RISK PREMIUM PROJECT

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RISK PREMIUM PROJECT

• Richard A. Derrig
• Senior Vice President
• Automobile Insurers Bureau of MA.

Baylor University March 14, 2001
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INSPIRATION

• Q1
• "When the rubber hits the road, corporate finance
  theory of the last twenty-five years is not
  particularly relevant.
• Ren? M. Stulz

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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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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.

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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.

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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.

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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.

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THEORETICAL CONCLUSION 5

• The risk of insurer default to the policyholder
  should be recognized in pricing the risk
  transfer.

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THEORETICAL CONCLUSION 1

• Q3
• "I argue that the mainstream approach to capital
  budgeting focuses excessively on the special case
  where diversifiable risks do not affect the
  contribution of a project to the value of the
  firm. This approach ignores the impact of a new
  project on a firm's total risk and therefore
  often leads to an inappropriate assessment of the
  value of the project. I present arguments for
  why total risk is often costly and discuss how
  taking total risk into account in capital
  budgeting is necessary to make capital budgeting
  and capital structure decisions consistent."
• Ren? M. Stulz

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THEORECTICAL CONCLUSION 1

• Q2
• "Intermediaries take risks by investing their
  capital in illiquid and information-intensive
  financial activities. It is these imperfections
  in financial markets that allow intermediaries to
  make profits. But the imperfections are not
  merely a source of profit - they also create
  costs. That is, intermediaries must finance
  themselves by issuing claims that are at least
  partially illiquid and information-intensive.
  This suggests that exogenous shocks to
  intermediaries' financial capital should have
  implications for the pricing and availability of
  the instruments in which they invest.
• Kenneth A. Froot

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THEORETICAL CONCLUSION 2

• Q4
• "Our work bridges a gap between two common modes
  of analysis in empirical finance cross-sectional
  analysis of multifactor models, and fundamental
  analysis using the present-value relation. The
  former analysis breaks risk down into
  sensitivities to various factors, while the
  latter distinguishes between cash flow risk and
  discount rate risk. Here we combine these two
  models, using both contemporaneous
  cross-sectional information and time-series
  information to describe the dynamic behavior of
  asset returns".
• John Y. Campbell Jianping Mei
• Where do Betas Come from? Asset Price
• Dynamics and the Sources of systematic Risk.

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THEORETICAL CONCLUSION 3

• Q5
• "We then show that traditional estimates of beta
  are uncorrelated with future stock returns over
  the 1931 through 1994 time period. On the other
  hand, adjusted beta estimates are positively
  correlated with future security returns.
  Moreover, we show that adjusted estimates of beta
  partially explain the size effect in common stock
  returns."
• Roger Ibbotson, Paul Kaplan James Peterson
• Estimates of Small Stock Betas Are Much Too Low

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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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THEORETICAL CONCLUSION 3

• Q6
• "The usefulness of the CAPM and beta for the
  purpose of estimating the required rate of return
  on equity has been called into question, most
  notably, by Fama and French (1992, 1993, and
  1997). The evidence against the CAPM and beta
  has left many practioners helpless since no
  theoretically justified alternative model is
  easily implemented. Largely because of this,
  researchers have turned their attention to issues
  involving implementation of the CAPM."
• Paul Kaplan James Peterson
• Full Information Industry Betas

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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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THEORETICAL CONCLUSION 4

• Q7
• "Option pricing methods can be used to estimate
  surplus requirements for insurance companies and
  to allocate surplus line by line. Given the
  line-by-line composition of the insurance
  company's business, that allocation is unique and
  not arbitrary. To calculate the cost of writing
  policies in different lines of insurance surplus
  requirements should be allocated so that the
  marginal default value is the same in all lines."
• Stewart Myers James Read
• Surplus Allocation for Insurance Companies

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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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THEORETICAL CONLUSION 4

• Q8
• "Since capital allocation depends on the market
  values of losses by layer, not just the expected
  loses, the underlying risk load process
  influences the economic basis for capital
  allocation to layer. Both the allocated capital
  and risk loads depend on the particular loss size
  distribution. They both also share the value
  additivity property, where the sum of capital and
  risk loads over a subdivision of policies or
  layers, equals the total value."
• " The expected return on capital by layer can be
  determined from the market or fair premium, which
  depends on the capital allocation and risk load
  by layer. Because the amount of capital and the
  risk load arise from different economic
  processes, the expected ROE will not be a
  constant across all layers. In fact, the lowest
  layer will produce an expected ROE equal to the
  riskless rate."
• Robert P. Butsic
• Capital Allocation for Property-Liability
  Insurers
• A Catastrophe Reinsurance Application

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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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THEORETICAL CONCLUSION 5

• Q9
• "This paper uses a contingent claims framework
  to develop a financial pricing model of insurance
  that overcomes one of the main shortcomings of
  previous models - the inability to price
  insurance by line in a multiple line insurer
  subject to default risk. The model predicts
  prices will vary across firms depending upon firm
  default risk, but within a given insurer prices
  should not vary after controlling for
  line-specific liability growth rates."
• "Empirical tests using data on publicly
  traded property-liability insurers support the
  hypotheses prices vary across firms depending
  upon overall-firm default risk and the
  concentration of business among subsidiaries but
  within a given firm, prices do not vary by line
  after adjusting for line-specific liability
  growth rates.
• Richard D. Phillips, J. David Cummins Franklin
  Allen
• Financial Pricing of Insurance in the
  Multiple-Line Insurance Company

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REFERENCES

• Butsic, Robert P, (1999), Capital Allocation for
  Property-Liability 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),
  Full-Information Industry Betas, Financial
  Management, Summer.
• Myers, Stewart C. and James A. Read, Jr., (1999),
  Surplus Allocations for Insurance Companies, AIB
  Working Paper, July.
• Phillips,Richard D., J. David Cummins Franklin
  Allen (1998), Financial Pricing of Insurance in
  the Multiple-Line Insurance Company, Journal of
  Risk and Insurance, 654579-636