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The expected rate of return of A stock is 30% and the standard deviation of the returns is 22%, while the expected rate of return of B stock is 18% and the standard deviation of the returns is 15%. The correlation between the returns of A and B shares is 0.40 and the risk-free rate of return of T-bills is 3%. The FTSE100 index has a rate of return of 15% during the same period.
Part A). Calculate the expected return and standard deviation of an equally-weighted portfolio containing stocks A and B.
Part B). A risk manager assumes that the joint distribution of returns is multivariate normal and calculates the following risk measures for a two-asset portfolio:
Asset
Position
Individual VaR
Marginal VaR
Component VaR
A
£100
-23.3
-0.176
-£17.6
B
-46.6
-0.44
-£44
Portfolio
£200
-61.6
-£61.6
If asset B is dropped from the portfolio, what is the reduction in portfolio Value at Risk (VaR)?
Part C). What are and relative to the portfolio?
Part D). A small investment management firm measures absolute risk with a 99%, one-year VaR, which gives -£1.5 million. The firm wants to allocate this risk to two portfolio managers, each with the same VaR budget. Given that the correlation between managers is -0.7, the VaR budget for each should be?
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