Managing Financial Risk for Insurers

On Becoming an Actuary of the Third Kind

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.

Actuarial Science Meets Financial Economics

Buhlmann’s classifications of actuariesActuaries of the first kind - Life

Deterministic calculationsActuaries of the second kind - Casualty

Probabilistic methodsActuaries of the third kind - Financial

Stochastic processes

Similarities

Both Actuaries and Financial Economists:

Are mathematically inclinedAddress monetary issuesIncorporate risk into calculationsUse specialized languages

Different Approaches

RiskInterest RatesProfitabilityValuationRisk Metrics

Risk

InsurancePure risk - Loss/No loss situationsLaw of large numbers

FinanceSpeculative risk - Includes chance of gainPortfolio risk

Portfolio Risk

Concept introduced by Markowitz in 1952Var (Rp) = (σ2/n)[1+(n-1)ρ]

Rp = Expected outcome for the portfolio

σ = Standard deviation of individual outcomesn = Number of individual elements in portfolioρ = correlation coefficient between any two

elements

Portfolio Risk

Diversifiable riskUncorrelated with other securitiesCancels out in a portfolio

Systematic riskRisk that cannot be eliminated by diversification

Interest Rates

InsuranceOne dimensional valueConstantConservative

FinanceMultiple dimensionsMarket versus historicalStochastic

Interest Rate Dimensions

Ex ante versus ex postReal versus nominalYield curveRisk premium

Yield Curves

0

2

4

6

8

10

12

1 5 10 20

Years to Maturity

Percent

UpwardSlopingInverted

Profitability

InsuranceProfit margin on salesWorse yet - underwriting profit margin that ignores investment income

FinanceRate of return on investment

Valuation

InsuranceStatutory valueAmortized values for bondsIgnores time value of money on loss reserves

FinanceMarket valueDifficulty in valuing non-traded items

Current State of Financial Economics

ValuationValuation modelsEfficient market hypothesisAnomalies in rates of return

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

Empirical Tests of the CAPM

Initially tended to support the modelAnomalies

Seasonal factors - January effectSize factorsEconomic factors

Systematic risk varies over timeRecent tests refute CAPM

Fama-French - 1992

Arbitrage Pricing Model (APM)

Rf’ = Zero systematic risk rate

bi,j = Sensitivity factor

λ = Excess return for factor j

E R R bi f i j jj

n

( ) ' ,

1

Empirical Tests of APM

Tend to support the modelNumber of factors is unclearPredetermined factors approach

Based on selecting the correct factorsFactor analysis

Mathematical process selects the factorsNot 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 buyPut option gives the holder the right to sell

Black-Scholes Option Pricing Model

Pc = Price of a call option

Ps = Current price of the asset

X = Exercise pricer = Risk free interest ratet = Time to expiration of the optionσ = Standard deviation of returnsN = Normal distribution function

P P N d Xe rt N dc s ( ) ( )1 2

2/112

2/121 /])2/()/[ln(

tdd

ttrXPd s

Diffusion ProcessesContinuous time stochastic processBrownian motion

NormalLognormalDriftJump

Markov processStochastic process with only the current value of variable relevant for future values

HedgingPortfolio insurance attempted to eliminate

downside investment risk - generally failedAsset-liability matching

Risk Metrics

• Interest rate sensitivity– Duration

• Insurance– Dynamic Financial Analysis (DFA)

• Finance– Risk profiles– Value at Risk (VaR)

Duration

D = -(dPV(C)/dr)/PV(C)

d = partial derivative operatorPV(C) = present value of stream of cash flowsr = current interest rate

Duration Measures

Macauley duration and modified durationAssume cash flows invariant to interest rate changes

Effective durationConsiders the effect of cash flow changes as interest rates change

Risk Profile

Graphical summary of relationship between two variables

Example: As interest rates increase, S&L value decreases

-20

0

20

-2% -1% 1% 2%

Change in interest rateC

hang

e in

val

ue o

f S&

L($

mill

ions

)

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

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

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

Return Distribution

Portfolio Gains/Losses

Prob

abili

ty

VaR

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

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

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

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

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

Applications of Financial Economics to Insurance

PensionsValuing PBGC insurance

Life insuranceEquity linked benefits

Property-liability insuranceCAPM to determine allowable UPMDiscounted cash flow models

Conclusion

Need for actuaries of the third kindFinancial guaranteesInvestment portfolio managementDynamic financial analysis (DFA)Financial risk managementImproved parameter estimationIncorporate insurance terminology

Next

• Review of bond pricing• Forward interest rates