular hedge instrument (if one is available).
The appropriate hedge ratios for each instrument are then deter
mined jointly to meet an overall risk-return target. As in the Com
monwealth Petroleum example, this does not necessarily mean the
same hedge ratio for each instrument. Rather, the particular hedge
ratios will depend on the relative cost and availability of the in
struments. Now, it may not be possible to hedge all types of risk
by focused hedge instruments. For example, pollution liability in
surance has been difficult to obtain in the United States in recent
years, and what is available is very costly and has low limits of
coverage. More generally, liability coverage has been available, but
limits of coverage rarely exceeds a few hundred million dollars,
which offers incomplete protection for the Fortune 500 firm facing
the possibility of multi-billion dollar suits. Thus, the attempt to
assemble a holistic risk management program through focused
hedges may well result in something of a patchwork.
Now contrast these rifle shot hedges with the use of a lev
erage strategy. For example, the firm has high leverage and its
earnings and value are very risky. This leads to high expected
bankruptcy costs, a severe discounting of bond values because
investors believe the firm will overvalue high risk projects (ignor
ing the default put), and an expectation that post-loss financing
will be extremely costly. Accordingly, the firm lowers its leverage
by repurchasing debt and decides that instead of borrowing to
fund a new plant, it will finance entirely with equity. It does not
matter where the risk came from; the value added by reducing
leverage accrues across all types. This strategy is by nature holis
tic. Now, a rifle shot can pick off one bird at a time, but a blun
derbuss can down a whole flock at short range (blunderbusses are
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PART 2
Risk Management Strategies
a little more colorful than shotguns). So too can the leverage strat
egy address all types of risk.
In Table 8-3 a number of sources of risk are listed in the
columns. This table is not exhaustive, and more columns could be
added. Strategies are shown in the rows. These fall into two dis
tinct groups. In the top half of the table, specimen hedge instru
ments are paired with the corresponding risk. In the bottom part
of the table, strategies such as simple leverage, contingent refi
nancing, and compensation design are shown to address risk re
gardless of cause.
CONCLUSION
In this chapter we looked again at the reasons why risk was costly
to firms, and from these costs derived several generic risk man
agement strategies. Deriving strategies directly from the costs of
risk led to a dual, or shadow, classification of strategies. If risk is
costly, these costs can be reduced by removing the risk; that is,
hedging. Alternatively, if we know why risk is causing loss of
value, the dual strategy lies in restructuring the firm so that it can
accommodate the risk. We can remove the risk or remove its effect.
Some of the risk management strategies derived by this approach
will be a secondary focus in the remainder of the book; not be
cause they are unimportant, but because they require specialized
skills outside the financial economics paradigm. These strategies
include tax management and design of managerial compensation
systems. Other strategies will receive more attention, including
hedging, leverage, contingent leverage, post-loss financing, con
tingent financing, limited liability, and organizational design. Each
of these strategies will be examined in detail in later chapters.
In earlier chapters we examined how diversification can re
duce risk. Combining risk exposures will cause the relative risk to
fall. This process suggests that risk management strategies should
be coordinated. This view was strengthened by the observation
that many of the costs of risks were related to the overall risk to
the firm, rather than to the risk to a specific division or the risk
from a specific source. In the final part of this chapter we looked
at integrated risk management strategies. The strategies derived
fall into two distinct groups. The hedge strategies focus on a spe
cific risk that is reduced or removed by being transferred to an
other party. One expression of integrated risk management is the
TABLE
8-3
Rifle Shots and Blunderbusses-Focused and Global Strategies
Tool —
Source 1
Property
Insurance
Liability
Insurance
Interest Rate
Cap or Floor
Foreign
Exchange
Forward
Short Industry
Index
Market
Derivative
Simple
Leverage
Contingent
Refinancing
rj
2
Contingent
Leverage
Compensation
Renegotiation
Tax Arbitrage
Property
Damage
Liability
Loss
Interest
Rate Risk
Foreign
Exchange
Risk
Industry
Risk
Market
Risk
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PART 2 Risk Management Strategies
current trend to bundle insurance coverages into a single product
that hedges across a number of sources of risk. However, the var
ious dual strategies are usually not specific to source of risk and
are naturally integrated. This discussion will prepare us for later
chapters. We finished the chapter by illustrating that integrated
risk management does not imply that we should hedge everything
in sight, or design equal levels of protection against different types
of risk. Rather, managing one risk has implications for other risks
and strategy is best coordinated.
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