5、The weights and returns for individual positions in a portfolio are shown below:
Position | Mkt. Value at | Return for 2005(%) |
A | 1.3 | –2.0 |
B | 1.4 | –4.2 |
C | 2.2 | +6.4 |
D | 3.9 | +2.1 |
E | 1.7 | –0.8 |
What is the return on the portfolio?
A) -1.20%.
B) +1.50%.
C) +2.48%.
D) +1.18%.
6、Claude Bellow, CFA, is an analyst with a real-estate focused investment firm. Today, one of the partners e-mails Bellow the following table and requests that he “run some numbers.” The table below gives five years of annual returns for Marley REIT (real estate investment trust) and a large urban apartment building. Marley REIT invests in commercial properties. (Note: For this question, calculate the mean returns using the arithmetic mean.)
Table 1: Annual returns (in %) | |||||
Asset | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
Marley REIT | 15.0 | 8.0 | 13.0 | 9.0 | 13.0 |
Apartment Bldg | 10.0 | -1.0 | 8.0 | 8.0 | 9.0 |
One of the office assistants begins to “run some numbers,” but is then called away to an important meeting. So far, the assistant calculated the variance of the apartment building returns at 15.76%. (He assumed that the returns given represent the entire population of returns.) Now, Bellow must finish the work.
Bellow should conclude that the standard deviation of the:
A) apartment building, if the given returns represent a sample of returns, is 19.70%.
B) REIT, assuming the given returns represent the entire population, is 2.97%.
C) apartment building, if the given returns represent a sample of returns, is 4.44%.
D) REIT, assuming the given returns represent a sample of returns, is 7.04%.
7、Assume that the following returns are a sample of annual returns for firms in the clothing industry. Given the following sample of returns, what are the sample variance and standard deviation?
Firm 1 | Firm 2 | Firm 3 | Firm 4 | Firm 5 |
15% | 2% | 5% | (7%) | 0% |
A) Variance Standard Deviation
64.5 8.0
B) Variance Standard Deviation
32.4 5.7
C) Variance Standard Deviation
22.0 4.7
D) Variance Standard Deviation
51.6 7.2
8、Given the following annual returns, what is the mean absolute deviation?
2000 | 2001 | 2002 | 2003 | 2004 |
15% | 2% | 5% | -7% | 0% |
A) 5.6%.
B) 3.0%.
C) 22.0%.
D) 2.0%.
答案和详解如下：
5、The weights and returns for individual positions in a portfolio are shown below:
Position | Mkt. Value at | Return for 2005(%) |
A | 1.3 | –2.0 |
B | 1.4 | –4.2 |
C | 2.2 | +6.4 |
D | 3.9 | +2.1 |
E | 1.7 | –0.8 |
What is the return on the portfolio?
A) -1.20%.
B) +1.50%.
C) +2.48%.
D) +1.18%.
The correct answer was D)
The return is equal to sum of the products of each position’s value and return divided by the beginning portfolio value.
Position | Mkt. Value at | Return for 2005(%) | Position Value X Return ($MM) |
A | 1.30 | –2.0 | 0.0260 |
B | 1.40 | –4.2 | 0.0588 |
C | 2.20 | +6.4 | 0.1408 |
D | 3.90 | +2.1 | 0.0819 |
E | 1.70 | –0.8 | 0.0136 |
Total | 10.50 | | 0.1243 |
0.1243 / 10.5($MM) = | +1.1838% | ||
6、Claude Bellow, CFA, is an analyst with a real-estate focused investment firm. Today, one of the partners e-mails Bellow the following table and requests that he “run some numbers.” The table below gives five years of annual returns for Marley REIT (real estate investment trust) and a large urban apartment building. Marley REIT invests in commercial properties. (Note: For this question, calculate the mean returns using the arithmetic mean.)
Table 1: Annual returns (in %) | |||||
Asset | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
Marley REIT | 15.0 | 8.0 | 13.0 | 9.0 | 13.0 |
Apartment Bldg | 10.0 | -1.0 | 8.0 | 8.0 | 9.0 |
One of the office assistants begins to “run some numbers,” but is then called away to an important meeting. So far, the assistant calculated the variance of the apartment building returns at 15.76%. (He assumed that the returns given represent the entire population of returns.) Now, Bellow must finish the work.
Bellow should conclude that the standard deviation of the:
A) apartment building, if the given returns represent a sample of returns, is 19.70%.
B) REIT, assuming the given returns represent the entire population, is 2.97%.
C) apartment building, if the given returns represent a sample of returns, is 4.44%.
D) REIT, assuming the given returns represent a sample of returns, is 7.04%.
The correct answer was C)
Suggested Strategy: Since you will have approximately 1.5 minutes for each question and this question appears very calculation intensive, it is likely that there is a “trick.” Here, start with the apartment building because the labor-intensive part of the calculation has been completed. Remember that the standard deviation is the square root of the variance and that both the formula for the population variance and the formula for the sample variance have the same numerator (the sum of the squared result of the observation less the mean). The denominator of the population variance is the entire data set n, (5 here). The denominator of the sample variance is n-1, (or 4 here).
Thus, the population variance = (the sum of the square result of the observation less the mean) / number of observations. Here, 15.76 = x / 5, x = 78.80.
So, the sample variance = 78.80 / 4 = 19.70, and the sample standard deviation = 19.701/2 = 4.44%.
The other statements are false. FYI, the calculations for the REIT are as follows:
§ Mean = (15 + 8 + 13 + 9 + 13) / 5 = 11.6
§ (The sum of the observation less the mean)2 = [(15-11.6)2 + (8 – 11.6)2 + (13 – 11.6)2 + (9 – 11.6)2 + (13 – 11.6)2] = 35.2
§ The population standard deviation = [(35.2 / 5.0)]1/2 = [7.04]1/2 = 2.65%
§ The sample standard deviation = [(35.2 / 4.0)]1/2 = [8.80]1/2 = 2.97%
7、Assume that the following returns are a sample of annual returns for firms in the clothing industry. Given the following sample of returns, what are the sample variance and standard deviation?
Firm 1 | Firm 2 | Firm 3 | Firm 4 | Firm 5 |
15% | 2% | 5% | (7%) | 0% |
A) Variance Standard Deviation
64.5 8.0
B) Variance Standard Deviation
32.4 5.7
C) Variance Standard Deviation
22.0 4.7
D) Variance Standard Deviation
51.6 7.2
The correct answer was A)
The sample variance is found by taking the sum of all squared deviations from the mean and dividing by (n-1). [(15-3)2 + (2-3)2 + (5-3)2 + (-7-3)2 + (0-3)2] / (5-1) = 64.5
The sample standard deviation is found by taking the square root of the sample variance. √64.5 = 8.03
8、Given the following annual returns, what is the mean absolute deviation?
2000 | 2001 | 2002 | 2003 | 2004 |
15% | 2% | 5% | -7% | 0% |
A) 5.6%.
B) 3.0%.
C) 22.0%.
D) 2.0%.
The correct answer was A)
The mean absolute deviation is found by taking the mean of the absolute values of deviations from the mean. ( |15-3| + |2-3| + |5-3| + |-7-3| + |0-3|)/5 = 5.60%
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