Question: Greta, an elderly investor, has a degree of risk aversion of A = 5 when applied to 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. (All rates are annual, continuously compounded.) The S&P 500 risk premium is estimated at 6% per year, with a SD of 20%. The hedge fund risk premium is estimated at 4% with a SD of 23%. 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.
Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation for S&P 500 and the Hedgefund?
What is the expected return on the portfolio?
What should be Greta's capital allocation for the risk free asset, hedgefund, and S&P?