Actuarial Science Meets Financial Economics

1. 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

2. Similarities Both Actuaries and Financial Economists: Are mathematically inclined Address monetary issues Incorporate risk into calculations Use specialized languages

3. Different Approaches Risk Interest Rates Profitability Valuation Risk Metrics

4. Risk Insurance Pure risk - Loss/No loss situations Law of large numbers Finance Speculative risk - Includes chance of gain Portfolio risk

5. 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

6. Portfolio Risk Diversifiable risk Uncorrelated with other securities Cancels out in a portfolio Systematic risk Risk that cannot be eliminated by diversification

7. Interest Rates Insurance One dimensional value Constant Conservative Finance Multiple dimensions Market versus historical Stochastic

8. Interest Rate Dimensions Ex ante versus ex post Real versus nominal Yield curve Risk premium

9. Yield Curves

10. Profitability Insurance Profit margin on sales Worse yet - underwriting profit margin that ignores investment income Finance Rate of return on investment

11. 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

12. Current State of Financial Economics Valuation Valuation models Efficient market hypothesis Anomalies in rates of return

13. Asset Pricing Models Capital Asset Pricing Model (CAPM) E(Ri) = Rf + βi[E(Rm)-Rf] Ri = Return on a specific security Rf = Risk free rate Rm = Return on the market portfolio βi = Systematic risk = Cov (Ri,Rm)/σm2

14. 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

15. Arbitrage Pricing Model (APM) Rf’ = Zero systematic risk rate bi,j = Sensitivity factor λ = Excess return for factor j

16. 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

17. 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

18. Black-Scholes Option Pricing Model Pc = Price of a call option Ps = Current price of the asset X = Exercise price r = Risk free interest rate t = Time to expiration of the option σ = Standard deviation of returns N = Normal distribution function

19. 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

20. Hedging Portfolio insurance attempted to eliminate downside investment risk - generally failed Asset-liability matching

21. Risk Metrics • Interest rate sensitivity • Duration • Insurance • Dynamic Financial Analysis (DFA) • Finance • Risk profiles • Value at Risk (VaR)

22. Duration D = -(dPV(C)/dr)/PV(C) d = partial derivative operator PV(C) = present value of stream of cash flows r = current interest rate

23. 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

24. Risk Profile • Graphical summary of relationship between two variables • Example: As interest rates increase, S&L value decreases

25. Risk Profile (Cont.) • NOTE: For S&Ls, this risk profile is apparent from the balance sheet • The balance sheet lists long-term vs. short-term assets and liabilities • Economic exposures require more work • Example: Construction company will be affected by higher interest rates • Enter correlation analysis

26. Value at Risk - A Definition • Value at risk is a statistical measure of possible portfolio losses • A percentile of the distribution of outcomes • Value at Risk (VaR) is the amount of loss that a portfolio will experience over a set period of time with a specified probability • Thus, VaR depends on some time horizon and a desired level of confidence

27. Value at Risk - An Example • Let’s use a 5% probability and a one-day holding period • VaR is the one day loss that will be exceeded only 5% of the time • It’s the tail of the return distribution • In the example, the VaR is about $60,000

28. First - Identify the Market Factors • There are three methods to calculate VaR, but the first step is to identify the “market factors” • Market factors are the variables that impact the value of the portfolio • Stock prices, exchange rates, interest rates, etc. • The different approaches to VaR are based on how the market factors are modeled

29. Methods of Calculating VaR • Historical simulation • Apply recent experience to current portfolio • Variance-covariance method • Assume a normal distribution and use the statistical properties to find VaR • Monte Carlo Simulation • Generate scenarios to determine changes in portfolio value

30. Historical Simulation • Historical simulation is relatively easy to do • Only requires knowing the market factors and having the historical information • Correlations between the market factors are implicit in this method • Assumes future will resemble the past

31. Variance-Covariance Method • Assume all market factors follow a multivariate normal distribution • The distribution of portfolio gains/losses can then be determined with statistical properties • From this distribution, choose the required percentile to find VaR • Conceptually more difficult given the need for multivariate analysis • Explaining the method to management may be difficult

32. Monte Carlo Simulation • Specify the individual distributions of the future values of the market factors • Generate random samples from the assumed distributions • Determine the final value of the portfolio • Rank the portfolio values and find the appropriate percentile to find VaR • Initial setup is costly, but thereafter simulation can be efficient • DFA is an example of this approach

33. 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

34. 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