Greta, an elderly investor, has a degree of risk aversion of A 3 when applied to
ID: 2779908 • Letter: G
Question
Greta, an elderly investor, has a degree of risk aversion of A 3 when applied to return on wealth over a 3- year horizon. She is pondering two portfolios, the S&P; 500 and a hedge fund, as well as a number of 3-year strategies. (All rates are annual, continuously compounded.) The S&P; 500 risk premium is estimated at 8% per year, with a SD of 22%. The hedge fund risk premium is estimated at 6% with a SD of 28%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management 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 believes this is far from certain. a-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. Round your answers to 2 decimal places. Omit the "%" sign in your response.) S&P; Hedge a-2. What is the expected return on the portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) a-3. What should be Greta's capital allocation? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the"%" sign in your response.) S&P; Hedge Risk-free assetExplanation / Answer
a-1)
Risk premium for the S&P portfolio = (1 + 0.08)3 - 1 = 0.259712= 25.9712%
Risk premium for the hedge fund portfolio = (1 +0.06)3 - 1= 0.191016= 19.1016%
S&P 3-year standard deviation = 0.22 * sqrt(3) = 0.381051 = 38.1051%
Hedge fund 3-year standard deviation = 0.28 * sqrt(3) = 0.484974= 48.4974%.
with corelation = 0
Ws&p = 25.9712*48.49742 / ( 25.9712*48.49742 + 19.1016*38.10512) = 68.7733% = 68.77%
Whedge = 1 - Ws&p = 1 - 68.7733% = 31.2267% = 31.23 %
a-2)
E(Rp) = 68.7733% * 25.9712% + 31.2267% * 19.1016%
= 23.8337% = 23.83%
a-3)
Portfolio's standard deviation = sqrt (Ws&p2 * SDs&p2 + Whedge2 * SDhedge2 )
= sqrt (68.7733%2 * 38.1051%2 + 31.2267%2 * 48.4974%2)
= sqrt (9.1611%)
= 30.2673%
Sharpe ratio of portfolio = return / SD = 23.8837% / 30.2673% = 78.7441%
With A = 3, invested weight in riasky asset is = 23.8837% / (3*30.2673%2) = 86.7209%
Invested in risk free is = 1 - 86.7209% = 13.28%
Invested in S&P is =68.7733% * 86.7209% = 59.64%
Invested in Hedge is = 31.2267% * 86.7209% = 27.08%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.