1. DISCOUNTED CASH FLOW MODELS
Richard A. Derrig
Senior Vice President
Automobile Insurers Bureau of MA
CAS Ratemaking Seminar
March 10, 2000
San Diego, CA

2. ONE ESTIMATION PROBLEM & FIVE DEVELOPMENTS
Excess Market Risk Premium
CAS Risk Premium Project
Small Stock Effect/Sum Betas
Full Information Betas
Surplus Allocation
Loss Distribution Betas

3. EXCESS MARKET RISK PREMIUM
Definition: MRP = RM - RF
RF depends on horizon length
RF = T-Bill, Int. Govt, Long Govt.
MRP = RM-Tbill,
RM-Int .Govt.
RM-Long Govt.

4. EXCESS MARKET RISK PREMIUM
Problem 1: How Do I Estimate MRP Value?
Problem 2: Does RF + Beta * MRP Work?

11. SIMPLE CAPM IS DEFICIENT ADD SMALL STOCK EFFECT

13. CAS RISK PREMIUM PROJECT
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

14. SMALL STOCK EFFECT/SUM BETA
Small Stock Effect: Smaller Decile (MKT CAP) Returns Exceed CAPM Expected
Theory: Non-Systematic Risk Based on Information Flow and Liquidity
Practice: Deciles 5 to 10, % (5) to 3.75% (10) Excess of CAPM
Example: MA Companies 1.3%
Ibbotson, Kaplan & Peterson (1997): Cross-Autocorrelations in Returns; “Sum Beta” adds One Lag; Sum  =  + -1
Sum Beta “Explains” Some of Small Stock Effect

15. FULL INFORMATION BETA Problem: Public Firms not all “Pure Play”
Solution: Industry Equity Beta via
Sales Weighted Full
Market Regression
P & C: Equity Beta 12/31/98 of 0.92
Sum Beta Effect: Not Calculated

16. SURPLUS ALLOCATION Surplus by Company stands behind all lines
Surplus by Line needed to allocate taxes and other by line Costs.
Myers-Read (1999): Theory Allows Unique Additive Allocation of Capital by “Fairness” to Guaranty Fund Criteria and Options Pricing Methods
Properties: Higher Line Covariance with Liab (Asset) Portfolio Implies Higher (Lower) Surplus
Key Equation: Default Option = F (Liabilities, Assets, A/L)

17. LOSS DISTRIBUTION BETAS
CAPM Loss Beta (Fairley, 1979) has
 = F(A,L,T,S, More (?)), No Default
Problem: All Liability Dollars Have Same Risk
Butsic (1999): Unique Surplus Allocation if Price Homogeneity (Same Marginal Default Option).
Surplus Allocation Across Coverage Layers (Loss Distribution)
Layer Beta and Surplus Increasing by Limit
Risk Loads by Layer
Example: Catastrophe Risk, Layer Betas 0.18 to 8.29
Stay Tuned for More Developments

18. REFERENCES
Kaplan, Paul D. and James D. Peterson, (1998), Full-Information Industry Betas, Financial Management, Summer.
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.
Myers, Stewart C. and James A. Read, Jr., (1999), Surplus Allocations for Insurance Companies, AIB Working Paper, July.
Butsic, Robert P, (1999), Capital Allocation for Property-Liability Insurers: A Catastrophe Reinsurance Application, Casualty Actuarial Society Forum, Spring.