Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a 1-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual, continuously compounded.) 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% 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 is not fully convinced of this claim.

a.) Assuming the correlation between the annual returns on the two portfolios is indeed 0, what is the optimal asset allocation?

b.) What should be Gretas capital allocation?

c.) If the correlation coefficient between annual portfolio returns is actually .3, what is the covariance between the returns?