Question

10 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 5.2% per year, with a SD of 20.2%. The hedge fund risk premium is estimated at 10.2% with a SD of 35.2%. 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. points What should be Greta's capital allocation? (Do not round your intermediate calculations. Round your answers to 2 decimal places.) eBook Print S&P Hedge Risk-free asset References

Answer 1

Answer:

The 1 year risk premium on the S&P portfolio is =5.2%

The 1 year risk premium on the hedge fund portfolio is = 10.2%

S&P 1 year standard deviation is = 20.2%

Hedge fund 1 year standard deviation is = 35.2%

With correlation = 0, the optimal asset allocation is

Weight of S&P =

(5.2135.2})-(10.210)(20.2)(35.2)) 5.2135.2)2 + 10.2(20.212 - (5.2 + 10.2)(10.2)(0)(20.2)(35.2)

= 0.6075

Weight of hedge fund = 1- 0.6075 = 0.3925

With these weights the expected return on portfolio = 0.6075*5.2 + 0.3925*10.2 = 7.1625

Variance = = 0.03743

(0.6075 +0.2022 + (0.3925 +0.352)

With risk aversion of A=3, the optimal capital allocation in risky portfolio is:

0.071625/(3*0.03743) = 0.6378

Resulting investment composition will be S&P = 0.6075 * 0.6378 = 0.3875 or 38.75%

In hedge fund = 0.3925 * 0.6378 = 0.2503 or 25.03%

The remaining 0.3622 or 36.22% will be invested in the risk-free asset.

Thank you.