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DISCOUNTED CASH FLOW MODELS
Richard A. Derrig Senior Vice President Automobile Insurers Bureau of MA CAS Ratemaking Seminar March 10, 2000 San Diego, CA
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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
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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.
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EXCESS MARKET RISK PREMIUM
Problem 1: How Do I Estimate MRP Value? Problem 2: Does RF + Beta * MRP Work?
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SIMPLE CAPM IS DEFICIENT ADD SMALL STOCK EFFECT
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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
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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
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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
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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)
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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
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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.
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