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. Both Actuaries and Financial Economists:
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

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

5. Var (Rp) = (σ2/n)[1+(n-1)ρ]
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

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

22. 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

23. 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

24. 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