CS – 15 Risk Premium for Insurance Product Pricing

1. CS – 15 Risk Premium for Insurance Product Pricing Steve Mildenhall, AON Re Dave Ingram, Milliman USA Don Mango, AM Re

2. Risk Premium for Insurance Product Pricing Stephen MildenhallCAS/SOA ERM SymposiumWashington DC, July 2003

3. Why a Risk Premium? • Need to make a profit • Need to be reasonably confident of making a profit • Risk Premium is an all encompassing term • Covers frictional costs • Covers pure risk (toss of fair coin) • Compensation for bearing risk under uncertainty • Philosophical distractions should be resisted

4. State of the world Policy Payout w L All of the above Financial Consequences of policy Probabilities Risk Premium: 2000BC-today

5. Standard deviation Variance Semi-Variance Percentile/VaR Tail-VaR Wang Transform Esscher Transform Utility-based Micro-view of single risk SD, Variance,… of what? Which measure is appropriate? Risk Premium

6. Measures of Risk • Problem: collapse distribution to a number • All moments may not be enough to determine distribution! • No consensus methodology • Rothschild-Stiglitz offer four possible definitions of when X is “more risky” than Y • X = Y + noise • Every risk averter prefers Y to X (utility) • X has more weight in the tails • Var(X) > Var(Y) 1, 2, and 3 are equivalent and are different from 4

7. Parameter Risk: don’t delude yourself • Variance of losses in your model is not the same thing as variance of losses! • Hayne’s Loss Reserving Example (CLRS) • Leverage, Excess Policies and Jensen’s inequality • Need to compute the mean correctly • Risk load should not be used to compensate for miscellaneous actuarial inadequacies Don’t believe a risk load formula that says a new small line is a good thing!

8. Size: what is a large risk? • Parameter risk is all that matters…almost • Process risk matters for large risks • Large? • 100M households in US • $1M loss = 1¢ per household • $100M loss = $1 per household • $1B loss = $10 per household • $10B loss = $100 per household Large

9. Size: what is a large risk? • Heterogeneous distribution of wealth • Demographics • Ultimate risk bearers are individual insureds • Population concentrations correlated to risk loads • Frequency of losses, size of market Don’t believe a risk load formula that does not account for population demographics

10. Big Picture: moving beyond individual policy risk States of the world relevant for one policy Policy Payout All states of the world Multiple states yielding same loss L for one policy w L Projection with loss of information

11. Big Picture: moving beyond individual policy risk

12. Big Picture: moving beyond individual policy risk • Rodney Kreps, co-measures • P/C: Catastrophe (re-)insurance • Cat models explicitly quantify correlation • Life: Hedging interest rate and investment risk

13. Three Points to Remember • Parameter Risk • Size • Think Big-Picture

14. Pricing for Risk David Ingram ERM Symposium Washington DC, July 2003

15. Pricing for Risk • RMTF Survey of current Practices • Methods for Setting Risk Margins • Charge for Risk Capital • Risk Adjusted Hurdle Rates • Adjusted Target Calculation • Replication

16. How Do you Price for Risk?

17. What is the basis for Risk Adjustment?

18. What is the basis for Risk Adjustment?

19. What is the basis for Risk Adjustment?

20. What is the basis for Risk Adjustment?

21. What is the basis for Risk Adjustment?

22. Methods for Setting Risk Charge • Judgment Methods • Quantitative Methods

23. Judgment Methods • Risk Premium based on • Prior products • Market prices • Comfort with particular risks • Relative perceived risk of company products

24. Quantitative Methods • Charge for Risk Capital • Risk Adjusted Hurdle Rates • Adjusted Target Calculation • Replication

25. Charge for Risk Capital • Most common quantitative risk adjustment to pricing • Charge is: • (HR – is) * RCt • Where HR is Hurdle Rate • is is the after tax earnings rate on surplus assets • RCt is the risk capital in year t

26. Charge for Risk Capital • Is it actually a charge for risk? • Or just a cost of doing business? • It is a charge that is proportionate to risk • If there are other risk charges or adjustments, need to be careful not to double charge for risk

