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DISCOUNTED CASH FLOW MODELS

DISCOUNTED CASH FLOW MODELS. Richard A. Derrig Senior Vice President Automobile Insurers Bureau of MA. CAS Ratemaking Seminar March 10, 2000 San Diego, CA. ONE ESTIMATION PROBLEM & FIVE DEVELOPMENTS. Excess Market Risk Premium CAS Risk Premium Project Small Stock Effect/Sum Betas

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DISCOUNTED CASH FLOW MODELS

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  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?

  5. SIMPLE CAPM IS DEFICIENTADD SMALL STOCK EFFECT

  6. 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

  7. 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, 1926-1998 0.87% (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

  8. 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

  9. 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)

  10. 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

  11. 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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