Chapter 24 - Portfolio Performance Evaluation
Chapter 24
Portfolio Performance Evaluation
Multiple Choice Questions
1. Hedge funds
I) are appropriate as a sole investment vehicle for an investor.
II) should only be added to an already well-diversified portfolio.
III) pose performance evaluation issues due to non-linear factor exposures.
IV) have down-market betas that are typically larger than up-market betas.
V) have symmetrical betas.
A. I only
B. II and V
C. I, III, and IV
D. II, III, and IV
E. I, III, and V
2. Mutual funds show ____________ evidence of serial correlation and hedge funds show
____________ evidence of serial correlation.
A. almost no; almost no
B. almost no; substantial
C. substantial; substantial
D. substantial; almost no
E. modest; modest
3. The comparison universe is __________.
A. a concept found only in astronomy
B. the set of all mutual funds in the world
C. the set of all mutual funds in the U.S.
D. a set of mutual funds with similar risk characteristics to your mutual fund
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
4. The comparison universe is not __________.
A. a concept found only in astronomy
B. the set of all mutual funds in the world
C. the set of all mutual funds in the U.S.
D. a set of mutual funds with similar risk characteristics to your mutual fund
E. a concept found only in astronomy, the set of all mutual funds in the world, and the set of
all mutual funds in the U. S.
5. __________ did not develop a popular method for risk-adjusted performance evaluation of
mutual funds.
A. Eugene Fama
B. Michael Jensen
C. William Sharpe
D. Jack Treynor
E. Eugene Fama and Michael Jensen
6. __________ developed a popular method for risk-adjusted performance evaluation of
mutual funds.
A. Eugene Fama
B. Michael Jensen
C. William Sharpe
D. Jack Treynor
E. Michael Jensen, William Sharpe, and Jack Treynor
7. Henriksson (1984) found that, on average, betas of funds __________ during market
advances.
A. increased very significantly
B. increased slightly
C. decreased slightly
D. decreased very significantly
E. did not change
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8. Most professionally managed equity funds generally __________.
A. outperform the S&P 500 index on both raw and risk-adjusted return measures
B. underperform the S&P 500 index on both raw and risk-adjusted return measures
C. outperform the S&P 500 index on raw return measures and underperform the S&P 500
index on risk-adjusted return measures
D. underperform the S&P 500 index on raw return measures and outperform the S&P 500
index on risk-adjusted return measures
E. match the performance of the S&P 500 index on both raw and risk-adjusted return
measures
9. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a higher beta than portfolio B. According to the Sharpe measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
10. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a higher beta than portfolio B. According to the Treynor measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
11. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a lower beta than portfolio B. According to the Treynor measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
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12. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a higher beta than Raider Fund. According to the Sharpe
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
13. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a higher beta than Raider Fund. According to the Treynor
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
14. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a lower beta than Raider Fund. According to the Treynor
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
15. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a higher beta than Gator Fund. According to the Sharpe
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
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16. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a lower beta than Gator Fund. According to the Sharpe
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
17. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a lower beta than Gator Fund. According to the Treynor
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
18. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a higher beta than Gator Fund. According to the Treynor
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct is true.
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Chapter 24 - Portfolio Performance Evaluation
19. Morningstar's RAR method
I) is one of the most widely used performance measures.
II) indicates poor performance by placing up to 5 darts next to the fund's name.
III) computes fund returns adjusted for loads.
IV) computes fund returns adjusted for risk.
V) produces ranking results that are the same as those produced with the Sharpe measure.
A. I, II, and IV
B. I, III, and IV
C. I, IV, and V
D. I, II, IV, and V
E. I, II, III, IV, and V
20. Suppose you purchase 100 shares of GM stock at the beginning of year 1, and purchase
another 100 shares at the end of year 1. You sell all 200 shares at the end of year 2. Assume
that the price of GM stock is $50 at the beginning of year 1, $55 at the end of year 1, and $65
at the end of year 2. Assume no dividends were paid on GM stock. Your dollar-weighted
return on the stock will be __________ your time-weighted return on the stock.
A. higher than
B. the same as
C. less than
D. exactly proportional to
E. More information is necessary to answer this question.
21. Suppose the risk-free return is 4%. The beta of a managed portfolio is 1.2, the alpha is 1%,
and the average return is 14%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 11.5%
B. 14%
C. 15%
D. 16%
E. None of these is correct.
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22. Suppose the risk-free return is 3%. The beta of a managed portfolio is 1.75, the alpha is
0%, and the average return is 16%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 12.3%
B. 10.4%
C. 15.1%
D. 16.7%
E. None of these is correct.
23. Suppose the risk-free return is 6%. The beta of a managed portfolio is 1.5, the alpha is 3%,
and the average return is 18%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 12%
B. 14%
C. 15%
D. 16%
E. None of these is correct.
24. Suppose a particular investment earns an arithmetic return of 10% in year 1, 20% in year 2
and 30% in year 3. The geometric average return for the year period will be __________.
A. greater than the arithmetic average return
B. equal to the arithmetic average return
C. less than the arithmetic average return
D. equal to the market return
E. Cannot tell from the information given.
25. Suppose you buy 100 shares of Abolishing Dividend Corporation at the beginning of year
1 for $80. Abolishing Dividend Corporation pays no dividends. The stock price at the end of
year 1 is $100, $120 at the end of year 2, and $150 at the end of year 3. The stock price
declines to $100 at the end of year 4, and you sell your 100 shares. For the four years, your
geometric average return is __________.
A. 0.0%
B. 1.0%
C. 5.7%
D. 9.2%
E. 34.5%
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Chapter 24 - Portfolio Performance Evaluation
26. You want to evaluate three mutual funds using the information ratio measure for
performance evaluation. The risk-free return during the sample period is 6%, and the average
return on the market portfolio is 19%. The average returns, residual standard deviations, and
betas for the three funds are given below.
The fund with the highest information ratio measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest.
E. Funds A and C are tied for highest.
27. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 6%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The fund with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest.
E. Funds A and C are tied for highest.
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Chapter 24 - Portfolio Performance Evaluation
28. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 4%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The fund with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest.
E. Funds A and C are tied for highest.
29. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 5%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The investment with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. the index
E. Funds A and C are tied for highest.
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Chapter 24 - Portfolio Performance Evaluation
30. You want to evaluate three mutual funds using the Treynor measure for performance
evaluation. The risk-free return during the sample period is 6%. The average returns, standard
deviations, and betas for the three funds are given below, in addition to information regarding
the S&P 500 index.
The fund with the highest Treynor measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest.
E. Funds A and C are tied for highest.
31. You want to evaluate three mutual funds using the Jensen measure for performance
evaluation. The risk-free return during the sample period is 6%, and the average return on the
market portfolio is 18%. The average returns, standard deviations, and betas for the three
funds are given below.
The fund with the highest Jensen measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest.
