Transcript PowerPoint Slides - College of Business

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 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 Metrics
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( Ps / X )  (r   / 2)t ] / t
2
d 2  d 1  t
Pc
Ps
X
r
t
σ
N
1/ 2
= 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
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
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 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
Risk Profile

20
Change in value of S&L
($ millions)
Graphical summary of
relationship between
two variables
 Example: As interest
rates increase, S&L
value decreases
0
-2% -1% 1%
2%
-20
Change in interest rate
Risk Profile (Cont.)

NOTE: For S&Ls, this risk profile is
apparent from the balance sheet
•

Economic exposures require more work
•

The balance sheet lists long-term vs. short-term
assets and liabilities
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
Return Distribution
Probability
Portfolio Gains/Losses
10
00
00
0
VaR
-1
00
00
0
• Let’s use a 5%
probability and a oneday 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
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
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
Next
• Review of bond pricing
• Forward interest rates