The following information applies to Problems 22 through 27: Greta has 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 continu- ously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a standard devia- tion of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation 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. 22. Compute the estimated annual risk premiums, standard deviations, and Sharpe ratios for the two portfolios. 23. Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? 24. What should be Greta's capital allocation? 25. If the correlation coefficient between annual portfolio returns is actually .3, what is the covari- ance between the returns? 26. Repeat Problem 23 using an annual correlation of .3. 27. Repeat Problem 24 using an annual correlation of .3.
The following information applies to Problems 22 through 27: Greta has 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 continu- ously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a standard devia- tion of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation 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. 22. Compute the estimated annual risk premiums, standard deviations, and Sharpe ratios for the two portfolios. 23. Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? 24. What should be Greta's capital allocation? 25. If the correlation coefficient between annual portfolio returns is actually .3, what is the covari- ance between the returns? 26. Repeat Problem 23 using an annual correlation of .3. 27. Repeat Problem 24 using an annual correlation of .3.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:The following information applies to Problems 22 through 27: Greta has 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 continu-
ously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a standard devia-
tion of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation 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.
22. Compute the estimated annual risk premiums, standard deviations, and Sharpe ratios for the two
portfolios.
23. Assuming the correlation between the annual returns on the two portfolios is indeed zero, what
would be the optimal asset allocation?
24. What should be Greta's capital allocation?
25. If the correlation coefficient between annual portfolio returns is actually .3, what is the covari-
ance between the returns?
26. Repeat Problem 23 using an annual correlation of .3.
27. Repeat Problem 24 using an annual correlation of .3.
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