E. Funds A and C are tied for highest.
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Chapter 24 - Portfolio Performance Evaluation
32. Suppose you purchase one share of the stock of Volatile Engineering Corporation at the
beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend, and buy one
more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each
share), and sell the shares for $36.45 each. The time-weighted return on your investment is
________.
A. −1.75%
B. 4.08%
C. 8.53%
D. 11.46%
E. 12.35%
33. Suppose you purchase one share of the stock of Volatile Engineering Corporation at the
beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend, and buy one
more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each
share), and sell the shares for $36.45 each. The dollar-weighted return on your investment is
_______.
A. −1.75%
B. 4.08%
C. 8.53%
D. 8.00%
E. 12.35%
34. Suppose you purchase one share of the stock of Cereal Correlation Company at the
beginning of year 1 for $50. At the end of year 1, you receive a $1 dividend, and buy one
more share for $72. At the end of year 2, you receive total dividends of $2 (i.e., $1 for each
share), and sell the shares for $67.20 each. The time-weighted return on your investment is
__________.
A. 10.0%
B. 8.7%
C. 19.7%
D. 17.6%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
35. Suppose you purchase one share of the stock of Cereal Correlation Company at the
beginning of year 1 for $50. At the end of year 1, you receive a $1 dividend, and buy one
more share for $72. At the end of year 2, you receive total dividends of $2 (i.e., $1 for each
share), and sell the shares for $67.20 each. The dollar-weighted return on your investment is
__________.
A. 10.00%
B. 8.78%
C. 19.71
D. 20.36%
E. None of these is correct.
36. Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B
earns a 9% return. In year 2, stock A earns an 18% return and stock B earns an 11% return.
__________ has the higher arithmetic average return.
A. Stock A
B. Stock B
C. The two stocks have the same arithmetic average return.
D. At least three periods are needed to calculate the arithmetic average return.
E. None of these is correct.
37. Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B
earns a 9% return. In year 2, stock A earns an 18% return and stock B earns an 11% return.
Which stock has the higher geometric average return?
A. Stock A
B. Stock B
C. The two stocks have the same geometric average return.
D. At least three periods are needed to calculate the geometric average return.
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
The following data are available relating to the performance of Sooner Stock Fund and the
market portfolio:
The risk-free return during the sample period was 3%.
38. What is the Sharpe measure of performance evaluation for Sooner Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 38.6%
E. 37.14%
39. What is the Treynor measure of performance evaluation for Sooner Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 9.44%
E. 37.14%
40. Calculate the Jensen measure of performance evaluation for Sooner Stock Fund.
A. 2.6%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
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Chapter 24 - Portfolio Performance Evaluation
41. Calculate the information ratio for Sooner Stock Fund.
A. 1.53
B. 1.30
C. 8.67
D. 31.43
E. 37.14
The following data are available relating to the performance of Monarch Stock Fund and the
market portfolio:
The risk-free return during the sample period was 4%.
42. What is the information ratio measure of performance evaluation for Monarch Stock
Fund?
A. 1.00%
B. 280.00%
C. 44.00%
D. 50.00%
E. None of these is correct.
43. Calculate Sharpe's measure of performance for Monarch Stock Fund.
A. 1.00%
B. 46.00%
C. 44.00%
D. 50.00%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
44. Calculate Treynor's measure of performance for Monarch Stock Fund.
A. 10.40%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
45. Calculate Jensen's measure of performance for Monarch Stock Fund.
A. 1.00%
B. 2.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
The following data are available relating to the performance of Seminole Fund and the
market portfolio:
The risk-free return during the sample period was 6%.
46. If you wanted to evaluate the Seminole Fund using the M2 measure, what percent of the
adjusted portfolio would need to be invested in T-Bills?
A. −36% (borrow)
B. 50%
C. 8%
D. 36%
E. 27%
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Chapter 24 - Portfolio Performance Evaluation
47. Calculate the M2 measure for the Seminole Fund.
A. 4.0%
B. 20.0%
C. 2.86%
D. 0.8%
E. 40.0%
48. If an investor has a portfolio that has constant proportions in T-bills and the market
portfolio, the portfolio's characteristic line will plot as a line with ___________; if the
investor can time bull markets, the characteristic line will plot as a line with ___________.
A. a positive slope; a negative slope
B. a negative slope; a positive slope
C. a constant slope; a negative slope
D. a negative slope; a constant slope
E. a constant slope; a positive slope
49. Studies of style analysis have found that ________ of fund returns can be explained by
asset allocation alone.
A. between 50% and 70%
B. less than 10%
C. between 40 and 50%
D. between 75% and 90%
E. over 90%
The following data are available relating to the performance of Wildcat Fund and the market
portfolio:
The risk-free return during the sample period was 7%.
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Chapter 24 - Portfolio Performance Evaluation
50. What is the information ratio measure of performance evaluation for Wildcat Fund?
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
51. Calculate Sharpe's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
52. Calculate Treynor's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
53. Calculate Jensen's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
The following data are available relating to the performance of Long Horn Stock Fund and
the market portfolio:
The risk-free return during the sample period was 6%.
54. What is the Sharpe measure of performance evaluation for Long Horn Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
55. What is the Treynor measure of performance evaluation for Long Horn Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
56. Calculate the Jensen measure of performance evaluation for Long Horn Stock Fund.
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
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Chapter 24 - Portfolio Performance Evaluation
57. Calculate the information ratio for Long Horn Stock Fund.
A. 1.33
B. 4.00
C. 8.67
D. 31.43
E. 37.14
In a particular year, Razorback Mutual Fund earned a return of 1% by making the following
investments in asset classes:
The return on a bogey portfolio was 2%, calculated from the following information.
58. The total excess return on the Razorback Fund's managed portfolio was __________.
A. −1.80%
B. −1.00%
C. 0.80%
D. 1.00%
E. None of these is correct.
59. The contribution of asset allocation across markets to the Razorback Fund's total excess
return was __________.
A. −1.80%
B. −1.00%
C. 0.80%
D. 1.00%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
60. The contribution of selection within markets to the Razorback Fund's total excess return
was __________.
A. −1.80%
B. −1.00%
C. 0.80%
D. 1.00%
E. None of these is correct.
In a particular year, Aggie Mutual Fund earned a return of 15% by making the following
investments in the following asset classes:
The return on a bogey portfolio was 10%, calculated as follows:
61. The total excess return on the Aggie managed portfolio was __________.
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct.
62. The contribution of asset allocation across markets to the total excess return was
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
63. The contribution of selection within markets to total excess return was
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct.
64. In measuring the comparative performance of different fund managers, the preferred
method of calculating rate of return is __________.
A. internal rate of return
B. arithmetic average
C. dollar-weighted
D. time-weighted
E. None of these is correct.
65. The __________ measures the reward to volatility trade-off by dividing the average
portfolio excess return by the standard deviation of returns.
A. Sharpe measure
B. Treynor measure
C. Jensen measure
D. information ratio
E. None of these is correct.
66. A pension fund that begins with $500,000 earns 15% the first year and 10% the second
year. At the beginning of the second year, the sponsor contributes another $300,000. The
dollar-weighted and time-weighted rates of return, respectively, were
A. 11.7% and 12.5%
B. 12.1% and 12.5%
C. 12.5% and 11.7%
D. 12.5% and 12.1%
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
67. The Value Line Index is an equally weighted geometric average of the returns of about
1,700 firms. The value of an index based on the geometric average returns of 3 stocks where
the returns on the 3 stocks during a given period were 32%, 5%, and −10%, respectively, is
__________.
A. 4.3%
B. 7.6%
C. 9.0%
D. 13.4%
E. 5.0%
68. Risk-adjusted mutual fund performance measures have decreased in popularity because
A. in nearly efficient markets it is extremely difficult for portfolio managers to outperform the
market.
