Question

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 = wr_A + (1 − w)r_B

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(r_A, r_B) = 30(%)² rather than −30(%)² , find E[rp] and Var(rp) again.

d) Would Cov(r_A, r_B) have an impact on E[rp]?

e) In order to more efficiently reduce the risk (i.e., variance) of the investment portfolio through diversification, should one look for financial assets that are positively correlated or negatively correlated?

Answer 1