Variance of portfolios
More complicated I buy $100 worth of IBM and $200 worth of GOOG. The SD of IBM is 10% and the SD of GOOG is 10%. What is the SD/variance of my portfolio? The problem: What does variance measure? What would happen to the portfolio if IBM and GOOG move together: go up at the same time, and go down at the same time? What would happen to the portfolio if IBM and GOOG move in opposite directions: one goes up when the other is going down? We need more information to find the variance of a portfolio
Covariance
Measures whether two assets move in the same or the opposite directions Definition:
COURA,RB)=E((RA-ERA)(RB-ERB)
What's the expected value of anything?
Example
State
Prob (ps)
RIBM (%)
RGOOG (%)
rsfiE(r) for IBM
rsfiE(r) for GOOG
Product of deviations
Boom
14
15
6
Normal
5
3
Bust
fi5
fi3
Covariance of the returns on IBM and GOOG:
Why is this covariance positive? When would the covariance be negative?
State
Prob (ps)
RIBM (%)
RXOM (%)
rsfiE(r) for IBM
rsfiE(r) for XOM
Product of deviations
Boom
15
fi1
Normal
1/2
5
3
Bust
14
fi5
4
Covariance of the returns on IBM and XOM:
Why is this covariance negative? What would happen if the covariance were zero?
Covariance
We can work out what happens to the portfolio : Portfolio with two assets, assets have a positive covariance : Portfolio with two assets, assets have a negative covariance Formula
Var(Rp)=w2Var(RA)+w2Var(Rp)+2wAWpCov(RA,RB)
Example
In the two examples where you calculated covariance, here are the other quantities you need
Var IBM Var GOOG
50 10.6875
Var XOM
3.6875
Cov(IBM,GOOG) 22.5
Find the variance of the following portfolios: ./ in IBM,/ in GOOG 1z in IBM,1z in X