The Efficient Frontier a) Megan has the utility function u(rp)=E[rp]2p2, where E[rp] and p2 denote the mean and variance, respectively, of the portfolio return rp. Assume the efficient frontier (with no risk-free asset) is given by the hyperbola 5E[rp]2E[rp]+0.1. Find the risk p and expected return E[rp] of the efficient portfolio p that Megan will choose to maximize her utility. (3 points) b) Now, assume that there is a risk-free bond that returns rf=0.05, and that the Sharpe ratio of all the portfolios found on the efficient frontier is =0.5. Find the risk p and expected return E[rp] of the efficient portfolio p that Megan would choose to maximize her utility. Show that her utility from the portfolio p is greater than her utility from the portfolio p. Can you explain why this is the case, in terms of the constrained optimization problem Megan is solving? (3 points) The Efficient Frontier a) Megan has the utility function u(rp)=E[rp]2p2, where E[rp] and p2 denote the mean and variance, respectively, of the portfolio return rp. Assume the efficient frontier (with no risk-free asset) is given by the hyperbola 5E[rp]2E[rp]+0.1. Find the risk p and expected return E[rp] of the efficient portfolio p that Megan will choose to maximize her utility. (3 points) b) Now, assume that there is a risk-free bond that returns rf=0.05, and that the Sharpe ratio of all the portfolios found on the efficient frontier is =0.5. Find the risk p and expected return E[rp] of the efficient portfolio p that Megan would choose to maximize her utility. Show that her utility from the portfolio p is greater than her utility from the portfolio p. Can you explain why this is the case, in terms of the constrained optimization problem Megan is solving? (3 points)