B. the measures usually result in negative performance results for the portfolio managers.
C. the high rates of return earned by the mutual funds have made the measures useless.
D. in nearly efficient markets it is extremely difficult for portfolio managers to outperform the
market and the measures usually result in negative performance results for the portfolio
managers.
E. None of these is correct.
69. The Sharpe, Treynor, and Jensen portfolio performance measures are derived from the
CAPM,
A. therefore, it does not matter which measure is used to evaluate a portfolio manager.
B. however, the Sharpe and Treynor measures use different risk measures, therefore the
measures vary as to whether or not they are appropriate, depending on the investment
scenario.
C. therefore, all measure the same attributes.
D. therefore, it does not matter which measure is used to evaluate a portfolio manager and
however, the Sharpe and Treynor measures use different risk measures, therefore the
measures vary as to whether or not they are appropriate, depending on the investment
scenario.
E. None of these is correct.
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Chapter 24 - Portfolio Performance Evaluation
70. The Jensen portfolio evaluation measure
A. is a measure of return per unit of risk, as measured by standard deviation.
B. is an absolute measure of return over and above that predicted by the CAPM.
C. is a measure of return per unit of risk, as measured by beta.
D. is a measure of return per unit of risk, as measured by standard deviation and is an absolute
measure of return over and above that predicted by the CAPM.
E. is an absolute measure of return over and above that predicted by the CAPM and is a
measure of return per unit of risk, as measured by beta.
71. The M-squared measure
A. considers only the return when evaluating mutual funds.
B. considers the risk-adjusted return when evaluating mutual funds.
C. considers only the total risk when evaluating mutual funds.
D. considers only the market risk when evaluating mutual funds.
E. None of these is correct.
72. The dollar-weighted return on a portfolio is equivalent to
A. the time-weighted return.
B. the geometric average return.
C. the arithmetic average return.
D. the portfolio's internal rate of return.
E. None of these is correct.
73. A portfolio manager's ranking within a comparison universe may not provide a good
measure of performance because
A. portfolio returns may not be calculated in the same way.
B. portfolio durations can vary across managers.
C. if managers follow a particular style or subgroup, portfolios may not be comparable.
D. portfolio durations can vary across managers and if managers follow a particular style or
subgroup, portfolios may not be comparable.
E. All of these are correct.
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Chapter 24 - Portfolio Performance Evaluation
74. The geometric average rate of return is based on
A. the market's volatility.
B. the concept of expected return.
C. the standard deviation of returns.
D. the CAPM.
E. the principle of compounding.
75. The M2 measure was developed by
A. Merton and Miller.
B. Miller and Miller.
C. Modigliani and Miller.
D. Modigliani and Modigliani.
E. the M&M Mars Company.
76. Rodney holds a portfolio of risky assets that represents his entire risky investment. To
evaluate the performance of Rodney's portfolio, in which order would you complete the steps
listed?
I) Compare the Sharpe measure of Rodney's portfolio to the Sharpe measure of the best
portfolio.
II) State your conclusions.
III) Assume that past security performance is representative of expected performance.
IV) Determine the benchmark portfolio that Rodney would have held if he had chosen a
passive strategy.
A. I, III, IV, II
B. III, IV, I, II
C. IV, III, I, II
D. III, II, I, IV
E. III, I, IV, II
77. The Modigliani M2 measure and the Treynor T2 measure
A. are identical.
B. are nearly identical and will rank portfolios the same way.
C. are nearly identical but might rank portfolios differently.
D. are somewhat different; M2 can be used to rank portfolios but T2 cannot.
E. are somewhat different; T2 can be used to rank portfolios but M2 cannot.
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Chapter 24 - Portfolio Performance Evaluation
78. To determine whether portfolio performance is statistically significant requires
A. a very long observation period due to the high variance of stock returns.
B. a short observation period due to the high variance of stock returns.
C. a very long observation period due to the low variance of stock returns.
D. a short observation period due to the low variance of stock returns.
E. a low variance of returns over any observation period.
Short Answer Questions
79. Define and discuss the Sharpe, Treynor, and Jensen measures of portfolio performance
evaluation, and the situations in which each measure is the most appropriate measure.
80. What is the problem with using the Sharpe measure for evaluation of an active portfolio
management strategy?
81. Discuss, in general, the performance attribution procedures.
24-25
Chapter 24 - Portfolio Performance Evaluation
82. You invested $1,000 through your broker three years ago. Your account balance at the
beginning of each period is shown in the table below.
- Calculate the annual return for each year. Show your calculations in the table.
- Your broker called to tell you the good news that your average annual return over the three
years has been 4%. Where did he get this number?
- At first you are confused. It seems as though the broker must be mistaken because you are
no better off than when you started investing three years ago. But then you remember
something from your favorite Investments class. Suggest an alternate measure for the average
return. Calculate this measure and explain to your broker why it is more appropriate.
- Explain to your broker when it would make sense to use the 4% result that he initially
quoted you.
24-26
Chapter 24 - Portfolio Performance Evaluation
83. Discuss the M2 measure of performance by answering the following questions. Why is M2
better than the Sharpe measure? What measure of risk does M2 use? How do you construct a
managed portfolio, P, to use in computing the M2 measure? What is the formula for M2?
Draw a graph that shows how M2 would be measured. Be sure to label the axes and all
relevant points.
24-27
Chapter 24 - Portfolio Performance Evaluation
Chapter 24 Portfolio Performance Evaluation Answer Key
Multiple Choice Questions
1. Hedge funds
I) are appropriate as a sole investment vehicle for an investor.
II) should only be added to an already well-diversified portfolio.
III) pose performance evaluation issues due to non-linear factor exposures.
IV) have down-market betas that are typically larger than up-market betas.
V) have symmetrical betas.
A. I only
B. II and V
C. I, III, and IV
D. II, III, and IV
E. I, III, and V
Hedge funds should only be added to an already well-diversified portfolio, pose performance
evaluation issues due to non-linear factor exposures, and have down-market betas that are
typically larger than up-market betas.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-28
Chapter 24 - Portfolio Performance Evaluation
2. Mutual funds show ____________ evidence of serial correlation and hedge funds show
____________ evidence of serial correlation.
A. almost no; almost no
B. almost no; substantial
C. substantial; substantial
D. substantial; almost no
E. modest; modest
Mutual funds show almost no evidence of serial correlation and hedge funds show substantial
evidence of serial correlation.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
3. The comparison universe is __________.
A. a concept found only in astronomy
B. the set of all mutual funds in the world
C. the set of all mutual funds in the U. S.
D. a set of mutual funds with similar risk characteristics to your mutual fund
E. None of these is correct
A mutual fund manager is evaluated against the performance of managers of funds of similar
risk characteristics.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
24-29
Chapter 24 - Portfolio Performance Evaluation
4. The comparison universe is not __________.
A. a concept found only in astronomy
B. the set of all mutual funds in the world
C. the set of all mutual funds in the U. S.
D. a set of mutual funds with similar risk characteristics to your mutual fund
E. a concept found only in astronomy, the set of all mutual funds in the world, and the set of
all mutual funds in the U. S.
