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 Pricing Areas for Further Study Concluding Comments 9/25/2020 2

Introduction • Hypothesis – One “Price of Risk” permeates all financial transactions • Definitions – Price of Risk – Price for One “Standard Unit of Risk” – volatility of measure relative to the expected measure, that is, the Coefficient of Variation 9/25/2020 3

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 9/25/2020 4

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 9/25/2020 5

Risky Cash Flows • There are two ways to be a buyer of risk – Pay Certain Amount Today => Get Uncertain Cash Flows in the Future ies uq it g E RR yu in hest I B le: : Hig p m ve Exa bjecti O IRR=10% Limited Downside Interpretation: Getting 10% return (Other investments must yield more than 10% to be more worthwhile) – Get Certain Amount Today => Pay Uncertain Cash Flows in the Future nce a r nsu R I ng IR elli west S le: : Lo p m ve Exa bjecti O IRR=10% Limited Upside Interpretation: Paying 10% return (Must get at least 10% return on premium to break even) 9/25/2020 6

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 9/25/2020 7

Risky Cash Flows – Market Price of Risk – We can use the S&P 500 and implied volatility to find 9/25/2020 8

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) 9/25/2020 9

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 9/25/2020 10

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” 9/25/2020 11

Underwriting Cycle • Price of Risk 9/25/2020 12

Underwriting Cycle • Price of Risk 9/25/2020 13

Underwriting Cycle • “Fair” Price of Insurance 9/25/2020 14

Underwriting Cycle • “Fair” Price of Insurance 9/25/2020 15

Underwriting Cycle • Historical Combined Ratios n U t u t n e r iffe b , s t men i t i r w der n ro i v n e le yc C ng ts s i s r pe High Equity and Bond Returns D Low inflation, low interest rates Inflation soars Source: A. M. Best 9/25/2020 16

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! 9/25/2020 17

Pricing • Traditional Insurance Pricing • Insurance Option Pricing • Creating two indexes 9/25/2020 18

Pricing • Systematic Over and Under Pricing In Sample Bear Bull Source: A. M. Best 9/25/2020 19

Pricing • Systematic Over and Under Pricing Out of Sample Source: A. M. Best 9/25/2020 20

Pricing • Systematic Over and Under Pricing Forecast Source: A. M. Best 9/25/2020 21

Areas for Further Study • Framework Expected Earnings Equity Prices Market Price of Risk Bond Prices Interest Rates Option Prices Insurance Prices – For example Equity Price = f(interest rates, earnings growth, price of risk) 9/25/2020 22

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” 9/25/2020 23

Framework/ Areas for Further Study • Difference between actual and implied earnings growth has 28% correlation with weekly equity returns since 1986 9/25/2020 24

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! 9/25/2020 25

Thanks!