Let A and B be random variables and let

W =A - n B

for some positive number n. (Thinking of long cash commodity and short

futures on that commodity.)

(a)Find V(w) in terms of variances of A and B , the covariance of A and B, and n. Your appendix on Random Variables gives you the relevant formulae.

(b)Treat V(w) as a function of n. What type of function is this? Describe the graph of this function. Does it have a maximum or minimum point? Explain.

(c)Using, find the n that produces the maximum or minimum value of V(w). Be sure to explain using calculus.

(d)The Correlation :