manchester88

The following figures provide performance data for two managers, Cumulus Managers and Saturn Managers.  The benchmark return is 12% and its standard deviation is 25%. The risk-free rate is 4.2%.

	Cumulus	Saturn
Return	15.0%	18.0%
Standard Deviation	29.0%	33.0%
Beta	0.9	1.3

Which of the following would be the most appropriate conclusion regarding their relative performance, using the M2 measure and the Treynor ratio?

A) Saturn is the superior manager using both the M2 measure and the Treynor ratio.

B) Saturn is the superior manager using the M2 measure but not the Treynor ratio.

C) Cumulus is the superior manager using both the M2 measure and the Treynor ratio.

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To calculate the M-squared ratio for Cumulus, use the following formula:

We would compare the 13.51% to the return on the market of 12% and conclude that the Cumulus Fund has superior performance. Using the same formula as above, the M-squared measure for the Saturn fund is 14.65%, which indicates that the Saturn fund has superior performance relative to both the market and Cumulus fund.
The Treynor ratio for Cumulus would be calculated as:

The Treynor ratio for the Saturn fund is 10.6, which indicates that the Cumulus fund has superior performance relative to the Saturn fund.
The discrepancy between the two measures is because the M-squared measure uses the standard deviation (total risk) as the measure of risk whereas the Treynor ratio uses beta (systematic risk). The Cumulus fund is poorly diversified relative to the Saturn fund. When unsystematic risk is captured in the M-squared measure, the Cumulus fund is not as attractive as the Saturn fund.

manchester88

The following performance data for an actively managed portfolio and the S&P 500 Index is reported:

	Actively Managed Portfolio	S&P 500
Return	50%	20%
Standard deviation	18%	15%
Beta	1.1	1.0

Risk-free rate = 6%. Determine the Sharpe measure, Treynor measure, and Jensen's alpha for the actively managed portfolio.

A) Sharpe measure = 1.04; Treynor measure = 0.14; Alpha = 0.04.

B) Sharpe measure = 2.44; Treynor measure = 0.40; Alpha = 0.29.

C) Sharpe measure = 1.05; Treynor measure = 0.17; Alpha = 0.04.

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Sharpe measure for active portfolio = (0.50 − 0.06)/0.18 = 2.44 Treynor measure for active portfolio = (0.50 − 0.06)/1.1 = 0.40
Alpha for active portfolio = 0.50 − [0.06+(0.20 − 0.06) × 1.1)] = 0.29

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Based on the results from determining the Sharpe measure, Treynor measure, and Jensen's alpha for the actively managed portfolio, does the portfolio manager outperform or underperform the S&P 500 index?

A) Sharpe measure → underperform; Treynor measure → outperform; Alpha → outperform

B) Sharpe measure → outperform; Treynor measure → outperform; Alpha → outperform.

C) Sharpe measure → outperform; Treynor measure → underperform; Alpha → underperform.

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Sharpe measure for S&P portfolio = (0.20 − 0.06)/0.15 = 0.93 Treynor Measure for S&P portfolio = (0.20 − 0.06)/1.0 = 0.14 Alpha for S&P portfolio = 0
Hence, the portfolio manager outperforms based on all the three performance evaluation methods.

manchester88

The Sharpe Ratio is correctly defined as a measure of a fund’s:

A) excess return earned compared to its systematic risk.

B) return earned compared to its total risk.

C) excess return earned compared to its total risk.

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The Sharpe ratio is defined as a fund’s excess return (fund’s return minus the risk-free rate) divided by the total risk (standard deviation).

manchester88

Which of the following statements about risk/return investment manager performance measures is least accurate?

A) The Sharpe measure includes company-specific risk as part of its performance measurement.

B) The Treynor measure includes company-specific risk as part of its performance measurement.

C) When measuring the performance of an equity fund, if the Sharpe ratio is 0.55, and the Treynor measure is 0.47, the difference is attributable to unsystematic (company-specific) risk.

