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 7.2% per year, with a SD of 22.2%. The hedge fund risk premium is estimated at 12.2% with a SD of 37.2%. 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.
S&P=                 %

Hedge=              %

Risk-Free Asset=              %

Answer 1

22.2% 37.2% 0.0% 0.0% 7.2% 12.2% 0.05 =B1^2 0.14 =B2^2 1 SD of S&P 500 2 SD of Hedge fund 3 Correlation between fund returns 4 Risk free rate of return (RF) 5 Expected risk premium on S&P 500 6 Expected risk premium on Hedge fund 7 8 Variance of S&P 500 9 Variance of Hedge fund 10 15 16 Portfolio invested in S&P 500 17 Portfolio invested in Hedge fund 18 19 Expected return on optimal risky portfolio [E(rp)] 20 21 SD of optimal risky portfolio (op) 22 23 Reward to volatility ratio of the feasible CAL 62.37% =((B5%B9)-(B6%B10))/((B5*B9)+(B6%B8)-(B5+B6)*B10) 37.63% =1-B16 9.08% =B16 B5+B17*B6 19.69% =(B16^2*B8+B1742%B9+2*B17 B16 B1*32*B3)^(1/2) 0.4612 =(B19-B4/B21 25 S&P 26 Hedge 27 Risk-free asset 48.70% =(B19/(3* (B21^2)))*B16 29.39% =(B19/3*(B21^2)*B17 21.92% -1-B26-B25

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