A mutual fund manager is evaluated against the performance of managers of funds of similar
risk characteristics.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
5. __________ did not develop a popular method for risk-adjusted performance evaluation of
mutual funds.
A. Eugene Fama
B. Michael Jensen
C. William Sharpe
D. Jack Treynor
E. Eugene Fama and Michael Jensen
Michael Jensen, William Sharpe, and Jack Treynor developed popular models for mutual fund
performance evaluation.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
24-30
Chapter 24 - Portfolio Performance Evaluation
6. __________ developed a popular method for risk-adjusted performance evaluation of
mutual funds.
A. Eugene Fama
B. Michael Jensen
C. William Sharpe
D. Jack Treynor
E. Michael Jensen, William Sharpe, and Jack Treynor
Michael Jensen, William Sharpe, and Jack Treynor developed popular models for mutual fund
performance evaluation.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
7. Henriksson (1984) found that, on average, betas of funds __________ during market
advances.
A. increased very significantly
B. increased slightly
C. decreased slightly
D. decreased very significantly
E. did not change
Portfolio betas should have a large value if the market is expected to perform well and a small
value if the market is not expected to perform well; thus, these results reflect the poor timing
ability of mutual fund managers.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-31
Chapter 24 - Portfolio Performance Evaluation
8. Most professionally managed equity funds generally __________.
A. outperform the S&P 500 index on both raw and risk-adjusted return measures
B. underperform the S&P 500 index on both raw and risk-adjusted return measures
C. outperform the S&P 500 index on raw return measures and underperform the S&P 500
index on risk-adjusted return measures
D. underperform the S&P 500 index on raw return measures and outperform the S&P 500
index on risk-adjusted return measures
E. match the performance of the S&P 500 index on both raw and risk-adjusted return
measures
Most mutual funds do not consistently, over time, outperform the S&P 500 index on the basis
of either raw or risk-adjusted return measures.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
9. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a higher beta than portfolio B. According to the Sharpe measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
The Sharpe index is a measure of average portfolio returns (in excess of the risk free return)
per unit of total risk (as measured by standard deviation).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-32
Chapter 24 - Portfolio Performance Evaluation
10. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a higher beta than portfolio B. According to the Treynor measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
11. Suppose two portfolios have the same average return, the same standard deviation of
returns, but portfolio A has a lower beta than portfolio B. According to the Treynor measure,
the performance of portfolio A __________.
A. is better than the performance of portfolio B
B. is the same as the performance of portfolio B
C. is poorer than the performance of portfolio B
D. cannot be measured as there is no data on the alpha of the portfolio
E. None of these is correct.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-33
Chapter 24 - Portfolio Performance Evaluation
12. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a higher beta than Raider Fund. According to the Sharpe
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Sharpe index is a measure of average portfolio returns (in excess of the risk free return)
per unit of total risk (as measured by standard deviation).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
13. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a higher beta than Raider Fund. According to the Treynor
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-34
Chapter 24 - Portfolio Performance Evaluation
14. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Aggie Fund has a lower beta than Raider Fund. According to the Treynor
measure, the performance of Aggie Fund
A. is better than the performance of Raider Fund.
B. is the same as the performance of Raider Fund.
C. is poorer than the performance of Raider Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
15. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a higher beta than Gator Fund. According to the Sharpe
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Sharpe index is a measure of average portfolio returns (in excess of the risk free return)
per unit of total risk (as measured by standard deviation).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-35
Chapter 24 - Portfolio Performance Evaluation
16. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a lower beta than Gator Fund. According to the Sharpe
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Sharpe index is a measure of average portfolio returns (in excess of the risk free return)
per unit of total risk (as measured by standard deviation).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
17. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a lower beta than Gator Fund. According to the Treynor
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-36
Chapter 24 - Portfolio Performance Evaluation
18. Suppose two portfolios have the same average return, the same standard deviation of
returns, but Buckeye Fund has a higher beta than Gator Fund. According to the Treynor
measure, the performance of Buckeye Fund
A. is better than the performance of Gator Fund.
B. is the same as the performance of Gator Fund.
C. is poorer than the performance of Gator Fund.
D. cannot be measured as there is no data on the alpha of the portfolio.
E. None of these is correct is true.
The Treynor index is a measure of average portfolio returns (in excess of the risk free return)
per unit of systematic risk (as measured by beta).
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
19. Morningstar's RAR method
I) is one of the most widely used performance measures.
II) indicates poor performance by placing up to 5 darts next to the fund's name.
III) computes fund returns adjusted for loads.
IV) computes fund returns adjusted for risk.
V) produces ranking results that are the same as those produced with the Sharpe measure.
A. I, II, and IV
B. I, III, and IV
C. I, IV, and V
D. I, II, IV, and V
E. I, II, III, IV, and V
II is incorrect - Morningstar uses up to 5 stars to indicate the quality of performance. V is
incorrect because the RAR method produces results that are similar to the Sharpe ratio but not
identical.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-37
Chapter 24 - Portfolio Performance Evaluation
20. Suppose you purchase 100 shares of GM stock at the beginning of year 1, and purchase
another 100 shares at the end of year 1. You sell all 200 shares at the end of year 2. Assume
that the price of GM stock is $50 at the beginning of year 1, $55 at the end of year 1, and $65
at the end of year 2. Assume no dividends were paid on GM stock. Your dollar-weighted
return on the stock will be __________ your time-weighted return on the stock.
A. higher than
B. the same as
C. less than
D. exactly proportional to
E. more information is necessary to answer this question
In the dollar-weighted return, the stock's performance in the second year, when 200 shares are
held, has a greater influence on the overall dollar-weighted return. The time-weighted return
ignores the number of shares held.
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
21. Suppose the risk-free return is 4%. The beta of a managed portfolio is 1.2, the alpha is 1%,
and the average return is 14%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 11.5%
B. 14%
C. 15%
D. 16%
E. None of these is correct
1% = 14% − [4% + 1.2(x − 4%)]; x = 11.5%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-38
Chapter 24 - Portfolio Performance Evaluation
22. Suppose the risk-free return is 3%. The beta of a managed portfolio is 1.75, the alpha is
0%, and the average return is 16%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 12.3%
B. 10.4%
C. 15.1%
D. 16.7%
E. None of these is correct
0% = 16% − [3% + 1.75(x − 3%)]; x = 10.4%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
23. Suppose the risk-free return is 6%. The beta of a managed portfolio is 1.5, the alpha is 3%,
and the average return is 18%. Based on Jensen's measure of portfolio performance, you
would calculate the return on the market portfolio as
A. 12%
B. 14%
C. 15%
D. 16%
E. None of these is correct
3% = 18% − [6% + 1.5(x − 6%)]; x = 12%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-39
Chapter 24 - Portfolio Performance Evaluation
24. Suppose a particular investment earns an arithmetic return of 10% in year 1, 20% in year 2
and 30% in year 3. The geometric average return for the year period will be __________.
