Exercises on Performance Evaluation
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Exercises on Performance Evaluation 1.__________ 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) A and B Answer: A Difficulty: Easy Rationale: Michael Jensen, William Sharpe, and Jack Treynor developed popular models for mutual fund performance evaluation. 2. 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 the above is true. Answer: B Difficulty: Moderate Rationale: 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). 3. 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 the above Answer: A Difficulty: Difficult Rationale: 1% = 14% - [4% + 1.2(x - 4%)]; x = 11.5%. 4. 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 Answer: C Difficulty: Moderate Rationale: The geometric mean will always be less than the arithmetic mean unless the returns in all periods are equal (in which case the two means will be equal). 5. 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, the price $120 at the end of year 2, and the price is $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% Answer: C Difficulty: Difficult Rationale: [(1.25)(1.20)(1.25)(0.6667)] 1/4 - 1.0 = 5.7% 1
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Transcript of Exercises on Performance Evaluation
Exercises on Performance Evaluation
1.__________ 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) A and B Answer: A Difficulty: Easy Rationale: Michael Jensen, William Sharpe, and Jack Treynor developed popular models for mutual fund performance evaluation.
2. 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 the above is true. Answer: B Difficulty: Moderate Rationale: 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).
3. 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 the above Answer: A Difficulty: Difficult Rationale: 1% = 14% - [4% + 1.2(x - 4%)]; x = 11.5%.
4. 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 Answer: C Difficulty: Moderate Rationale: The geometric mean will always be less than the arithmetic mean unless the returns in all periods are equal (in which case the two means will be equal).
5. 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, the price $120 at the end of year 2, and the price is $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% Answer: C Difficulty: Difficult Rationale: [(1.25)(1.20)(1.25)(0.6667)]1/4 - 1.0 = 5.7%
6. 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
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D) Funds A and B are tied for highest E) Funds A and C are tied for highest Answer: C Difficulty: Moderate Rationale: 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.
7. 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 Answer: A Difficulty: Difficult Rationale: 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.
Use the following to answer questions 8-10:The following data are available relating to the performance of Sooner Stock Fund and the market portfolio:
8. 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% Answer: D Difficulty: Moderate Rationale: (20% - 3%)/44% = 0.386, or 38.6%.
9. 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%
Answer: D Difficulty: Moderate Rationale: (20% - 3%)/1.8 = 9.44%.
10. 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%
Answer: A Difficulty: Moderate Rationale: αP = 20% - [3% + 1.8(11% - 3%)] = 2.6%.
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