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FIN-10:Risk and Return - Actuarial Considerations

CAS Seminar on Ratemaking Las Vegas, Ne March 11-13, 2001 Moderator/Panelist Robert F. Wolf William M. Mercer/MMC Enterprise Risk Panelists Russ Bingham Hartford Financial Services. FIN-10:Risk and Return - Actuarial Considerations. Agenda. Overview

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FIN-10:Risk and Return - Actuarial Considerations

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  1. CAS Seminar on RatemakingLas Vegas, NeMarch 11-13, 2001Moderator/PanelistRobert F. WolfWilliam M. Mercer/MMC Enterprise RiskPanelistsRuss BinghamHartford Financial Services FIN-10:Risk and Return - Actuarial Considerations

  2. Agenda • Overview • Net Present Value & Internal Rate of Return Models - Characteristics and Considerations • Complete Rate of Return Model • Compare and Contrast • Questions and Answers • FIN-11: Parameter Estimation/ Current Research

  3. Marginal Balance Sheet Impact Useful to Look at a hypothetical Balance Sheet where all elements are at market values, not statutory accounting values. Assets Liabilities K Let K = Policyholder Supplied Funds. Let S = Shareholder Supplied Funds K+S Capital S

  4. Costs RL Returns RA Costs RE Marginal Balance Sheet Impact Let RA = Return on Assets supplied by both policyholders and shareholders. RL = Cost of Debt. Borrowing From Policyholders. Borrowing PHSF RE = Cost of Capital. Using SHSF K+S K S

  5. Costs RL Returns RA Costs RE Marginal Balance Sheet Impact This relationship develops into the generally accepted view that an insurance company is a levered trust. K+S K Levered Trust (K+S)RA = KRL + SRE S

  6. Mission Determine Fair Premium

  7. Marginal Balance Sheet Impact Product Market Supply = F(cost of capital) Policyholders supply funds (premiums) in return for compensation for adverse financial outcomes from fortuitous contingent events. PHSF Flow = Premiums in return for expenses and losses. Financial Market Stockholder Invests S to Back Policyholder Supplied Funds (K) In Return, Equityholders Demand a Return (Re) on Stockholder Supplied Funds (S) (Dividends or future appreciation of enterprise value) SRe K S

  8. Derivation of Equilibrium Underwriting Profit ….So Equityholders want SRE Insurance Company Can Provide Equityholders a Portion of Their Return by Investing S in portfolio of securities. ...Have to return the remainder S (RE-RA) from Insurance Operations (i.e. Returns on Policyholder Supplied Funds)

  9. Why is RE> RA? ….because equityholder are taking the risk. They can achieve RA by investing in the same portfolio of securities on their own.

  10. Fair Rate of Return Solve for RL such that Stockholder demand in returns in excess of investment returns equates to the economic return on Policyholder Supplied Funds PHSF SHSF = K(RA-RL) S (RE-RA)

  11. Cost of Debt Capital ===> Profit Load • ……If we solve for RL, RL = RA - (S/K)(RE- RA) • RL should serve as Risk Adjusted Discount Rate for Loss Reserves • Risk Adjusted Rate < RA • Let Ru = Underwriting Profit Margin • RU = - K RL/Premium • Insurance Company Earns Positive Economic Returns on Underwriting if RA > RL (Ru> - (K/Premium) RA )

  12. Fair Rate of Return Solve for RU such that Stockholder demand in returns in excess of investment returns equates to the economic return on Policyholder Supplied Funds PHSF SHSF = (K/Prem) RA+RU (S/Prem) (RE-RA)

  13. Underwriting Leverage Investment Leverage Solving for Return on Equity …….We get the usual leverage formula: RE = (1 + K/S)RA + (Prem/S)RU Parameters RE, RA, K, S What Should You Use for Each?

