CAS RISK PREMIUM PROJECT
Richard A. Derrig - Moderator
Auto Insurers Bureau of Massachusetts
Richard D. Phillips
Georgia State University
Robert P. Butsic
Fireman’s Fund Insurance
CAS Loss Reserve Seminar
Minneapolis, MN
Sept. 19, 2000
THE RISK PREMIUM PROJECT (RPP)
Phase I and II Report
Committee on Theory of Risk
 Discount Rate for Liabilities
 Literature Review
 Actuarial: Process and Parameter Risk
 Financial: Systematic Risk
 Academic: Dave Cummins, Rich Phillips
 Industry: Bob Butsic, Rich Derrig

THE RISK PREMIUM PROJECT (RPP)
Phase I and II Report
(www.casact.org/cotor/rpp)
1.
2.
3.
4.
Introduction
Literature Search
Theoretical Conclusion
Proposals for Phase III
Appendix A. Risk Premium Project Bibliography
Appendix B. Implications for Fair Value Accounting
THEORETICAL CONCLUSION #1

The opinions of financial economists and
actuaries regarding the role of systematic
vs. non-systematic risks in determining the
equilibrium insurance prices are converging.
Both see a role for non-systematic risk in
pricing.
THEORETICAL CONCLUSION #2

A systematic risk adjustment for the
duration of the cash flows associated with
a line of insurance should be included in
the discount rate used to determine the
fair value of the insurance premium.
The adjustment to the discount rate will
be a function of the maturity structure of
the liabilities.
THEORETICAL CONCLUSION #3

The average returns of financial assets
cannot be adequately explained by the CAPM
beta. Researchers have shown extensions of
the CAPM which include additional factors
significantly enhance the explanatory power
of the models. In addition, although
research using more sophisticated empirical
tests has been published extending the
CAPM, similar research focusing on insurance
company returns does not currently exist.
THEORETICAL CONCLUSION #4

A theoretically consistent way to allocate
the costs of holding equity capital to
individual lines of insurance has been
identified. Thus, the costs associated with
holding capital can now be charged to
individual lines of insurance.
THEORETICAL CONCLUSION #5
 The
risk of insurer default to the
policyholder should be recognized
in pricing the risk transfer.
Fair Value Accounting Implications

Market Value Balance Sheet
– Treatment of Insurer Default
– Franchise Value
Accounting for the Risk Load
 Process Risk and Value Additivity

– Risk Management Costs
– Allocation of Joint Costs
Market Value Balance Sheet
One-period, idealized
 No default
 B/S at time policy is sold:

Assets
Investments
Liabilities
P+S
Claims
L
Income Taxes
T
Equity
S
Default Option
No guaranty fund, limited liability
 Fair Premium = P - D
 B/S at time policy is sold:

Assets
Investments
P–D+S
Liabilities
Claims
L–D
Income Taxes
T
Equity
S
Liability Treatment
Liability as reduced amount L -D
 Separate liability offset (-D)

Assets
Investments
P–D+S
Liabilities
Contractual Claims
Expected Default
L
–D
Income Taxes
T
Equity
S
Default Under Guaranty Fund
Premiums as if no default
 Liability to GF offsets expected default

Assets
Investments
Liabilities
P+S
Claims
G Fund Liability
Income Taxes
Equity
L-D
Dg
T
S + D - Dg
Franchise Value for Ongoing Insurer
Surplus includes value of intangibles
 Breakup value of surplus is Sf
 With no guaranty fund:

Assets
Investments
Liabilities
P - D + Sf Contract. Claims
Franchise V
F
Income Taxes
Default
D
Equity
L
T
Sf + F
Consequences of Default with FV
Default and franchise value are inversely
related
 Effect of increasing firm risk
 Owners are worse off if (change in F) >
(change in D)
 Not showing F as asset creates perverse
results

Process Risk and Value Additivity
Process risk commands a price
 Risk management costs (Stulz)
 Reinsurance, capital, diversification
 These costs don’t appear in risk loads

Types of Residual Risk

Non-priced process risk

Priced process risk

Priced systematic
Allocation of Joint Costs

Systematic risk loads have natural
value additivity
– Finance models such as CAPM, APM

