Transcript Actuarial Science Meets Financial Economics

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)  Xert N ( d 2)
d 1  [ln( P s / X )  ( r  
2
d 2  d 1   t 1/ 2
Pc
Ps
X
r
t
σ
N
= 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