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 λ0, λ1, λ2 of the corresponding beta pricing model. That is, find λ0, λ1, λ 2 such that E[r^T] −λ01^T = λ^T Σ(from F to -1) C(f, r), where r=matrix that first row is r1 and second row is r2, λ=matrix that first row is λ1 and second row is λ2, C(f, r) i,j = Cov(fi, rj ), (ΣF ) i,j = Cov(fi, fj ). 2. Find portfolios rf1 and rf2 such that rf1 = α1 f1, rf2 = α2 f2. where α1 and α2 are functions of r0, a1 and a2. You have to explicitly determine α1 and α2 in terms of r0, a1 and a2. 3. Verify that λ0 λ1 = E[rf1],λ0 λ2 = E[rf2].