A. greater than the arithmetic average return
B. equal to the arithmetic average return
C. less than the arithmetic average return
D. equal to the market return
E. cannot tell from the information given
The geometric mean will always be less than the arithmetic mean unless the returns in all
periods are equal.
AACSB: Analytic
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
25. Suppose you buy 100 shares of Abolishing Dividend Corporation at the beginning of year
1 for $80. Abolishing Dividend Corporation pays no dividends. The stock price at the end of
year 1 is $100, $120 at the end of year 2, and $150 at the end of year 3. The stock price
declines to $100 at the end of year 4, and you sell your 100 shares. For the four years, your
geometric average return is
A. 0.0%
B. 1.0%
C. 5.7%
D. 9.2%
E. 34.5%
[(1.25)(1.20)(1.25)(0.6667)]1/4 − 1.0 = 5.7%
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-40
Chapter 24 - Portfolio Performance Evaluation
26. You want to evaluate three mutual funds using the information ratio measure for
performance evaluation. The risk-free return during the sample period is 6%, and the average
return on the market portfolio is 19%. The average returns, residual standard deviations, and
betas for the three funds are given below.
The fund with the highest information ratio measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest
E. Funds A and C are tied for highest
Information ratio = P/(eP); A: P = 20 − 6 − .8(19 − 6) = 3.6; 3.6/4 = 0.9; B: P = 21 − 6 −
1(19 − 6) = 2.0; 2/1.25 = 1.6; C: P = 23 − 6 − 1.2(19 − 6) = 1.4; 1.4/1.20 = 1.16.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-41
Chapter 24 - Portfolio Performance Evaluation
27. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 6%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The fund with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest
E. Funds A and C are tied for highest
A: (24% − 6%)/30% = 0.60; B: (12% − 6%)/10% = 0.60; C: (22% − 6%)/20% = 0.80; S&P
500: (18% − 6%)/16% = 0.75.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-42
Chapter 24 - Portfolio Performance Evaluation
28. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 4%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The fund with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest
E. Funds A and C are tied for highest
A: (18% − 4%)/38% = 0.368; B: (15% − 4%)/27% = 0.407; C: (11% − 4%)/24% = 0.292;
S&P 500: (10% − 4%)/22% = 0.273.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-43
Chapter 24 - Portfolio Performance Evaluation
29. You want to evaluate three mutual funds using the Sharpe measure for performance
evaluation. The risk-free return during the sample period is 5%. The average returns, standard
deviations and betas for the three funds are given below, as is the data for the S&P 500 index.
The investment with the highest Sharpe measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. the index
E. Funds A and C are tied for highest
A: (23% − 5%)/30% = 0.60; B: (20% − 5%)/19% = 0.789; C: (19% − 5%)/17% = 0.824; S&P
500: (18% − 5%)/15% = 0.867.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-44
Chapter 24 - Portfolio Performance Evaluation
30. You want to evaluate three mutual funds using the Treynor measure for performance
evaluation. The risk-free return during the sample period is 6%. The average returns, standard
deviations, and betas for the three funds are given below, in addition to information regarding
the S&P 500 index.
The fund with the highest Treynor measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest
E. Funds A and C are tied for highest
A: (13% − 6%)/0.5 = 14; B: (19% − 6%)/1.0 = 13; C: (25% − 6%)/1.5 = 12.7; S&P 500: (18%
− 6%)/1.0 = 12.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-45
Chapter 24 - Portfolio Performance Evaluation
31. You want to evaluate three mutual funds using the Jensen measure for performance
evaluation. The risk-free return during the sample period is 6%, and the average return on the
market portfolio is 18%. The average returns, standard deviations, and betas for the three
funds are given below.
The fund with the highest Jensen measure is __________.
A. Fund A
B. Fund B
C. Fund C
D. Funds A and B are tied for highest
E. Funds A and C are tied for highest
A: 17.6% − [6% + 1.2(18% − 6%)] = −2.8%; B: 17.5% − [6% + 1.0(18% − 6%)] = −0.5; C:
17.4% − [6% + 0.8(18% − 6%)] = +1.8.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
32. Suppose you purchase one share of the stock of Volatile Engineering Corporation at the
beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend, and buy one
more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each
share), and sell the shares for $36.45 each. The time-weighted return on your investment is
________.
A. -1.75%
B. 4.08%
C. 8.53%
D. 11.46%
E. 12.35%
Year 1: ($30 + $2 − $36)/$36 = −11.11%; Year 2: ($36.45 + $2 − $30)/$30 = 28.17%;
Average: 8.53%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-46
Chapter 24 - Portfolio Performance Evaluation
33. Suppose you purchase one share of the stock of Volatile Engineering Corporation at the
beginning of year 1 for $36. At the end of year 1, you receive a $2 dividend, and buy one
more share for $30. At the end of year 2, you receive total dividends of $4 (i.e., $2 for each
share), and sell the shares for $36.45 each. The dollar-weighted return on your investment is
_______.
A. -1.75%
B. 4.08%
C. 8.53%
D. 8.00%
E. 12.35%
$36 + $30/(1 + r) = $2/(1 + r) + $4/(1 + r)2 + $72.90/(1 + r)2; r = 12.35%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
34. Suppose you purchase one share of the stock of Cereal Correlation Company at the
beginning of year 1 for $50. At the end of year 1, you receive a $1 dividend, and buy one
more share for $72. At the end of year 2, you receive total dividends of $2 (i.e., $1 for each
share), and sell the shares for $67.20 each. The time-weighted return on your investment is
__________.
A. 10.0%
B. 8.7%
C. 19.7%
D. 17.6%
E. None of these is correct
Year 1: ($72 + $1 − $50)/$50 = 46%; Year 2: ($67.20 + $1 − $72)/$72 = −5.28%; Timeweighted average = (1.46*(1 − .0528))1/2 − 1 = .1760 = 17.6%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-47
Chapter 24 - Portfolio Performance Evaluation
35. Suppose you purchase one share of the stock of Cereal Correlation Company at the
beginning of year 1 for $50. At the end of year 1, you receive a $1 dividend, and buy one
more share for $72. At the end of year 2, you receive total dividends of $2 (i.e., $1 for each
share), and sell the shares for $67.20 each. The dollar-weighted return on your investment is
__________.
A. 10.00%
B. 8.78%
C. 19.71
D. 20.36%
E. None of these is correct
$50 + $72/(1 + r) = $1/(1 + r) + $2/(1 + r)2 + $134.40/(1 + r)2; r = 8.78%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
36. Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B
earns a 9% return. In year 2, stock A earns an 18% return and stock B earns an 11% return.
__________ has the higher arithmetic average return.
A. Stock A
B. Stock B
C. The two stocks have the same arithmetic average return
D. At least three periods are needed to calculate the arithmetic average return
E. None of these is correct
A: (2% + 18%)/2 = 10%; B: (9% + 11%)/2 = 10%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-48
Chapter 24 - Portfolio Performance Evaluation
37. Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B
earns a 9% return. In year 2, stock A earns an 18% return and stock B earns an 11% return.
Which stock has the higher geometric average return?
A. Stock A
B. Stock B
C. The two stocks have the same geometric average return
D. At least three periods are needed to calculate the geometric average return
E. None of these is correct
A: [(1.02)(1.18)]1/2 − 1 = 9.71%; B: [(1.09)(1.11)]1/2 − 1 = 10.00%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
The following data are available relating to the performance of Sooner Stock Fund and the
market portfolio:
The risk-free return during the sample period was 3%.
