21、There is a 30% chance that the economy will be good and a 70% chance that it will be bad. If the economy is good, your returns will be 20% and if the economy is bad, your returns will be 10%. What is your expected return?
A) 15%.
B) 17%.
C) 18%.
D) 13%.
22、Given P(X=2)=0.3, P(X=3)=0.4, P(X=4)=0.3. What is the variance of x?
A) 0.3.
B) 0.6.
C) 3.0.
D) 0.5
23、After repeated experiments, the average of the outcomes should converge to:
A) the expected value.
B) the variance.
C) zero.
D) one.
24、Use the following data to calculate the standard deviation of the return:
§ 50% chance of a 12% return
§ 30% chance of a 10% return
§ 20% chance of a 15% return
A) 2.5%.
B) 1.7%.
C) 3.0%.
D) 3.3%.
25、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 returns on portfolio A?
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) 4.53%.
B) 1.140%.
C) 5.992%.
D) 8.76%.
答案和详解如下：
21、There is a 30% chance that the economy will be good and a 70% chance that it will be bad. If the economy is good, your returns will be 20% and if the economy is bad, your returns will be 10%. What is your expected return?
A) 15%.
B) 17%.
C) 18%.
D) 13%.
The correct answer was D)
Expected value is the probability weighted average of the possible outcomes of the random variable. The expected return is: ((0.3)*(0.2)) + ((0.7)*(0.1)) = (0.06) + (0.07) = 0.13.
22、Given P(X=2)=0.3, P(X=3)=0.4, P(X=4)=0.3. What is the variance of x?
A) 0.3.
B) 0.6.
C) 3.0.
D) 0.5
The correct answer was B)
The variance is the sum of the squared deviations from the expected value weighted by the probability of each outcome.
The expected value is E(X) = 0.3*2 + 0.4*3 + 0.3*4 = 3.
The variance is 0.3*(2-3)2 + 0.4*(3-3)2 + 0.3*(4-3)2 = 0.6.
23、After repeated experiments, the average of the outcomes should converge to:
A) the expected value.
B) the variance.
C) zero.
D) one.
The correct answer was A)
This is the definition of the expected value. It is the long-run average of all outcomes.
24、Use the following data to calculate the standard deviation of the return:
§ 50% chance of a 12% return
§ 30% chance of a 10% return
§ 20% chance of a 15% return
A) 2.5%.
B) 1.7%.
C) 3.0%.
D) 3.3%.
The correct answer was B)
The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: = (0.5)*(0.12) + (0.3)*(0.1) + (0.2)*(0.15) = 0.12. The variance is: (0.5)*(0.12-0.12)2 + (0.3)*(0.1-0.12)2 + (0.2)*(0.15-0.12)2 = 0.0003. The standard deviation is the square root of 0.0003 = .017 or 1.7%.
25、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 returns on portfolio A?
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) 4.53%.
B) 1.140%.
C) 5.992%.
D) 8.76%.
The correct answer was A)
E(RA) = 11.65%
σ2 = 0.0020506 = .15(.18-.1165)2 + .2(.17-.1165)2 + .25(.11-.1165)2 + .4(.07-.1165)2
σ = 0.0452836
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