  14. Cost of Capital (RE) Dividend Growth Model CAPM Cost of Holding Capital RBC Best’s Undiscounted Reserves Policyholder Supplied Funds (K) Business as Usual Investment Income (RA)- New Money Yields Imbedded Yields Risk Free Rate How Much Capital (S) Allocated v. Apportioned Marginal P = D (1+Growth)/(1+ Cost of Capital) + D(1+Growth)2/(1+ Cost of Capital)2+... = D(1+Growth)/(Cost of Capital - Growth) Considerations: Parameters

  15. Discounted Cash Flow Models Two General Types Net Present Value Internal Rate of Return

  16. Net Present Value Models • More Emphasis on Policyholder and Insurance Company Flows (Myers/Cohn) • Select IRR = Cost of Capital • NPV = CF1 / (1+IRR) + CF2/(1+IRR)2+ ... • If NPV > 0, Good Deal • If NPV < 0, Bad Deal • Set Premiums P, such that NPV = 0 • Solve for Ru : P = L(1+G) + F 1- V-Ru

  17. Internal Rate of Return • Policyholder Supplied Funds important only to extent it effects Shareholders and the Insurance Company Flows • 0 = CF1 / (1+IRR) + CF2/(1+IRR)2+ ... • Solve for IRR • If IRR > Cost of Capital then Good Deal • If IRR < Cost of Capital, then Bad Deal • Set Premiums P, such that IRR = Cost of Capital

  18. Discounted Cash Flows Examples Certain and Uncertain CFs

  19. DCF Model - Cashflows are Certain All Cash Flows are Risk Free. Hence all cashflows are discounted at the risk free rate CFs are at end of period. Loss Paid at end of year

  20. Solve for LR such that NPV=0

  21. Indifference between a certain loss ratio of 79.5% and an uncertain LR of 75.0% Risky Cashflows By Definition, Inv Income Certainty Equivalent is risk-free rate

  22. Assumptions Premiums of $100 Paid 80% @Inception, 20% a year later Losses are paid at the end of each of the next three years in proportions of 30%,20%, 10% Expense Ratio is 20% of premium, 75%of which is paid @inceptions, 25% a year later. Investment Yield is 10.0% No Federal Income Taxes Reserve/Surplus Ratio is 2.5 Another Hypothetical Example

  23. Discount Cash Flows Discounted at the Rate of the Cost of Capital With a -5.0% profit load, NPV >0, therefore we should write these policies

  24. Solve for Premium such that NPV=0 One can write at an 88.7%LR to cover cost of capital A -8.7% profit load is floor benchmark

  25. Set Discounted Cash Flows to 0 and Solve for IRR With a -5.0% profit load, the IRR = 20.5% therefore we should write these policies as it exceeds cost of capital of 15.0%

  26. Solve for Premium such that IRR=Cost of Capital One can write at an 88.7%LR to cover cost of capital. Again, -8.7% profit load is floor benchmark

  27. If Premium Payment Patterns are Revised From 80/20 Payouts to 45/45/10, then IRR moves from 20.5% to 13.2%. If revised from 80/20 to 100/0, the IRR moves from 20.5% to 23.8% If Loss Payments Revised From 50/30/20 to 20/30/50, the IRR moves from 20.5% to 23.4%. If revised to 90/10, then the IRR moves to 15.2% Assumption Variations

  28. If Less Surplus is Required, say reserves/surplus ratio = 3, then IRR moved from from 20.5% to 22.5% More Leverage If More Surplus is Required, say Reserves/Surplus Ratio = 2, then IRR moves from 20.5% to 18.5% Less Leverage Assumption Variations

  29. Myers-Cohn (a Particular NPV Application) Assumptions • Insurance Company Invests Efficiently - Ru Should Not Compensate for Inefficient Insurer Investment Portfolios • Equityholders (SH) are Efficient Investors - Ru Should not Compensate for Inefficient Equityholders • S: Surplus Can be Imputed to a Policy • Underwriting Models Should Only Reflect Systematic Risk (i.e. Risk That is Undiversifiable)

  30. Myers-Cohn (a Particular NPV Application) Assumptions • ….also directly considers the double taxation issue for shareholders and considers is a cost born by Policyholders

  31. Myers-Cohn Equation Net Present Value of Policy = Present Value of Collected Premium - The Present Value of Loss and Loss Adjustment Expense - Present Value of Other Expenses - Present Value of Tax on Underwriting Profit - Present Value of Tax on Investment Income on Policyholder and Stockholder Supplied Funds

  32. …….One Approach to estimate risk adjusted rate uses Capital Asset Pricing Model

  33. Capital Asset Pricing Model Expected Return Expected Return 20.1 R*= 15.4  Risk Premium Rf= 6.0 1.0 1.5  = Risk R* = rf + * (market risk premium)

