The returns r;, of the assets satisfy the two-factor model ri = Boi + Blifi + Baife tei, i = 1, ...,n, (1) where Bri and By are factor loadings of the risk factors fi and fo re- spectively. Let r = (1, . .., rn)T, Bo = (Bol . . ., Bon)T, F = (f1, f2) ,e = (e1, . .., en), and B = . .. Bin B21 . .. B2n (a) Show that the two-factor model (1) can be expressed as " = Bot BF+e. (2) (b) Show that the variance-covariance matrix for r is given by Er = BEFB+ Ce, (3) where EF and E are the variance-covariance matrices of F and e respectively. (c) Let B; = (Bij, B2;)T (j = 1,...,n) be the j-th column of the matrix B. Show that the variance of the j-th return is Var(r;) = BJEFB, to.,. (d) Show further that Cov(ri, r;) = BFEFB;. (e) Can you give a reason why one would consider estimating Er using equation (3) instead of using the sample variance-covariance matrix of r directly