38. What is the Sharpe measure of performance evaluation for Sooner Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 38.6%
E. 37.14%
(20% − 3%)/44% = 0.386, or 38.6%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-49
Chapter 24 - Portfolio Performance Evaluation
39. What is the Treynor measure of performance evaluation for Sooner Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 9.44%
E. 37.14%
(20% − 3%)/1.8 = 9.44%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
40. Calculate the Jensen measure of performance evaluation for Sooner Stock Fund.
A. 2.6%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
P = 20% − [3% + 1.8(11% − 3%)] = 2.6%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-50
Chapter 24 - Portfolio Performance Evaluation
41. Calculate the information ratio for Sooner Stock Fund.
A. 1.53
B. 1.30
C. 8.67
D. 31.43
E. 37.14
P = 20% − [3% + 1.8(11% − 3%)] = 2.6%, 2.6%/2.00% = 1.3.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-51
Chapter 24 - Portfolio Performance Evaluation
The following data are available relating to the performance of Monarch Stock Fund and the
market portfolio:
The risk-free return during the sample period was 4%.
42. What is the information ratio measure of performance evaluation for Monarch Stock
Fund?
A. 1.00%
B. 280.00%
C. 44.00%
D. 50.00%
E. None of these is correct
P = 16% − [4% +1.15(12% − 4%)] = 2.8%; P/(eP) = 2.8%/1% = 2.8, or 280%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
43. Calculate Sharpe's measure of performance for Monarch Stock Fund.
A. 1.00%
B. 46.00%
C. 44.00%
D. 50.00%
E. None of these is correct
(16 − 4)/26 = .46
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-52
Chapter 24 - Portfolio Performance Evaluation
44. Calculate Treynor's measure of performance for Monarch Stock Fund.
A. 10.40%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct
(16 − 4)/1.15 = 10.4
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
45. Calculate Jensen's measure of performance for Monarch Stock Fund.
A. 1.00%
B. 2.80%
C. 44.00%
D. 50.00%
E. None of these is correct
16 − [4 + 1.15 (12 − 4)] = 2.80%
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
The following data are available relating to the performance of Seminole Fund and the
market portfolio:
The risk-free return during the sample period was 6%.
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Chapter 24 - Portfolio Performance Evaluation
46. If you wanted to evaluate the Seminole Fund using the M2 measure, what percent of the
adjusted portfolio would need to be invested in T-Bills?
A. -36% (borrow)
B. 50%
C. 8%
D. 36%
E. 27%
22/30 = .7333 or 73.33% invested in Seminole Fund and 1 − 73.33% = 26.67% in T-Bills
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
47. Calculate the M2 measure for the Seminole Fund.
A. 4.0%
B. 20.0%
C. 2.86%
D. 0.8%
E. 40.0%
22/30 = .7333; 1 − .7333 = .2667; M2 = [.7333 (18) + .2667 (6)] − 14 = 0.8%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-54
Chapter 24 - Portfolio Performance Evaluation
48. If an investor has a portfolio that has constant proportions in T-bills and the market
portfolio, the portfolio's characteristic line will plot as a line with ___________; if the
investor can time bull markets, the characteristic line will plot as a line with ___________.
A. a positive slope; a negative slope
B. a negative slope; a positive slope
C. a constant slope; a negative slope
D. a negative slope; a constant slope
E. a constant slope; a positive slope
These characteristics are shown in Figure 24.5. If the proportions are constant the beta of the
portfolio stays constant. If the investor switches the proportions in favor of the marker
portfolio to take advantage of bull markets the beta will increase during times of higher
market risk premiums. This will cause the slope of the curve to increase.
AACSB: Analytic
Bloom's: Understand
Difficulty: Challenge
Topic: Performance evaluation
49. Studies of style analysis have found that ________ of fund returns can be explained by
asset allocation alone.
A. between 50% and 70%
B. less than 10%
C. between 40 and 50%
D. between 75% and 90%
E. over 90%
Sharpe (1992) and Brinson, Singer and Beebower (1991) found that style explained 91.5%
and as much as 97% of fund returns.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-55
Chapter 24 - Portfolio Performance Evaluation
The following data are available relating to the performance of Wildcat Fund and the market
portfolio:
The risk-free return during the sample period was 7%.
50. What is the information ratio measure of performance evaluation for Wildcat Fund?
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct
P = 18% − [7% +1.25(15% − 7%)] = 1%; P/(eP) = 1%/2% = 0.50, or 50.00%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
51. Calculate Sharpe's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct
(18 − 7)/25 = .44
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-56
Chapter 24 - Portfolio Performance Evaluation
52. Calculate Treynor's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct
(18 − 7)/1.25 = 8.8
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
53. Calculate Jensen's measure of performance for Wildcat Fund.
A. 1.00%
B. 8.80%
C. 44.00%
D. 50.00%
E. None of these is correct
18 − [7 + 1.25 (15 − 7)] = 1.00%
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
The following data are available relating to the performance of Long Horn Stock Fund and
the market portfolio:
The risk-free return during the sample period was 6%.
24-57
Chapter 24 - Portfolio Performance Evaluation
54. What is the Sharpe measure of performance evaluation for Long Horn Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
(19% − 6%)/35% = 0.3714, or 37.14%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
55. What is the Treynor measure of performance evaluation for Long Horn Stock Fund?
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
(19% − 6%)/1.5 = 8.67%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-58
Chapter 24 - Portfolio Performance Evaluation
56. Calculate the Jensen measure of performance evaluation for Long Horn Stock Fund.
A. 1.33%
B. 4.00%
C. 8.67%
D. 31.43%
E. 37.14%
P = 19% − [6% + 1.5(12% − 6%)] = 4.00%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-59
Chapter 24 - Portfolio Performance Evaluation
57. Calculate the information ratio for Long Horn Stock Fund.
A. 1.33
B. 4.00
C. 8.67
D. 31.43
E. 37.14
P = 19% − [6% + 1.5(12% − 6%)] = 4.00%, 4.00%/3.00% = 1.33.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
In a particular year, Razorback Mutual Fund earned a return of 1% by making the following
investments in asset classes:
The return on a bogey portfolio was 2%, calculated from the following information.
58. The total excess return on the Razorback Fund's managed portfolio was __________.
A. -1.80%
B. -1.00%
C. 0.80%
D. 1.00%
E. None of these is correct
1% − 2% = −1%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-60
Chapter 24 - Portfolio Performance Evaluation
59. The contribution of asset allocation across markets to the Razorback Fund's total excess
return was __________.
A. -1.80%
B. -1.00%
C. 0.80%
D. 1.00%
E. None of these is correct
See table below.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
60. The contribution of selection within markets to the Razorback Fund's total excess return
was __________.
