Question

Greta has 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. (All rates are annual, and continuously compounded). The S&P 500 risk premium is 8% per year, with a standard deviation of 22%. The Hedge Fund risk premium is 10%, with a standard deviation of 37%. The returns on both of these in any particular year are uncorrelated with its own returns in other years; they are also uncorrelated with the return of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on the S&P 500 and the Hedge Fund in the same year is zero, but Greta isn't fully convinced by this claim.

a) Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the Optimal Asset Allocation?

b) What is the Expected Risk Premium on the portfolio?

Answer 1