An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor's 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Annual Average Standard Deviation Rate of Return of Return Beta Portfolio X 11% 18% 0.40 S&P 500 13 14 1.00 T-bills 6 n/a n/a n/a = not applicable a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places. Treynor measure Sharpe measure Portfolio X % S&P 500 % Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. Based on the Treynor measure Portfolio X-Select- v the market index because Treynor measure for Portfolio X is -Select- v than Treynor measure for the S&P 500. Based on the Sharpe measure Portfolio X -Select- v the market index because Sharpe measure for Portfolio X is -Select- v than Sharpe measure for the S&P 500. b. Based on the performance of Portfolio X relative to the S&P 500 calculated in Part a, briefly explain the reason for the conflicting results when using the Treynor measure
An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor's 500 Index), and U.S. Treasury bills (T-bills) during the past eight years. Annual Average Standard Deviation Rate of Return of Return Beta Portfolio X 11% 18% 0.40 S&P 500 13 14 1.00 T-bills 6 n/a n/a n/a = not applicable a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places. Treynor measure Sharpe measure Portfolio X % S&P 500 % Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. Based on the Treynor measure Portfolio X-Select- v the market index because Treynor measure for Portfolio X is -Select- v than Treynor measure for the S&P 500. Based on the Sharpe measure Portfolio X -Select- v the market index because Sharpe measure for Portfolio X is -Select- v than Sharpe measure for the S&P 500. b. Based on the performance of Portfolio X relative to the S&P 500 calculated in Part a, briefly explain the reason for the conflicting results when using the Treynor measure
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:An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table
provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor's 500 Index), and U.S. Treasury bills (T-bills) during the
past eight years.
Annual Average Standard Deviation
Rate of Return
of Return
Beta
Portfolio X
11%
18%
0.40
S&P 500
13
14
1.00
T-bills
6
n/a
n/a
n/a = not applicable
a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place
and for the Sharpe measure to three decimal places.
Treynor measure
Sharpe measure
Portfolio X
S&P 500
%
Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe
measure.
Based on the Treynor measure Portfolio X-Select-
v V
| the market index because Treynor measure for Portfolio X is Select-
| than Treynor measure for the S&P
500.
Based on the Sharpe measure Portfolio X -Select-
v the market index because Sharpe measure for Portfolio X is -Select- V than Sharpe measure for the S&P 500.
b. Based on the performance of Portfolio X relative to the S&P 500 calculated in Part a, briefly explain the reason for the conflicting results when using the Treynor measure
versus the Sharpe measure.
As Treynor measure considers -Select-
Vrisk while Sharpe measures considers -Select-
v risk so a -Select- v diversified
portfolio could show better performance relative to the market if the Treynor measure is used but lower performance relative to the market if the Sharpe measure is
used. As a result, Portfolio X has a large amount of -Select-
v risk.
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