A. -1.80%
B. -1.00%
C. 0.80%
D. 1.00%
E. None of these is correct
See table below.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-61
Chapter 24 - Portfolio Performance Evaluation
In a particular year, Aggie Mutual Fund earned a return of 15% by making the following
investments in the following asset classes:
The return on a bogey portfolio was 10%, calculated as follows:
61. The total excess return on the Aggie managed portfolio was __________.
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct
15% − 10% = 5%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Topic: Performance evaluation
24-62
Chapter 24 - Portfolio Performance Evaluation
62. The contribution of asset allocation across markets to the total excess return was
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct
See table below.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
63. The contribution of selection within markets to total excess return was
A. 1%
B. 3%
C. 4%
D. 5%
E. None of these is correct
See table below.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Topic: Performance evaluation
24-63
Chapter 24 - Portfolio Performance Evaluation
64. In measuring the comparative performance of different fund managers, the preferred
method of calculating rate of return is __________.
A. internal rate of return
B. arithmetic average
C. dollar-weighted
D. time-weighted
E. None of these is correct
For the investor, the internal rate of return (or dollar-weighted rate of return) is the preferred
measure because if the investor chooses to invest heavily in one investment vehicle that
performs extremely well, an increased return results, which is reflected in A (or C). However,
the mutual fund manager does not usually make the decision as to the amount to invest in a
particular vehicle; therefore, the time-weighted rate of return is usually used to evaluate these
managers. Arithmetic average is a good measure for estimating future returns (if expectations
are unchanged).
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
65. The __________ measures the reward to volatility trade-off by dividing the average
portfolio excess return by the standard deviation of returns.
A. Sharpe measure
B. Treynor measure
C. Jensen measure
D. information ratio
E. None of these is correct
The Sharpe measure is a measure of average excess average portfolio returns divided by the
total risk of the portfolio returns (standard deviation).
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
24-64
Chapter 24 - Portfolio Performance Evaluation
66. A pension fund that begins with $500,000 earns 15% the first year and 10% the second
year. At the beginning of the second year, the sponsor contributes another $300,000. The
dollar-weighted and time-weighted rates of return, respectively, were
A. 11.7% and 12.5%
B. 12.1% and 12.5%
C. 12.5% and 11.7%
D. 12.5% and 12.1%
E. None of these is correct
$500,000 + $300,000/(1 + r) = $75,000/(1 + r) + $880,000/(1 + r)2; r = 12.059%; Timeweighted average = (1.15* 1.1)1/2 − 1 = .1247 = 12.47%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
67. The Value Line Index is an equally weighted geometric average of the returns of about
1,700 firms. The value of an index based on the geometric average returns of 3 stocks where
the returns on the 3 stocks during a given period were 32%, 5%, and -10%, respectively, is
__________.
A. 4.3%
B. 7.6%
C. 9.0%
D. 13.4%
E. 5.0%
[(1.32)(1.05)(0.90)]1/3 − 1.0 = 7.6%.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
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Chapter 24 - Portfolio Performance Evaluation
68. Risk-adjusted mutual fund performance measures have decreased in popularity because
A. in nearly efficient markets it is extremely difficult for portfolio managers to outperform the
market.
B. the measures usually result in negative performance results for the portfolio managers.
C. the high rates of return earned by the mutual funds have made the measures useless.
D. in nearly efficient markets it is extremely difficult for portfolio managers to outperform the
market and the measures usually result in negative performance results for the portfolio
managers.
E. None of these is correct.
Risk-adjusted mutual fund performance measures have decreased in popularity because in
nearly efficient markets it is extremely difficult for portfolio managers to outperform the
market and the measures usually result in negative performance results for the portfolio
managers.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
69. The Sharpe, Treynor, and Jensen portfolio performance measures are derived from the
CAPM,
A. therefore, it does not matter which measure is used to evaluate a portfolio manager.
B. however, the Sharpe and Treynor measures use different risk measures, therefore the
measures vary as to whether or not they are appropriate, depending on the investment
scenario.
C. therefore, all measure the same attributes.
D. therefore, it does not matter which measure is used to evaluate a portfolio manager and
however, the Sharpe and Treynor measures use different risk measures, therefore the
measures vary as to whether or not they are appropriate, depending on the investment
scenario.
E. None of these is correct.
The Sharpe measure uses standard deviation, or total risk, as the risk measure; the Treynor
measure uses beta, or systematic risk, as the risk measure.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-66
Chapter 24 - Portfolio Performance Evaluation
70. The Jensen portfolio evaluation measure
A. is a measure of return per unit of risk, as measured by standard deviation.
B. is an absolute measure of return over and above that predicted by the CAPM.
C. is a measure of return per unit of risk, as measured by beta.
D. is a measure of return per unit of risk, as measured by standard deviation and is an absolute
measure of return over and above that predicted by the CAPM.
E. is an absolute measure of return over and above that predicted by the CAPM and is a
measure of return per unit of risk, as measured by beta.
The measure of return per unit of risk, as measured by standard deviation is the Sharpe
measure, the measure of return per unit of risk, as measured by beta is the Treynor measure.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
71. The M-squared measure
A. considers only the return when evaluating mutual funds.
B. considers the risk-adjusted return when evaluating mutual funds.
C. considers only the total risk when evaluating mutual funds.
D. considers only the market risk when evaluating mutual funds.
E. None of these is correct.
The M-squared measure adjusts the fund by hypothetically borrowing or lending until the
total portfolio matches the risk level of an index, then ranks the fund on the basis of this riskadjusted return.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-67
Chapter 24 - Portfolio Performance Evaluation
72. The dollar-weighted return on a portfolio is equivalent to
A. the time-weighted return.
B. the geometric average return.
C. the arithmetic average return.
D. the portfolio's internal rate of return.
E. None of these is correct.
The dollar-weighted return on a portfolio is equivalent to finding the internal rate of return on
the cash flows to the portfolio.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
73. A portfolio manager's ranking within a comparison universe may not provide a good
measure of performance because
A. portfolio returns may not be calculated in the same way.
B. portfolio durations can vary across managers.
C. if managers follow a particular style or subgroup, portfolios may not be comparable.
D. portfolio durations can vary across managers and if managers follow a particular style or
subgroup, portfolios may not be comparable.
E. All of these are correct.
Returns are typically time-weighted for all portfolios and broad risk classes or styles are
grouped together, but particular subgroups and differences in duration are typically not
considered.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-68
Chapter 24 - Portfolio Performance Evaluation
74. The geometric average rate of return is based on
A. the market's volatility.
B. the concept of expected return.
C. the standard deviation of returns.
D. the CAPM.
E. the principle of compounding.
The geometric average is the rate that would give the same result if applied over an n-year
period as the individual years' returns. The present value can be compounded by r1, r2,  ,rn
or compounded by rG for n periods to yield the same future value.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
75. The M2 measure was developed by
A. Merton and Miller.
B. Miller and Miller.
C. Modigliani and Miller.
D. Modigliani and Modigliani.
E. the M&M Mars Company.
The model was developed by Leah Modigliani of Morgan Stanley Dean Witter and Franco
Modigliani, her grandfather who is a Nobel laureate.
AACSB: Analytic
Bloom's: Remember
Difficulty: Basic
Topic: Performance evaluation
24-69
Chapter 24 - Portfolio Performance Evaluation
76. Rodney holds a portfolio of risky assets that represents his entire risky investment. To
evaluate the performance of Rodney's portfolio, in which order would you complete the steps
listed?