  34. Capital Asset Pricing ModelQuick Review • Investors are Risk Averse • Only Care About Mean and Variance of Portfolios • E(Ri) = Rf + Bi (E(Rm) - Rf) • Ri = Rate of Return on Asset i • Rf = Risk Free Rate • Rm = Rate of Return on Market Portfolio • Bi = Cov (Ri.Rm)/Var (Rm)

  35. Estimation of Underwriting Betas Be = (1+K/S)Ba +(1/S)Bu . One Way to do it. See Derivation in Appendix.

  36. Observations on Equilibrium E(Ru) = -KRf + Bu(E(Rm)-Rf) • Derivation in Appendix • Similar to Certainty-Equivalent Formula • Does Not Depend on Investment Income • Does Not Depend on any Return on Equity Target • Does Not Depend on Premium to Surplus Leverage • Risk Premium (E(Rm)-Rf) Fairly Stable

  37. Estimating Underwriting Betas directly has some issues…... • Line of Business Considerations • State Betas Difficult to Estimate • Few Pure Property/Casualty Insurers Publicly Traded • Prior Underwriting Profits Based Upon Prior Methodologies - Nonapplicable

  38. NPV v. IRR • Personal Bias - I like NPV better. • Bad Experiences with IRR • Case Study: Captive Feasibility and Tax Deductibility

  39. Case Study • Client is self-insured • Deducts Losses when Losses are paid. • If accident year has 10 year pay-out, tax deductions are amortized over ten years • If pay a premium to insurer, tax is deducted upon payment of premium (implicitly deducting for future paid losses in year one).

  40. Case Study • Client can Form a Captive Insurance Company • If special conditions are met, premium paid to Captive may be deducted. • Feasibility - Is this Worthwhile?

  41. $100 Million of Tax Deductions Taken as Losses are Paid If you form a Captive, and certain conditions are met….. …then you can take your deductions as premiums Cash Flow Difference If your investment in the Captive is no more than $26.7 Million, then form the captive. At $26.7 Million, the NPV=0.

  42. NPV Approach • As longs as marginal Cost of the Captive is less than $26.7 Million... … • It’s a good deal.

  43. …..Now Let’s do it the IRR Way

  44. $100 Million of Tax Deductions Taken as Losses are Paid Set NPV to 0 Cash Flow Difference If you invest $20.0 Million in captive, your accelerated tax deductions imply IRR of 9.3% which is < cost of capital of 15.0% …….therefore bad deal?

  45. IRR Approach • The Greater the Cost of the Captive the Better the IRR? • …the better the Deal? • …what’s going on?

  46. IRR- Practical Pitfalls • Variation of the Classic IRR Pitfall “Oil Pump” Case • …and I fell right into it. • Moral of the Story, if you can’t explain it intuitively, it’s probably wrong. • NPV never served me wrong yet. • ….Use NPV.

  47. IRR - Practical Pitfalls Consider two Choices - Cost of Capital =12.5% Investment A Borrowing B Time 0 -100.0 Million Time 1 + 50.0Million Time 2 +75.0 Million Time 0 100.0 Million Time 1 -50.0Million Time 2 -75.0 Million IRR(A) = 15.1% IRR(B) = 15.1% Bad Deal Because as Borrower, because you want IRR<Cost of Capital Good deal because 15.1%>12.5%

  48. IRR Pitfalls • Property/Casualty Cash Flows may have >1 sign reversal • deposit premiums + audit premiums • retrospective premium adjustments • Agents Balances • Are you borrowing/investing? • Reinvestment Rate Assumption

  49. IRR v NPV Consider two Investments Investment A Investment B Time 0 -12.0 Million Time 1 + 10.0Million Time 2 +6.5 Million Time 0 -12.0 Million Time 1 + 5.0Million Time 2 +12.5 Million Using NPV, Investment B is better as long as discount rate <20.0%, otherwise Investment A is Better. Because NPV(A) < NPV(B) if IRR<20.0% Why? NPV(B)<NPV(A) if IRR>20.0%

  50. IRR v. NPV Again Consider Two Investments Investment A Investment B Time 0 -12.0 Million Time 1 + 10.0Million Time 2 +6.5 Million Time 0 -12.0 Million Time 1 + 5.0Million Time 2 +12.5 Million Now Using IRR, IRR(A) = 26.3% while IRR(B) = 25.0% …Implies …..Investment A better than Investment B True…..only if Cashflows in A are reinvested at a rate 26.3%

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