You are considering investing in three funds, A, B and C, whose

annual returns(as a proportion of the amount invested) are random variables with

the following parameters:

Fund A B C

Expected return 0.03 0.08 0.1

Standard Deviation of Return 0 0.1 0.15

Say that you also know that Cov(A,B) = 0.015.

(a) Find Cov(B,C) and Cov(A,C).

(b) Are A and B independent? Explain your answer.

(c) You have $10 000 to invest, which you break up into three parts xA, xB and xC to be invested in the corresponding fund. (So xA + xB + xC = 10000.) What is your expected return in terms of xA, xB and xC? (d) What is the variance of your return in terms of xA, xB and xC?

(e) Which investment strategy maximizes your expected returns? Which one min

imizes your risk of losing money?