I) Compare the Sharpe measure of Rodney's portfolio to the Sharpe measure of the best
portfolio.
II) State your conclusions.
III) Assume that past security performance is representative of expected performance.
IV) Determine the benchmark portfolio that Rodney would have held if he had chosen a
passive strategy.
A. I, III, IV, II
B. III, IV, I, II
C. IV, III, I, II
D. III, II, I, IV
E. III, I, IV, II
This sequence is appropriate if his entire risky investment is in this portfolio. If other risky
assets are involved other factors need to be considered.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
77. The Modigliani M2 measure and the Treynor T2 measure
A. are identical.
B. are nearly identical and will rank portfolios the same way.
C. are nearly identical but might rank portfolios differently.
D. are somewhat different; M2 can be used to rank portfolios but T2 cannot.
E. are somewhat different; T2 can be used to rank portfolios but M2 cannot.
Both measures are percentages and are similar. Both can be used to rank portfolios in terms of
performance relative to risk. But the measures might give different rankings.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
24-70
Chapter 24 - Portfolio Performance Evaluation
78. To determine whether portfolio performance is statistically significant requires
A. a very long observation period due to the high variance of stock returns.
B. a short observation period due to the high variance of stock returns.
C. a very long observation period due to the low variance of stock returns.
D. a short observation period due to the low variance of stock returns.
E. a low variance of returns over any observation period.
Performance evaluation is difficult because of high-variance stock returns. To compensate, a
large number of observations is required to obtain statistical significance.
AACSB: Analytic
Bloom's: Remember
Difficulty: Intermediate
Topic: Performance evaluation
Short Answer Questions
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Chapter 24 - Portfolio Performance Evaluation
79. Define and discuss the Sharpe, Treynor, and Jensen measures of portfolio performance
evaluation, and the situations in which each measure is the most appropriate measure.
Sharpe's measure, (rP - rf)/sP, is a relative measure of the average portfolio return in excess of
the average risk-free return over a period time per unit of risk, as measured by the standard
deviation of the returns of the portfolio over that time period.
Treynor's measure, (rP - rf)/bP, is a relative measure of the average portfolio return in excess of
the average risk-free return over a period of time per unit of risk, as measured by the beta of
the portfolio over that time period.
Jensen's measure, P = rP -[rf + P(rM - rf)], is a measure of absolute return (average return on
the portfolio over a period of time) over and above that predicted by the CAPM.
As the risk measure in the Sharpe measure of portfolio performance evaluation is total risk,
this measure is appropriate for portfolio performance evaluation if the portfolio being
evaluated represents the investor's complete portfolio of assets.
As the risk measure in the Treynor measure of portfolio performance evaluation is beta, or
systematic risk, this measure is the appropriate portfolio performance evaluation measure if
the portfolio being evaluated is only a small part of a large investment portfolio. This measure
is also appropriate for evaluation of managers of "subportfolios" of large funds, such as large
pension plans.
As the Jensen measure, or Jensen's alpha, measures the return of a portfolio relative to that
predicted by the CAPM, this measure is appropriate for the evaluation of managers of
"subportfolios" of large funds. However, the Treynor measure is an even better measure for
such a scenario.
Feedback: The rationale for this question is to ascertain that students understand the
differences and appropriateness among the popular measures of portfolio performance
evaluation including the Sharpe, Jensen, and Treynor measures
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-72
Chapter 24 - Portfolio Performance Evaluation
80. What is the problem with using the Sharpe measure for evaluation of an active portfolio
management strategy?
The Sharpe measure penalizes for portfolio variance. If a portfolio is actively managed, the
variance of returns is likely to vary considerably over any time period, thus reflecting poor
performance as indicated by the Sharpe measure (unless the portfolio returns are much higher
as a result of the active management).
Feedback: The rationale for this questions is emphasize that as the composition of a portfolio
changes due to active management, the various returns are likely to increase.
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
81. Discuss, in general, the performance attribution procedures.
The portfolio management decision process typically involves three choices: (1) allocation of
funds across broad asset categories, such as stocks, bonds, and the money market; (2) industry
(sector) choice within each category; and (3) security selection within each sector. The returns
resulting from each of these decisions are measured against a benchmark return resulting from
a passive, index-investment approach. The excess returns (if any) resulting from these
decisions over and above those earned from a passive indexing strategy are attributed to the
success of the portfolio manager.
Feedback: The rationale of this question is to ascertain whether the student understands the
general performance attribution procedures.
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Intermediate
Topic: Performance evaluation
24-73
Chapter 24 - Portfolio Performance Evaluation
82. You invested $1,000 through your broker three years ago. Your account balance at the
beginning of each period is shown in the table below.
- Calculate the annual return for each year. Show your calculations in the table.
- Your broker called to tell you the good news that your average annual return over the three
years has been 4%. Where did he get this number?
- At first you are confused. It seems as though the broker must be mistaken because you are
no better off than when you started investing three years ago. But then you remember
something from your favorite Investments class. Suggest an alternate measure for the average
return. Calculate this measure and explain to your broker why it is more appropriate.
- Explain to your broker when it would make sense to use the 4% result that he initially
quoted you.
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Chapter 24 - Portfolio Performance Evaluation
See the table below.
The broker calculated the arithmetic average return: (20% + 25% − 33.33%)/3 = 4%.
The geometric average would be more appropriate for this purpose because it will accurately
reflect the compounded value of your investment. The geometric return is
rG=[(1.20)*(1.25)*(0.67)]1/3 − 1 = 0%. This rate can be applied over each of the three periods
to give the final value of $1,000. It is a better measure of how your investment actually grew.
The 4% arithmetic average would be the best estimate of how the investment will grow in the
coming year.
Feedback: This question focuses on the arithmetic and geometric mean concepts and the
appropriate use of each.
AACSB: Reflective Thinking
Bloom's: Apply
Difficulty: Intermediate
Topic: Performance evaluation
24-75
Chapter 24 - Portfolio Performance Evaluation
83. Discuss the M2 measure of performance by answering the following questions. Why is M2
better than the Sharpe measure? What measure of risk does M2 use? How do you construct a
managed portfolio, P, to use in computing the M2 measure? What is the formula for M2?
Draw a graph that shows how M2 would be measured. Be sure to label the axes and all
relevant points.
The Sharpe measure indicates whether a portfolio underperformed the market index, but the
difference between the market's Sharpe measure and the portfolio's Sharpe measure is difficult
to interpret. M2 uses the same measure of risk as the Sharpe measure—variation in total
return, calculated as the standard deviation. For managed portfolio P an adjusted portfolio P*
is formed by combining P with borrowing or lending at the risk-free rate to the point where P*
has the same volatility as a market index (M). Then since M and P have the same standard
deviation they can be directly compared using the M2 measure. M2 = rP* − rM. If P*
outperforms M the measure will be positive, which means the CAL on which P* lies will have
a steeper slope than the CML on which M lies. M2 is the distance between the CAL and the
CML.
The graph should look like the one in Figure 24.2.
Feedback: This question tests whether the student understands the characteristics and the
construction of the M2 measure.
AACSB: Reflective Thinking
Bloom's: Understand
Difficulty: Challenge
Topic: Performance evaluation
24-76