26、Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario, as shown in the table below. Given this information, what is the standard deviation of expected returns on portfolio B?
Scenario | Probability | Return on Portfolio A | Return on Portfolio B |
A | 15% | 18% | 19% |
B | 20% | 17% | 18% |
C | 25% | 11% | 10% |
D | 40% | 7% | 9% |
A) 4.34%.
B) 9.51%.
C) 12.55%.
D) 8.35%.
27、Based on the following data, what is ABC Co.'s projected growth rate?
| Bear | Bull | |
Probability | 30% | 40% | 30% |
ROE | 10% | 15% | 30% |
Ret. Rate | 60% | 40% | 30% |
A) 5.0 percent.
B) 7.0 percent.
C) 6.9 percent.
D) 7.5 percent.
28、Compute the standard deviation of a two-stock portfolio if stock A (40% weight) has a variance of 0.0015, stock B (60% weight) has a variance of 0.0021, and the correlation coefficient for the two stocks is –0.35?
A) 1.39%.
B) 2.64%.
C) 0.07%.
D) 2.92%.
29、Given the following probability distribution, find the standard deviation of expected returns.
Event | P(RA) | RA |
Recession | 0.10 | -5% |
Below Average | 0.30 | -2% |
0.50 | 10% | |
Boom | 0.10 | 31% |
A) 7.00%.
B) 12.45%.
C) 10.04%.
D) 15.67%.
答案和详解如下：
26、Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario, as shown in the table below. Given this information, what is the standard deviation of expected returns on portfolio B?
Scenario | Probability | Return on Portfolio A | Return on Portfolio B |
A | 15% | 18% | 19% |
B | 20% | 17% | 18% |
C | 25% | 11% | 10% |
D | 40% | 7% | 9% |
A) 4.34%.
B) 9.51%.
C) 12.55%.
D) 8.35%.
The correct answer was A)
Scenario | Probability | Return on Portfolio B | P * [RB – E(RB)]2 |
A | 15% | 19% | 0.000624 |
B | 20% | 18% | 0.000594 |
C | 25% | 10% | 0.000163 |
D | 40% | 9% | 0.000504 |
| | E(RB) = 12.55% | σ2 = 0.001885 |
| | | σ = 0.0434166 |
27、Based on the following data, what is ABC Co.'s projected growth rate?
| Bear | Bull | |
Probability | 30% | 40% | 30% |
ROE | 10% | 15% | 30% |
Ret. Rate | 60% | 40% | 30% |
A) 5.0 percent.
B) 7.0 percent.
C) 6.9 percent.
D) 7.5 percent.
The correct answer was C)
The expected growth rate is calculated by summing the probability times the growth rate for each possible outcome. The growth rate (g) is the return on equity (ROE) times the retention rate (RE). The computed growth rates are: g bear = (0.1)*(0.6) = 0.06, g normal = (0.15)*(0.4) = 0.06, and g bull = (0.3)*(0.3) = 0.09. The expected growth rate is: g = (0.3)*(0.06) + (0.4)*(0.06) + (0.3)*(0.09) = 0.069 or 6.9 percent.
28、Compute the standard deviation of a two-stock portfolio if stock A (40% weight) has a variance of 0.0015, stock B (60% weight) has a variance of 0.0021, and the correlation coefficient for the two stocks is –0.35?
A) 1.39%.
B) 2.64%.
C) 0.07%.
D) 2.92%.
The correct answer was B)
The standard deviation of the portfolio is found by:
= [W12 σ12 + W22 σ22 + 2W1W2σ1σ2ρ1,2]0.5
= [(0.40)2(0.0015) + (0.60)2(0.0021) + (2)(0.40)(0.60)(0.0387)(0.0458)(–0.35)]0.5
= 0.0264, or 2.64%.
29、Given the following probability distribution, find the standard deviation of expected returns.
Event | P(RA) | RA |
Recession | 0.10 | -5% |
Below Average | 0.30 | -2% |
0.50 | 10% | |
Boom | 0.10 | 31% |
A) 7.00%.
B) 12.45%.
C) 10.04%.
D) 15.67%.
The correct answer was C)
Find the weighted average return (0.10)(-5) + (0.30)(-2) + (0.50)(10) + (0.10)(31) = 7%.
Next, take differences, square them, multiply by the probability of the event and add them up. That is the variance. Take the square root of the variance for Std. Dev. (-5-7)2 (0.1) + (-2-7)2(0.3) + (10-7)2(0.5) + (31-7)2 (0.1) = 100.8 = variance.
100.80.5 = 10.04%.
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