Let R = (R1, . . . , Rn) be returns of n assets in the market, = (E(R1), . . . , E(Rn)) = (1, ..., n) T be expected returns, and = (Cov(Ri , Rj ))1jn = (ij )1jn be the variance of returns. With a weight vector w = (w1, ..., wn) T , we can form a portfolio P with a return Pn j=1 wjRj . Suppose that is invertible.

a) Solve for the optimal portfolio using the Lagrange multiplier method min wRn w T w + 1(w T ) + 2(w T 1 1). Compare with the optimal portfolio obtain in the class notes.

b) Is the risk free asset included in the above n-assets? Explain.