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 9% per year, with a standard deviation of 17%. The hedge fund risk premium is estimated at 11% with a standard deviation of 32%. 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.) Risk premiums Standard deviations Sharpe ratios S&P Portfolio Hedge Fund Portfolio

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 9% per year, with a standard deviation of 17%. The hedge fund risk premium is estimated at 11% with a standard deviation of 32%. 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.) Risk premiums Standard deviations Sharpe ratios S&P Portfolio Hedge Fund Portfolio

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 5P

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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% per year, with a SD of 20%. The hedge fund risk premium is estimated at 10% with a SD of 35%. 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.Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation?
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