Download - Actuarial Science Meets Financial Economics
![Page 1: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/1.jpg)
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
![Page 2: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/2.jpg)
Similarities
Both Actuaries and Financial Economists:
Are mathematically inclined
Address monetary issues
Incorporate risk into calculations
Use specialized languages
![Page 3: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/3.jpg)
Different Approaches
Risk
Interest Rates
Profitability
Valuation
![Page 4: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/4.jpg)
Risk
Insurance
Pure risk - Loss/No loss situations
Law of large numbers
Finance
Speculative risk - Includes chance of gain
Portfolio risk
![Page 5: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/5.jpg)
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
![Page 6: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/6.jpg)
Portfolio Risk
Diversifiable risk
Uncorrelated with other securities
Cancels out in a portfolio
Systematic risk
Risk that cannot be eliminated by diversification
![Page 7: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/7.jpg)
Interest Rates
Insurance
One dimensional value
Constant
Conservative
Finance
Multiple dimensions
Market versus historical
Stochastic
![Page 8: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/8.jpg)
Interest Rate Dimensions
Ex ante versus ex post
Real versus nominal
Yield curve
Risk premium
![Page 9: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/9.jpg)
Yield Curves
0
2
4
6
8
10
12
1 5 10 20
Years to Maturity
Percent
UpwardSlopingInverted
![Page 10: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/10.jpg)
Profitability
Insurance
Profit margin on sales
Worse yet - underwriting profit margin that ignores investment income
Finance
Rate of return on investment
![Page 11: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/11.jpg)
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
![Page 12: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/12.jpg)
Current State of Financial Economics
Valuation
Valuation models
Efficient market hypothesis
Anomalies in rates of return
![Page 13: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/13.jpg)
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
![Page 14: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/14.jpg)
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
![Page 15: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/15.jpg)
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 j
j
n
( ) ' ,
1
![Page 16: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/16.jpg)
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
![Page 17: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/17.jpg)
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
![Page 18: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/18.jpg)
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
P P N d Xe rt N dc s ( ) ( )1 2
d P X r t t
d d t
s12 1 2
2 11 2
2
[ln( / ) ( / ) ] / /
/
![Page 19: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/19.jpg)
Diffusion ProcessesContinuous time stochastic process
Brownian motion
Normal
Lognormal
Drift
Jump
Markov process
Stochastic process with only the current value of variable relevant for future values
![Page 20: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/20.jpg)
Hedging
Portfolio insurance attempted to eliminate downside investment risk - generally failed
Asset-liability matching
![Page 21: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/21.jpg)
Duration
D = -(dPV(C)/dr)/PV(C)
d = partial derivative operator
PV(C) = present value of stream of cash flows
r = current interest rate
![Page 22: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/22.jpg)
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
![Page 23: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/23.jpg)
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
![Page 24: Actuarial Science Meets Financial Economics](https://reader033.vdocuments.net/reader033/viewer/2022051116/56814e8d550346895dbc32e2/html5/thumbnails/24.jpg)
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