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The Treynor measure does not include company-specific risk, it uses beta in the denominator, which only measures systematic risk. Note that the Sharpe measure uses standard deviation in its denominator, which is a measure of total risk.

manchester88

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. Using Jensen’s Alpha to measure the risk/return performance of the Equity fund and the S&P 500, which of the following conclusions is CORRECT?

	Equity Fund	S&P 500
Return	23%	27%
Standard Deviation	15%	19%
Beta	1.09	1.00
Risk-free rate is 3.50%

A) The equity fund underperformed the S&P 500 by 6.12%.

B) The S&P 500 underperformed the equity fund by 2.67%.

C) The S&P 500 outperformed the equity fund by 3.24%.

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Jensen’s Alpha: 0.23 – [0.035 + (0.27 – 0.035)1.09] = -0.0612 or -6.12%. The negative means it underperformed the S&P 500.

manchester88

An analyst has generated the following information about risk/return performance using the Sharpe ratio and the Treynor measure:

	Equity Fund	S&P 500
Sharpe ratio	0.47	0.42
Treynor measure	0.31	0.34

Which of the following statements about the relative risk/return performance of the funds is CORRECT?

A) The Treynor measure shows the fund outperformed the S&P 500 on a systematic risk-adjusted basis.

B) The Sharpe ratio shows the equity fund outperformed the S&P 500 on a total risk- adjusted basis.

C) The Treynor measure shows the fund underperformed the S&P 500 on a total risk-adjusted basis.

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With either the Sharpe or Treynor methodology, a higher number means a higher risk-adjusted return. Since the Sharpe ratio is 0.05 higher, it outperformed the S&P 500. Note that the key difference between the Sharpe and Treynor measures is that the Sharpe ratio measures return per unit of total risk, while Treynor measures return per unit of systematic risk.

manchester88

The Treynor measure is correctly defined as a measure of a fund’s:

A) return earned compared to its systematic risk.

B) excess earned compared to its systematic risk.

C) return earned compared to its unsystematic risk.

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The Treynor measure is defined as a fund’s excess return (fund’s return minus the risk-free rate) divided by its systematic risk (beta).

manchester88

Jensen’s alpha for a portfolio measures the:

A) fund’s return in excess of the required rate of return given the unsystematic risk of the portfolio.

B) difference between a fund’s return and the market return.

C) fund’s return in excess of the required rate of return given the systematic risk of the portfolio.

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Jensen’s alpha measures the return above the required rate of return based on the fund’s systematic risk. Said differently, Jensen’s alpha is the amount of return earned by the fund over and above the return predicted for the fund based on the capital asset pricing model, given the fund’s systematic risk.

manchester88

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                                -12%                    -16%         

                    Standard Deviation                15%                     19%

                    Beta                                  1.18                     1.00

                    Risk-free rate is 6.00%

The difference between the Treynor measure for the equity fund and the Treynor measure for the S&P 500 is:

A) 0.15.

B) 0.07.

C) 0.17.

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The equity fund: (-0.12 – 0.06)/1.18 = -0.15
The S&P 500: (-0.16 – 0.06)/1.00 = -0.22
The equity fund is (-0.15 – (-0.22) = 0.07 higher

manchester88

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                           32%                    26%            

                           Standard Deviation          41%                    29%

                           Beta                            0.98                    1.00

                           Risk-free rate is 6.00%

The difference between the Sharpe ratio for the equity fund and the Sharpe ratio for the S&P 500 is the:

A) S&P 500 is 0.04 lower.

B) equity fund is 0.06 lower.

C) S&P 500 is 0.09 higher.

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The equity fund Sharpe ratio: (0.32 – 0.06)/0.41 = 0.63
The S&P 500 Sharpe ratio: (0.26 – 0.06)/0.29 = 0.69
The equity fund is (0.63 – 0.69) = -0.06 lower