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An Examination of Insurance Pricing and Underwriting Cycles

An Examination of Insurance Pricing and Underwriting Cycles. AFIR Conference, September 2003, Maastricht, NL Chris K. Madsen, GE Frankona Re, Copenhagen, Denmark Hal W. Pedersen, University of Manitoba, Winnipeg, Canada. Overview. Introduction Risky Cash Flows Underwriting Cycle

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An Examination of Insurance Pricing and Underwriting Cycles

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  1. An Examination of Insurance Pricing andUnderwriting Cycles AFIR Conference, September 2003, Maastricht, NL Chris K. Madsen, GE Frankona Re, Copenhagen, Denmark Hal W. Pedersen, University of Manitoba, Winnipeg, Canada

  2. Overview • Introduction • Risky Cash Flows • Underwriting Cycle • Pricing • Areas for Further Study • Concluding Comments

  3. Introduction • Hypothesis • One “Price of Risk” permeates all financial transactions • Definitions • Price of Risk • Price for One “Standard Unit of Risk” • “Standard Unit of Risk” • volatility of measure relative to the expected measure, that is, the Coefficient of Variation

  4. Risky Cash Flows • When “Price of Risk” Increases • prices of equities fall • prices of corporate bonds fall (spreads widen) • prices of options rise • prices of insurance rise • When “Price of Risk” Decreases • prices of equities rise • prices of corporate bonds rise • prices of options fall • prices of insurance fall

  5. Risky Cash Flows • Present Value of Cash Flows • Basic discounting cannot account for this behavior. • Discount rate or cost of capital reflect the cost of money, not the cost of risk • The discount rate used for asset pricing is (most likely) not appropriate for insurance pricing • Present value calculations do not account for the inherent optionality of insurance

  6. Risky Cash Flows • There are two ways to be a buyer of risk • Pay Certain Amount Today => Get Uncertain Cash Flows in the Future • Get Certain Amount Today => Pay Uncertain Cash Flows in the Future IRR=10% Example: Buying Equities Objective: Highest IRR Interpretation: Getting 10% return (Other investments must yield more than 10% to be more worthwhile) Limited Downside IRR=10% Example: Selling Insurance Objective: Lowest IRR Limited Upside Interpretation: Paying 10% return (Must get at least 10% return on premium to break even)

  7. Risky Cash Flows • What is Insurance? • Financial transaction on losses • Selling (naked) call options on losses • Since insurance is an option, it would make sense to use option theory to price

  8. Risky Cash Flows • Market Price of Risk • We can use the S&P 500 and implied volatility to find

  9. Risky Cash Flows • Adding the “Price of Risk” the Black Scholes option pricing model • Breaking volatility in two: • Price of Risk (fluctuates constantly) • Coefficient of variation on loss returns (constant for a given loss scenario)

  10. Risky Cash Flows • Incorporating the “Price of Risk” into utility theory • Gerber and Pafumi (using exponential utility) • Including “Price of Risk” • Price of insurance in a portfolio • Total portfolio premium

  11. Underwriting Cycle • A.M.Best (A.M.Best Report, February, 1999) • “A.M. Best believes the property/casualty underwriting cycle has been replaced by a permanent ‘down market’” • Irving Fisher (Yale University, September, 1929) • “Stocks have been replaced by what looks like a permanently high plateau”

  12. Underwriting Cycle • Price of Risk

  13. Underwriting Cycle • Price of Risk

  14. Underwriting Cycle • “Fair” Price of Insurance

  15. Underwriting Cycle • “Fair” Price of Insurance

  16. Underwriting Cycle • Historical Combined Ratios High Equity and Bond Returns Different environments, but Underwriting Cycle persists Inflation soars Low inflation, low interest rates Source: A.M.Best

  17. Underwriting Cycle • Combined Ratio Model • Note: C is a significant indicator with a p-value of 1.3%, but it has the “wrong” sign. When option prices go up, so does the combined ratio!

  18. Pricing • Traditional Insurance Pricing • Insurance Option Pricing • Creating two indexes

  19. Pricing • Systematic Over and Under Pricing In Sample Bear Bear Bull Source: A.M.Best

  20. Pricing • Systematic Over and Under Pricing Out of Sample Source: A.M.Best

  21. Pricing • Systematic Over and Under Pricing Forecast Source: A.M.Best

  22. Areas for Further Study • Framework • For example Equity Price = f(interest rates, earnings growth, price of risk) Market Price of Risk Interest Rates Expected Earnings Equity Prices Bond Prices Option Prices Insurance Prices

  23. Areas for Further Study • Equity Index Prices (S&P 500) • Theoretical level (no earnings growth): risk-adjusted perpetuity • With earnings growth • Solve for Earnings Growth to get “Implied Earnings Growth”

  24. Framework/ Areas for Further Study • Difference between actual and implied earnings growth has 28% correlation with weekly equity returns since 1986

  25. Concluding Comments • Examination of “Price of Risk” to bridge asset pricing and insurance pricing • Development of insurance pricing option model • Review of underwriting cycle based on traditional pricing indexes and option pricing indexes • We have to get a handle on this!

  26. Thanks!

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