ikoreaii

The following information is available for the Trumark Fund:

• The Trumark Fund has an average annual return of 12% over the last five years.
• Trumark has a beta value of 1.35.
• Trumark has a standard deviation of returns of 16.80%.
• During the same time period, the average annual T-bill rate was 4.5%.
• During the same time period, the average annual return on the S&P 500 portfolio was 18%.

What is the Sharpe ratio for the Trumark Fund?

A) 0.80.

B) 0.45.

C) 5.56.

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Sharpe Ratio = Sj = (Rj – RF) / σj = (12 − 4.50) / 16.80 = 0.45

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What is the Treynor measure for Trumark Fund?

A) 0.45.

B) -0.04.

C) 0.06.

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Treynor measure = Tj = (Rj – RF) / βj = (0.12 − .0450) / 1.35 = 0.0556

ikoreaii

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) Jensen's alpha and the Treynor measure.

C) Sharpe measure.

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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.

ikoreaii

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

                                                               Equity Fund                 S&P 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) 0.570.

B) 0.064.

C) 0.048.

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(0.13 – 0.0525)/1.21 = 0.064.

ikoreaii

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

                                                         Equity Fund            S&P 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) 0.87.

B) 0.76.

C) 0.84.

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(0.21 – 0.045)/0.19 = 0.87.

ikoreaii

The Sharpe ratio, Treynor measure, the M2 measure and Jensen’s 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) Using the capital market line the M2 compares the account's return to the market return and is a comparative measure.

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

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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.

ikoreaii

The ratio of return to systematic risk for an investment portfolio is 0.70, while the market is 0.50. This information suggests that the portfolio:

A) exhibits inferior performance because it has more risk than the market.

B) exhibits superior performance because the return per unit of risk is above that of the market.

C) is not diversified enough, and more securities should be purchased to bring the portfolio in line with the market.

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Risk-averse investors prefer a portfolio with a higher ratio of return to systematic risk to a portfolio with a lower ratio. In this case, we can also say that the portfolio would plot above the SML since the portfolio's ratio is above that of the market. Since portfolios that plot above the SML are undervalued, they are likely to provide an above average return. Note: The ratio (Treynor's Measure) implicitly assumes a diversified portfolio, hence the use of beta (or systematic risk) in the denominator.

ikoreaii

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

A) Both measures are equally appropriate.

B) Treynor measure.

C) Sharpe ratio.

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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 investor’s overall asset base.

manchester88

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

A) Sharpe ratio.

B) Jensen's Alpha.

C) Both measures are equally appropriate.

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Jensen’s Alpha measures the value added of an active portfolio strategy.

manchester88

Which of the following statements about the evaluation of portfolio performance is least accurate?

A) 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.

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

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

manchester88

Which of the following statements regarding diversification and risk adjusted performance measures is least accurate?

A) Treynor's performance measure should be used to evaluate portfolios that will be an addition to an overall larger portfolio.

B) Treynor's performance measure assumes a well diversified portfolio.

C) Investors want their portfolio managers to completely diversify their portfolios.

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If a portfolio manager completely diversifies (i.e., eliminates all non-systematic risk), then the appropriate rate of return would be that of the market. However, why would you pay active management fees to get the same return of a passively managed index product? Treynor uses beta as its risk measure, which means that it should be used in the context of a diversified portfolio.