DISCOUNTED CASH FLOW MODELS

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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 DEFICIENTADD 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, 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

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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.