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Actuarial Science Meets Financial Economics Buhlmann’s classifications of actuaries Actuaries of the first kind - Life Deterministic calculations Actuaries of the second kind - Casualty Probabilistic methods Actuaries of the third kind - Financial Stochastic processes Similarities Both Actuaries and Financial Economists: Are mathematically inclined Address monetary issues Incorporate risk into calculations Use specialized languages Different Approaches Risk Interest Rates Profitability Valuation Risk Insurance Pure risk - Loss/No loss situations Law of large numbers Finance Speculative risk - Includes chance of gain Portfolio risk Portfolio Risk Concept introduced by Markowitz in 1952 Var (Rp) = (σ2/n)[1+(n-1)ρ] Rp = Expected outcome for the portfolio σ = Standard deviation of individual outcomes n = Number of individual elements in portfolio ρ = correlation coefficient between any two elements Portfolio Risk Diversifiable risk Uncorrelated with other securities Cancels out in a portfolio Systematic risk Risk that cannot be eliminated by diversification Interest Rates Insurance One dimensional value Constant Conservative Finance Multiple dimensions Market versus historical Stochastic Interest Rate Dimensions Ex ante versus ex post Real versus nominal Yield curve Risk premium Yield Curves 12 P 10 e 8 r c 6 e 4 n t 2 Upward Sloping Inverted 0 1 5 10 Years to Maturity 20 Profitability Insurance Profit margin on sales Worse yet - underwriting profit margin that ignores investment income Finance Rate of return on investment Valuation Insurance Statutory value Amortized values for bonds Ignores time value of money on loss reserves Finance Market value Difficulty in valuing non-traded items Current State of Financial Economics Valuation Valuation models Efficient market hypothesis Anomalies in rates of return Asset Pricing Models Ri Rf Rm βi Capital Asset Pricing Model (CAPM) E(Ri) = Rf + βi[E(Rm)-Rf] = Return on a specific security = Risk free rate = Return on the market portfolio = Systematic risk = Cov (Ri,Rm)/σm2 Empirical Tests of the CAPM Initially tended to support the model Anomalies Seasonal factors - January effect Size factors Economic factors Systematic risk varies over time Recent tests refute CAPM Fama-French - 1992 Arbitrage Pricing Model (APM) n E ( R i ) R f ' b i , j j j 1 Rf ’ = Zero systematic risk rate bi,j = Sensitivity factor λ = Excess return for factor j Empirical Tests of APM Tend to support the model Number of factors is unclear Predetermined factors approach Based on selecting the correct factors Factor analysis Mathematical process selects the factors Not clear what the factors mean Option Pricing Model An option is the right, but not the obligation, to buy or sell a security in the future at a predetermined price Call option gives the holder the right to buy Put option gives the holder the right to sell Black-Scholes Option Pricing Model Pc PsN ( d1) Xert N ( d 2) d 1 [ln( P s / X ) ( r d 2 d 1 t Pc Ps X r t σ N 2 1/ 2 = Price of a call option = Current price of the asset = Exercise price = Risk free interest rate = Time to expiration of the option = Standard deviation of returns = Normal distribution function / 2 ) t ] / t 1/ 2 Diffusion Processes Continuous time stochastic process Brownian motion Normal Lognormal Drift Jump Markov process Stochastic process with only the current value of variable relevant for future values Hedging Portfolio insurance attempted to eliminate downside investment risk - generally failed Asset-liability matching Duration D = -(dPV(C)/dr)/PV(C) d = partial derivative operator PV(C) = present value of stream of cash flows r = current interest rate Duration Measures Macauley duration and modified duration Assume cash flows invariant to interest rate changes Effective duration Considers the effect of cash flow changes as interest rates change Applications of Financial Economics to Insurance Pensions Valuing PBGC insurance Life insurance Equity linked benefits Property-liability insurance CAPM to determine allowable UPM Discounted cash flow models Conclusion Need for actuaries of the third kind Financial guarantees Investment portfolio management Dynamic financial analysis (DFA) Financial risk management Improved parameter estimation Incorporate insurance terminology
