lecture 24. example correlation coefficient =.4 stocks % of portfolioavg return abc corp2860% 15%...
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DerivativesLecture 24
Diversification
)rx()r(x Return PortfolioExpected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
Portfolio DiversificationExample Correlation Coefficient = .4Stocks s % of Portfolio Avg ReturnABC Corp 28 60% 15%Big Corp 42 40% 21%
Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1
Additive Standard Deviation (common sense):= 28 (60%) + 42 (40%) = 33.6 WRONG
Real Standard Deviation:= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1 CORRECT
Value at Risk (VaR)
Value at Risk = VaR
Newer termAttempts to measure riskRisk defined as potential lossLimited use to risk managers
FactorsAsset valueDaily VolatilityDays Confidence interval
Value at Risk (VaR)
Standard Measurements10 days
99% confidence interval
VaR
1010 day
33.2%99
easset valu)33.2( 10 VaR
Value at Risk (VaR)ExampleYou own a $10 mil portfolio of IBM stock. IBM has a
daily volatility of 2%. Calculate the VaR over a 10 day time period at a 99% confidence level.
%74.14
33.20632.)%(99
621,473,1$
000,000,101473.
VaR
%32.6
1002.10
Value at Risk (VaR)
ExampleYou also own $5 mil of AT&T, with a daily
volatility of 1%. AT&T and IBM have a .7 correlation coefficient.
What is the VaR of AT&T and the combined portfolio?
405,368$
621,473,1$
&
TAT
IBM
VaR
VaR
026,842,1$& IBMTATVaR
379,751,1$PortfolioVaR647,90$
BenefitationDiversific