27. Risk Adjusted Hurdle Rates • Efficient Frontier Analysis • Market Analysis

28. Efficient Frontier Analysis Process • Brainstorming • Modeling • Display / Identify Frontier • Determine Risk/Reward Trade-off Parameters

29. Efficient Frontier Efficient Frontier

30. Market Analysis • Study Relationship between Return and • Product Concentration • Income/ ROE volatility For a group of successful companies. • Develop Target returns • Based on Products • Based on volatility

31. Product Concentration Product A – 12% Product B – 15% Product C – 10% ROE Volatility Target ROE = Risk-free rate + 3.7  22.83% +1.83% ln() 7.5% +  Market Analysis

32. Market Analysis While this is “quantitative”… Data is so thin that much judgment is needed to develop targets

33. Study of Insurance Company ROE ROE Std Dev Ratio Group I 13.96% 6.71% 48% Group II 10.52% 11.32% 107% Group III 10.12% 16.02% 158% Group IV 4.86% 25.96% 534% Group V (3.69%) 21.13% NM

34. Adjusted Target • Instead of concentrating on 50th Percentile results (or average results) • In a stochastic pricing model • Pricing Target adjusted to 60th, 70th or 80th Percentile

35. Adjusting Target

36. Replication • Finance – Law of One Price • Two sets of securities that have the same cashflows under all situations will have the same price • Replication – if you can replicate the cashflows of an insurance product with marketable securities then market price of securities is the correct price for product

37. Risk & Return • Bonds – Volatility of Bond Prices 8.6% • Average Return on Bonds – 5.8% compound Average, 6.1% Arithmetic Average • Risk/Reward = 139% to 148% • Stocks – Volatility of Stock Returns 20.5% • Average Return – 10.5%, 12.2% • Risk Reward = 168% to 194%

38. Insurance Products • Cannot easily hedge with 100% efficiency • But can compare…

39. VA Product vs. Common Stocks • Insurance Product – VA • $10 B AV • Std Dev = 200, CTE 90=429 Compare to • Common Stock Fund A • $300 M Fund • Std Dev= 200, CTE 90= 390 • Common Stock Fund B • $330 M Fund • Std Dev= 220, CTE 90= 429

40. Returns • Insurance Product – VA • 75 Expected Return • Common Stock Fund A • 100 Expected Return • Common Stock Fund B • 110 Expected Return

41. Recommendations • Work on evolving from Judgment to Quantitative • Quantitative methods need to be based on Pricing Risk Metric • Ultimately should tie to market pricing for risks

42. Risk Premiums Don Mango AM Re

43. Where Are We Going? • Commonalities • Simulation Modeling • Explicit Valuation • Aggregate Risk Modeling • Interaction Effects

44. Commonalities • Valuation of Contingent Obligations (“VALCON”) • Levered investment trusts • Strong dependencies on economic and capital market conditions

45. Commonalities • Long time horizons and held-to-maturity (“HTM”) portfolios • We sell “long-dated, illiquid, OTC derivatives” • We have an incomplete, inefficient secondary market • We retain magnitudes of risk that bankers would never dream of

46. Commonalities • IMPLICATIONS: • This seminar should be the norm, not the exception. • There may be hybrid products in our future. • We may not be able to simply borrow capital market techniques.

47. Simulation Modeling • Aka “Monte Carlo valuation” • Financial engineers use it to price long-dated, illiquid, OTC derivatives • Devil is in the parameters and dependence structure

48. Simulation Modeling • IMPLICATIONS: • We are heading the same direction. • We need transparency or at least explicitness of assumptions.

49. Explicit Valuation • Complete, efficient market affords participants the luxury of not having to think or care or have any opinion of the fundamental value of a product • Counting on the continued presence of counterparties to limit downside • Bloomberg gives you “the price”

50. Explicit Valuation • Incomplete, inefficient market requires some explicit valuation by its participants • True, you could be a “delta” off a content provider • 10% below Swiss Re or Met Life