Greta has risk aversion of A = 5 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 5-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 10% per year, with a standard deviation of 16%. The hedge fund risk premium is estimated at 12% with a standard deviation of 31%. 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 return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim. Compute the estimated 1-year risk premiums, standard deviations, and Sharpe ratios for the two portfolios. (Do not round your intermediate calculations. Round "Sharpe ratios" to 4 decimal places and other answers to 2 decimal places.)

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Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 5P
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Just need help finding the Sharpe Ratios. 

Horizon period in years:
1
Risk Aversion
5
S&P risk premium
0.1
S&P standard dev.
0.16
Hedge fund risk premium
0.12
Hedge fund standard dev.
0.31
Optimal Risky Portfolio of Horizon Period
Correlation between funds
Assets
Standard dev. risk prem.
S&P
0.16
0.1
Hedge fund
0.2683281573
1.100341658
Computed values
Standard dev of optimal risky portfolio
0.8579857206
proportion of S&P in optimal portfolio
0.2035695558
proportion of hedge fund in optimal portfoll 0.7964304442
Expected return of optimal portfolio
0.8967025507
Sharpe ratio
0.2436229967
Capital Allocation
S&P
0.0495942252
Hedge Fund
0.1940287714
Risk free assets
0.7563770033
Transcribed Image Text:Horizon period in years: 1 Risk Aversion 5 S&P risk premium 0.1 S&P standard dev. 0.16 Hedge fund risk premium 0.12 Hedge fund standard dev. 0.31 Optimal Risky Portfolio of Horizon Period Correlation between funds Assets Standard dev. risk prem. S&P 0.16 0.1 Hedge fund 0.2683281573 1.100341658 Computed values Standard dev of optimal risky portfolio 0.8579857206 proportion of S&P in optimal portfolio 0.2035695558 proportion of hedge fund in optimal portfoll 0.7964304442 Expected return of optimal portfolio 0.8967025507 Sharpe ratio 0.2436229967 Capital Allocation S&P 0.0495942252 Hedge Fund 0.1940287714 Risk free assets 0.7563770033
Greta has risk aversion of A= 5 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 5-year strategies. (All rates are annual and
continuously compounded.) The S&P 500 risk premium is estimated at 10% per year, with a standard deviation of 16%.
The hedge fund risk premium is estimated at 12% with a standard deviation of 31%. 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
return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this
claim.
Compute the estimated 1-year risk premiums, standard deviations, and Sharpe ratios for the two portfolios. (Do not
round your intermediate calculations. Round "Sharpe ratios" to 4 decimal places and other answers to 2 decimal
places.)
x Answer is not complete.
Hedge Fund
Portfolio
S&P Portfolio
Risk premiums
0.10
0.12
Standard deviations
0.16
0.31
Sharpe ratios
Transcribed Image Text:Greta has risk aversion of A= 5 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 5-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 10% per year, with a standard deviation of 16%. The hedge fund risk premium is estimated at 12% with a standard deviation of 31%. 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 return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim. Compute the estimated 1-year risk premiums, standard deviations, and Sharpe ratios for the two portfolios. (Do not round your intermediate calculations. Round "Sharpe ratios" to 4 decimal places and other answers to 2 decimal places.) x Answer is not complete. Hedge Fund Portfolio S&P Portfolio Risk premiums 0.10 0.12 Standard deviations 0.16 0.31 Sharpe ratios
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