2. 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 & 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 10% 18% 0.60 S&P 500 13 1.00 12 n/a T-bills 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. Briefly explain whether Portfolio X underperformed, equaled, or outper- formed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. 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.
2. 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 & 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 10% 18% 0.60 S&P 500 13 1.00 12 n/a T-bills 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. Briefly explain whether Portfolio X underperformed, equaled, or outper- formed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. 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.
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:2. 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 & 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
10%
18%
0.60
S&P 500
13
1.00
12
n/a
T-bills
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. Briefly explain whether Portfolio X underperformed, equaled, or outper-
formed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the
Sharpe measure.
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.
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