Exercise 1 . Greta, an elderly investor, is a mean-variance optimizer with a degree of risk aversion of A = 3 when applied to her return on wealth over a 3-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 3-year strategies. The S&P 500 risk premium is estimated at 5% per year, with a SD of 20%. The hedge fund risk premium is estimated at 10% per year, with a SD of 35%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain (a) Compute the estimated 3-year risk premiums, SDs, and Sharpe ratios for the two portfolios (b) Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? What should be Greta's capital allocation? (c) If the correlation coefficient between annual portfolio returns is 0.3, what is the annual covariance? (d) With correlation of 0.3, what is the covariance between the 3-year returns? (Take three correlation to be the same as annual correlation.) (e) Repeat part (b) using an annual correlation of 0.3