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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Bill Carter, CFA and Bob Walters, CFA are analyzing the recent return of several funds they have been assigned to manage. The funds are Fund A, Fund B, Fund C, and Fund D as indicated in the table below.

		Fund A	Fund B	Fund C	Fund D	Market
Return		7.80%	7.20%	8.20%	7.60%	7.00%
Beta		1.10	0.90	1.20	1.05	1.00
Return Std.Dev.		4.00%	3.44%	4.15%	3.50%	3.55%
Tracking Error*		0.82%	0.45%	1.02%	0.67%
*Tracking error is the standard deviation of the difference between the Fund Return and the Market Index Return

The risk-free rate of return for the relevant period was 3.5%.

The management of the firm that Carter and Walters works for is very proud of the fact that all of the four funds had a higher return than the overall market as indicated on the table. The firms management wants to advertise how, using the market as a benchmark, these funds have had returns higher than that benchmark. The firms management asks Carter and Walters to compute several performance measures such as the Treynor measure, the Sharpe ratio, and the M² measure. The firms management also asks for the construction of quality control charts.

In going over the results, Carter is skeptical of the results and using the market as a benchmark because that benchmark was not specified in advance. Walters says that he is skeptical too because it is not clear if the market is an appropriate benchmark in all cases. They want to proceed cautiously because the firms management recently instituted policies for manager continuation. For each manager, the firms management has set up the null hypothesis that a manager has no skill and the alternative hypothesis is that the manager has skill in adding value.

Carter and Walters discuss constructing a custom benchmark for some of these or other funds they might manage. A few of these funds hold cash positions to take advantage of good investment opportunities when they arise. Carter says that the benchmark they construct should include cash in the weighting scheme. They set aside a few weeks to construct a preliminary benchmark for several funds. Walters wants to be thorough, because once they construct the benchmark, he doesnt plan to make any modifications to the custom benchmark.

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If the returns of each fund were plotted over a quality control chart using the market as a benchmark, the final point of the value-added line would be above zero, i.e., above the horizontal axis for:

A) all of the funds except C only.

B) B only.

C) none of the funds.

D) all of the funds.

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Answer and Explanation

Since all of the funds returns are higher than the benchmark for the period, all of the funds would have a positive end point for the cumulative value-added line.

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With respect to the reasons for Carter and Walters being skeptical of using the market as a benchmark:

A) both Carter and Walters are correct.

B) both Carter and Walters are wrong.

C) Carter is correct and Walters is wrong.

D) Carter is wrong and Walters is correct.

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Answer and Explanation

Their objections are both justified. A benchmark should be specified in advance and deemed appropriate for the style of the fund.

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With respect to the considerations that Carter and Walters put into preparing a custom benchmark, including a weighting for cash and not making modifications:

A) Carter and Walters are both correct.

B) Carter is correct and Walters is wrong.

C) Carter and Walters are both wrong.

D) Carter is wrong and Walters is correct.

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Answer and Explanation

Carter is correct in that a custom benchmark should include an appropriate weight for cash holdings. Walters is wrong in that a benchmark should be modified on a preset schedule.

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The firm that Carter and Walters work for have set up a null hypothesis for each manager. In such a case, the firm would make a type II error if it:

A) keeps an unskilled manager.

B) hires a second manager to help a doubtful manager.

C) uses a course filter rather than a fine filter in the evaluation process.

D) fires a skilled manager.

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Answer and Explanation

In this case, we assume a manager does not add value and try to gather information that the manager does. Without sufficient evidence to prove value is added, the manager would be fired. Random noise could lead to this conclusion even though the manager does add value.

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接着上一帖的题

Using the Sharpe Measure, rank the four funds in terms of the risk-adjusted excess returns starting with the highest performing fund and ending with the lowest performing fund:

A) Bould, Adams, Dixon, Winterburn.

B) Adams, Bould, Winterburn, Dixon.

C) Bould, Adams, Winterburn, Dixon.

D) Adams, Bould, Dixon, Winterburn.

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Answer and Explanation

Thus the ranking is 1) Adams 2) Bould 3) Dixon 4) Winterburn.

Thus the ranking is 1) Adams 2) Bould 3) Dixon 4) Winterburn.

Thus the ranking is 1) Adams 2) Bould 3) Dixon 4) Winterburn.

[此贴子已经被作者于2008-9-17 18:26:57编辑过]

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The following information is available for the Trumark Fund:

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

What is the Sharpe ratio for the Trumark Fund?

A) 5.56.

B) 0.45.

C) 0.80.

D) 7.50.

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Answer and Explanation

Sharpe Ratio = S_j = (R_j
    R_F) / σ_j = (12 - 4.50) / 16.80 = 0.45
  

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What is the Treynor measure for Trumark Fund?

A) 0.45.

B) 0.80.

C) 0.06.

D) -0.04.

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Answer and Explanation

Treynor measure = T_j = (R_j
    R_F) / β_j = (.12 - .0450) / 1.35 = 0.0556
  

[此贴子已经被作者于2008-9-17 18:19:55编辑过]

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The Treynor measure is correctly defined as a measure of a funds:

A) return earned compared to its systematic risk.

B) return earned compared to its unsystematic risk.

C) excess earned compared to its systematic risk.

D) excess return earned compared to its total risk.

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Answer and Explanation

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

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Jensens alpha for a portfolio measures the:

A) funds return in excess of the required rate of return given the unsystematic risk of the portfolio.

B) difference between a funds return and the market return.

C) funds return in excess of the required rate of return given the systematic risk of the portfolio.

D) difference between the funds Sharpe ratio and Treynor measure.

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Answer and Explanation

Jensens alpha measures the return above the required rate of return based on the funds systematic risk. Said differently, Jensens 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 funds systematic risk.

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The Sharpe Ratio is correctly defined as a measure of a funds:

A) excess return earned compared to its systematic risk.

B) excess return earned compared to its total risk.

C) return earned compared to its unsystematic risk.

D) return earned compared to its total risk.

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Answer and Explanation

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

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If a portfolio had an alpha of −10 bps, then the portfolio:

A) had less risk than the market.

B) earned 10 bps less than the market on a risk-adjusted basis.

C) earned 10 bps less than the market.

D) had a return of 10 bps.

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Answer and Explanation

Recall that Jensens alpha measures excess return for a given level of risk. It is a risk-adjusted measure of return.

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

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

Risk-free rate = 6 percent.

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.

D) Sharpe measure = 1.06; Treynor measure = 0.12; Alpha = 0.02.

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Answer and Explanation

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) x 1.1)] = 0.29

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) x 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& 500 index?

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

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

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

D) Sharpe measure → underperform; Treynor measure → underperform; Alpha → underperform.

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Answer and Explanation

Sharpe measure for S& portfolio = (0.20 - 0.06)/0.15 = 0.93

Treynor Measure for S& portfolio = (0.20 - 0.06)/1.0 = 0.14

Alpha for S& portfolio = 0

Hence, the portfolio manager outperforms based on all the three performance evaluation methods.

Treynor Measure for S& portfolio = (0.20 - 0.06)/1.0 = 0.14

Alpha for S& portfolio = 0

Hence, the portfolio manager outperforms based on all the three performance evaluation methods.

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

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

C) is too diversified, and some securities should be sold to bring the portfolio in line with the market.

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

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Answer and Explanation

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.