1. Managing Financial Risk for Insurers
On Becoming an Actuary of the Third Kind 1

2. Message from a student in Fin 432 last year.
Time passes really fast. And I have already been working for AEGON for about 4 months. Everything is settled down now. Moving is painful and it takes for a while to get familiar with the local area. I really think of Champaign and our university.
Right now I mostly work on Economic Framework. We deal with Economic Capital Model (ECM) a lot. Now I realized that what you taught us is extremely helpful and practical. Basically you introduced the comprehensive and systematic Financial Risk Management System to us. The Embedded Value, Scenarios testing and Monte Carlo Simulation, etc, those concepts and techniques are so useful in the real business world. Especially for ECM, to me nearly every term and technique we are using is familiar except some proprietary modeling software. I am not saying I already knew everything, but I did learn a lot in your class.

3. 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

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

5. Different Approaches Risk Interest Rates Profitability Valuation
Risk Metrics

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

7. 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

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

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

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

11. Yield Curves

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

13. 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

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

15. 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

16. 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

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

18. 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

19. 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

20. 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

21. 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

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

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

24. 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

25. 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

26. Risk Profile Graphical summary of relationship between two variables
Example: As interest rates increase, S&L value decreases 6

27. 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 7

28. 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 3

29. 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 4

30. 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 6

31. 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 7

32. 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 12

33. 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 13

34. 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 16

35. 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

36. 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

37. Next
Review of bond pricing
Forward interest rates