Reading 43: Evaluating Portfol....rmance－LOS p contrast, including, interpret, class

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CFA Institute Area 3-5, 7, 12, 14-18: Portfolio Management
Session 16: Performance Evaluation and Attribution
Reading 43: Evaluating Portfolio Performance
LOS p: Calculate, interpret, and contrast alternative risk-adjusted performance measures, including (in their ex post forms) alpha, information ratio, Treynor measure, Sharpe ratio, and M ².

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Which of the following statements about the evaluation of portfolio performance is FALSE?

A) When using the Sharpe ratio, the portfolio with the highest capital allocation line (CAL) slope is the best portfolio.

B) In the decomposition of portfolio performance, a naive portfolio is constructed with its standard deviation set equal to the total risk of the manager's portfolio that is being evaluated.

C) Beta is unstable over time and is dependant on the specific market index used in its calculation.

D) The security market line (SML) represents an active investment strategy when Jensen's Alpha is used as the measure for portfolio performance.

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 Answer and Explanation

The SML is a passive strategy in that the investor invests in a combination of the market portfolio and the risk free asset. Jensens Alpha measures the value added return due to active management.

The SML is a passive strategy in that the investor invests in a combination of the market portfolio and the risk free asset. Jensens Alpha measures the value added return due to active management.

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Of the Sharpe, Treynor, and Jensens Alpha measures, when measuring the risk/return performance of actively managed portfolios, which is the most appropriate to use?

A) Treynor measure.

B) Jensen's Alpha.

C) Sharpe ratio.

D) All three measures are equally appropriate.

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Answer and Explanation

Jensens Alpha measures the value added of an active portfolio strategy.

Jensens Alpha measures the value added of an active portfolio strategy.

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Of the Sharpe, Treynor, and Jensens Alpha measures, when dealing with a sector fund which will be added to the investors overall larger portfolio, which is the most relevant measurement technique to assess relative risk/return performance?

A) Treynor measure.

B) Sharpe ratio.

C) Jensen's Alpha.

D) All three measures are equally appropriate.

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Answer and Explanation

The Treynor measure calculates excess return relative to systematic risk and should be used to evaluate portfolios that will be an addition to an overall larger portfolio. Sharpe ratio, which uses standard deviation as the risk measure, should be used to evaluate portfolios that will comprise the majority of the investors overall asset base.

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The Sharpe ratio, Treynor measure, the M² measure and Jensens Alpha techniques all measure the risk/return performance of portfolios. Which of the following statements about these measurement techniques is least accurate?

A) The Sharpe ratio measures the slope of the capital allocation line (CAL), with the lowest slope having the most desirable risk/return combination.

B) While the Treynor measure computes excess return per unit of risk, Jensen's Alpha measures differential return for a given level of risk.

C) Using the capital market line the M2 compares the account's return to the market return and is a comparative measure.

D) The distinction between the Sharpe and Treynor measures is that Sharpe uses standard deviation of the portfolio as the risk measure, whereas Treynor uses the portfolio's beta.

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Answer and Explanation

Although it is true that the Sharpe ratio measures the slope of the CAL, the higher the slope the more desirable the portfolio. Your goal is to select the portfolio that has the highest Sharpe measure, which will also have the steepest slope. At any given risk level, the higher the slope the greater the return.

Although it is true that the Sharpe ratio measures the slope of the CAL, the higher the slope the more desirable the portfolio. Your goal is to select the portfolio that has the highest Sharpe measure, which will also have the steepest slope. At any given risk level, the higher the slope the greater the return.

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Which of the following measures used to evaluate the performance of a portfolio manager is/are NOT subject to the assumptions of the capital asset pricing model (CAPM)?

A) Jensen's alpha.

B) Treynor measure.

C) Sharpe measure.

D) Jensen's alpha and the Treynor measure.

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Answer and Explanation

Both the Treynor measure and the Jensen's alpha assume that the CAPM is the underlying risk-adjustment model. The Sharpe measure on the other hand does not make this assumption. It uses total risk of a portfolio, unlike the Treynor measure and Jensen's alpha, which use the systematic (undiversifiable) risk as measured by beta to compute the risk-adjusted return of a portfolio.

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Which of the following risk measures is NOT dependent on capital asset pricing model (CAPM)?

A) Jensen measure.

B) Treynor measure.

C) Sharpe measure.

D) None of the above.

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Answer and Explanation

The Sharpe measure uses standard deviation as its risk measure. The others use beta.

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An analyst has gathered the following information about the performance of an equity fund and the S& 500 index over the same time period.  

An analyst has gathered the following information about the performance of an equity fund and the S& 500 index over the same time period.  

                                                         Equity Fund            S& 500

                           Return                             21%                  24%           

                           Standard Deviation            19%                  17%

                           Beta                              1.05                    1.00

                           Risk-free rate is 4.50%

The Sharpe ratio for the equity fund is:

A) 0.76.

B) 0.87.

C) 0.98.

D) 0.84.

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Answer and Explanation

(0.21 0.045)/0.19 = 0.87.

(0.21 0.045)/0.19 = 0.87.

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An analyst has gathered the following information about the performance of an equity fund and the S& 500 index over the same time period.  

                                                               Equity Fund                 S& 500

               Return                                            13%                          10.5%              

               Standard Deviation                           22%                          20%

               Beta                                             1.21                          1.00

               Risk-free rate is 5.25%

The Treynor measure for the equity fund is:

A) 0.064.

B) 0.570.

C) 0.048.

D) 0.071.

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Answer and Explanation

(0.13 0.0525)/1.21 = 0.064.

(0.13 0.0525)/1.21 = 0.064.

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An analyst has gathered the following information about the performance of an equity fund and the S& 500 index over the same time period.  

An analyst has gathered the following information about the performance of an equity fund and the S& 500 index over the same time period.  

                                                      Equity Fund            S& 500

                  Return                                  27%                   29%        

                  Standard Deviation                33%                    20%

                  Beta                                    0.95                   1.00

                  Risk-free rate is 4.00%

The Treynor measure and the Sharpe ratio, in that order, for the S& 500 are:

A) 0.18 and 1.11.

B) 0.25 and 1.25.

C) 0.56 and 1.01.

D) 0.33 and 0.97.

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Answer and Explanation

Treynor measure: (0.29 0.04)/1.00 = 0.25

Sharpe ratio: (0.29 0.04)/0.20 = 1.25

Sharpe ratio: (0.29 0.04)/0.20 = 1.25

Treynor measure: (0.29 0.04)/1.00 = 0.25

Sharpe ratio: (0.29 0.04)/0.20 = 1.25

Sharpe ratio: (0.29 0.04)/0.20 = 1.25