3.3. Let rot be the return of a stock index at time t. Sharpe's single-index model assumes that the log returns of the n stocks in the index are gen- erated by rit = ai Birot Eit, 1 i p, where it is uncorrelated with rot and Cov(Eit, jt) = 021 {ij}. The model also assumes that (rot, ..., Tpt), 1t n, are i.i.d. vectors. 1{ (a) Suppose Var(rot) = 02. Show that the covariance matrix F = (fij) of the log return of the n stocks under the single-index model is given by F = +0I, where = (, . . .p)T. = (b) Let ij = Cov(rit, jt) and = (ij)1