2. 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 j=1nwjRj. Suppose that is invertible. a) Solve for the optimal portfolio using the Lagrange multiplier method minwRnwTw+1(wT)+2(wT11). Compare with the optimal portfolio obtain in the class notes. b) Is the risk free asset included in the above n-assets? Explain. 2. 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 j=1nwjRj. Suppose that is invertible. a) Solve for the optimal portfolio using the Lagrange multiplier method minwRnwTw+1(wT)+2(wT11). Compare with the optimal portfolio obtain in the class notes. b) Is the risk free asset included in the above n-assets? Explain