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

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

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

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

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 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

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.

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

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.

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.