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 7.6% per year, with a SD of 22.6%. The hedge fund risk premium is estimated at 12.6% with a SD of 37.6%. 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. a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, 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 return on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Expected return

Answer 1

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

C D Risk Premium Std. Deviation of return Correlation S&P 500 7.60% 22.60% 0.30 Hedge Fund 12.60% 37.60% Optimal risky Portfolio Portfolio invested in S&P 500 9 a-1. 10 11 a-2. Portfolio invested in Hedge Fund Expected return of Optimal portfolio 0.6261 0.3739 0.0947

Cell reference -

D S&P 500 Hedge Fund Risk Premium Std. Deviation of return Correlation 0.076 0.226 0.3 0.126 0.376 Optimal risky Portfolio 9 a-1. Portfolio invested in S&P 500 =((C3)*D4^2-(D3) *C5*C4*D4)/((C3)*D4^2+(D3)*C4^2-((C3)+(D3)) *C5*C4*D4) 10 Portfolio invested in Hedge Fund =1-09 11 a-2. Expected return of Optimal portfolio =C9*C3+C10*D3 13

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