Suppose that the return of stock A is normally distributed with mean 4% and standard deviation 5%, the return of stock B is normally distributed with mean 8% and standard deviation 10%, and the covariance between the returns of stock A and stock B is -30(%)2 . Now you have an endowment of 1 dollar, and you decide to invest w dollar in stock A and 1 - w dollar in stock B. Let rp be the overall return of your portfolio, then:
rp = wrA + (1 - w)rB
Answer the following questions using w = 0.5.
a) Compute the expectation and variance of your portfolio. (i. e., E[rp] and Var(rp))
b) Find the 5th percentile of rp. (This quantity is often called the 5% Value at Risk.)
c) If Cov(rA, rB) = 30(%)2 rather than -30(%)2 , find E[rp] and Var(rp) again.
d) Would Cov(rA, rB) have an impact on E[rp]?