Two stocks are believed to satisfy the following statistical factor model: r1 = a1 + 2f1 + f2, r2 = a2 + 3f1 + 4f2. In addition there is a risk free asset with a rate of return of 10%. Suppose E[r1] = 15% and E[r2] = 20%. 1. Show that the factors are pricing factors, and find the prices of risk 0, 1, 2 of the corresponding beta pricing model. That is, find 0, 1, 2 such that E[r^T] 01^T = ^T (from F to -1) C(f, r), where r=matrix that first row is r1 and second row is r2, =matrix that first row is 1 and second row is 2, C(f, r) i,j = Cov(fi, rj ), (F ) i,j = Cov(fi, fj ). 2. Find portfolios rf1 and rf2 such that rf1 = 1 + f1, rf2 = 2 + f2. where 1 and 2 are functions of r0, a1 and a2. You have to explicitly determine 1 and 2 in terms of r0, a1 and a2. 3. Verify that 0 + 1 = E[rf1],0 + 2 = E[rf2]