Question

Greta, an elderly investor, has a degree of risk aversion of A = 5 when applied to return on wealth over a one-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 and continuously compounded.) The S&P 500 risk premium is estimated at 7% per year, with a SD of 19%. The hedge fund risk premium is estimated at 11% with a SD of 38%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund 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 by this claim. 3-1. Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) S&P Hedge a-2. What is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Expected risk premium

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

S&P 500 Risk Premium Standard deviation 7% 19% Hedge Fund 11% 38% Correlation (S&P,Hedge) a.1 8 9 Optimal Asset Allocation S&P 500 Hedge Fund 0.7179 0.2821 10 13 a.2 Expected risk premium 8.13%

Cell reference -

В. D S&P 500 Hedge Fund EN + L ON Risk Premium Standard deviation 0.11 0.38 0.19 Correlation (S&P,Hedge) 0 a.1 8 9 Optimal Asset Allocation S&P 500 Hedge Fund =(C3*D4^2-D3*C4*D4*C6)/(C3*D4^2+D3*C4^2-(C3+D3)*C4*D4*C6) =1-09 10 11 12 13 a.2 Expected risk premium =C3*C9+D3*C10 15 10

Please note: We can compute the allocation of assets in optimal portfolio (Two- Assets) with following equation:

Wa = RPA * 05 RPA* 07 - RP * 09* 05 * Pab RP,* o + RP.* 02 - (RPa + RP) * 0,* 05 * Pab

where,

RP = Risk premium

o = standard deviation

Pab = correlation of a and b

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.