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Insurance Pricing & Underwriting Cycles Analysis

Explore the correlation between price of risk and asset pricing in the insurance industry. Discuss underwriting cycles, pricing mechanisms, and areas for further study.

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Insurance Pricing & Underwriting Cycles Analysis

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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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