Question

Greta, an elderly investor, has a degree of risk aversion of A = 3 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 one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 8.2% per year, with a SD of 23.2%. The hedge fund risk premium is estimated at 13.2% with a SD of 38.2%. 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.

What should be Greta’s capital allocation? (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

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

В DE S&P 500 -NM O Risk Premium Standard deviation 8.2% 23.2% Hedge Fund 13.2% 38.2% Correlation (S&P, Hedge) a.1 Optimum Capital Allocation S&P 500 Hedge Fund 62.74% 37.26% PEN

Cell reference -

в S&P 500 Hedge Fund Risk Premium Standard deviation 0.082 0.232 0.132 0.382 Correlation (S&P, Hedge) 0 Optimum Capital 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

Please note:

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

RP, жо? – RP, жOa * 0, * Paь RPа * o3 + RP, жо? — (RP. + RPь) жол жо, * paь "

where,

RP = Risk premium

a = First asset (here, S&P 500)

b = Second asset (here, Hedge fund)

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.