How does market treat cost of
residual process risk?
– Examples: cost of holding capital, risk
load for catastrophes
Solution: Economic Allocation
Methods
Microeconomic model of joint cost
allocation
 Look at marginal impact on total of
separate (line) inputs
 Economic allocations have value
additivity

EMPIRICAL PROJECTS
Phase III #1
Full Information Beta For Insurance Lines
 If Full Information P&C is 0.92 (1998), How
Does That Distribute By Line?
 DATA: CRSP and NAIC
 The FI Equity Beta With Sum Betas
(Autocorrelation) Included And/Or FamaFrench Model
 Industry Level And Firm Level
 Relatively Straightforward Datawise;
Output Will be Understandable

EMPIRICAL PROJECTS
PHASE III #2
Allocation of Surplus by Line of Insurance
 Myers-Read Model Applied to
Representative Insurer(s)
 Calculation of Covariances of Asset and
Liability Types
 DATA: CRSP and NAIC at Georgia State
and More(?)
 Output Compared to Real World Data

PHASE III
REFERENCES
Butsic,
Robert P, (1999), Capital Allocation for PropertyLiability Insurers: A Catastrophe Reinsurance Application,
Casualty Actuarial Society Forum, Spring.
Ibbotson,
Roger G, Paul D. Kaplan and James D. Peterson,
(1997), Estimates of Small Stock Betas are Much Too Low,
Journal of Portfolio Management, Summer.
Kaplan, Paul D. and James D. Peterson, (1998), FullInformation Industry Betas, Financial Management, Summer.
Myers,
Stewart C. and James A. Read, Jr., (1999), Surplus
Allocations for Insurance Companies, AIB Working Paper, July.
APPENDIX A
LITERATURE RECOMMENDATIONS
[TOP TEN NON-CAS]
Campbell,
John Y., Andrew W Lo, and Craig A. MacKinlay
(1997), The Econometrics of Financial Markets (RPP 134)
Campbell,
John Y. (2000), Asset Pricing at the Millennium,
NBER Working Paper (RPP238)
Cochrane,
John H. (1999), New Facts in Finance, NBER
Working Paper (RPP188)
Cummins,
J. David, and Richard D. Phillips, (2000),
Applications of Financial Pricing Models in Property-Liability
Insurance, The Handbook of Insurance Economics (RPP130)
Cornell,
Bradford (1999), Risk, Duration and Capital
Budgeting: New Evidence on Some Old Questions, Journal of
Business, 72:2 (RPP37)
APPENDIX A
LITERATURE RECOMMENDATIONS
[TOP TEN NON-CAS]
Froot,
Kenneth A., and Jeremy C. Stein (1999), Risk Management, Capital
Budgeting, and Capital Structure Policy for Financial Institutions: An
Integrated Approach, Journal of Financial Economics, 47:1 (RPP9)
Froot,
Kenneth A., Jeremy C. Stein, and David S. Scharfstein (1993), Risk
Management: Coordinating Corporate Investment and Financing Policies,
Journal of finance, 48:1 (RPP10)
Merton,
Robert C. and Andre F. Perold, (1993), Theory of Risk Capital in
Financial Firms, Journal of Applied Corporate Finance,6:3 (RPP177)
Babbel,
David F. (1999), Components of Insurance Firm Value, and the
Present Value of Liabilities, Investment management for Insurers
(RPP225)
Barberis,
Nicholas, Ming Huang, and Tano Santos (1999), Prospect Theory
and Asset Prices, NBER Working Paper (RPP218)
EMPIRICAL PROJECTS
FUTURE
Equity Beta for Insurer via Multifactor
Asset Pricing Models
 Campbell-Mei, Fama-French and other
Multifactor Models Estimated for Insurers
 Alternative Factors Relating to Insurance
Tested for Additional Explanatory Power
 DATA: CRSP and NAIC at Georgia State
and More
 Output Compared to Standard and Other
Equity Betas for Insurers

EMPIRICAL PROJECTS
FUTURE
Risk Load and Pricing via Cummins, Allen
and Phillips Model
 Insolvency Put, Growth and Company
 Type Variables are Calculated to Estimate
The Economic Premium Inclusive of Risk,
Tax and Friction Loadings
 DATA: CRSP and NAIC at Georgia State
 Relatively Straightforward Datawise;
Output Will be Understandable
