Consider an investment in the Macy's stock over the next year. Let R denote the monthly simple return and assume that R ~ N(0.08,(0.10)2 ). That is, E[R] = 0.08 and var(R) = (0.10)2 . Let W0 = $1,000 denote the initial investment (at the beginning of the month), and let W1 =W0(1 + R) denote the investment value at the end of the month.
(a) Compute E[W1], Var(W1) and sd(W1).
E[W1 ] =
Var(W1) =
sd(W1) =
(b) What is the value of the covariance between the initial investment W0 and the investment value at the end of the month W1? Are those variables independent?
Cov[W0, W1] =