Q11. 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) 2.64%.
B) 1.39%.
C) 0.07%.
Q12. For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.20, Var(RA) = 0.25, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the expected return of a portfolio that is equally invested in the two assets?
A) 0.3050.
B) 0.1500.
C) 0.2275.
Q13. A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?
A) $1.50.
B) $17.67.
C) $2.47.
Q14. The following information is available concerning expected return and standard deviation of Pluto and Neptune Corporations:
| Expected Return | Standard Deviation |
Pluto Corporation | 11% | 0.22 |
Neptune Corporation | 9% | 0.13 |
If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.
A) 10.3% expected return and 2.58% standard deviation.
B) 10.3% expected return and 16.05% standard deviation.
C) 10.0% expected return and 16.05% standard deviation.
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Q15. Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?
A) 4.18%.
B) 0.00%.
C) 0.17%.
答案和详解如下：
Q11. 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) 2.64%.
B) 1.39%.
C) 0.07%.
Correct answer is A)
The standard deviation of the portfolio is found by:
[W12σ12 + W22σ2 2+ 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%.
Q12. For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.20, Var(RA) = 0.25, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the expected return of a portfolio that is equally invested in the two assets?
A) 0.3050.
B) 0.1500.
C) 0.2275.
Correct answer is B)
The expected return of a portfolio composed of n-assets is the weighted average of the expected returns of the assets in the portfolio: ((w1) × (E(R1)) + ((w2) × (E(R2)) = (0.5 × 0.1) + (0.5 × 0.2) = 0.15.
Q13. A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?
A) $1.50.
B) $17.67.
C) $2.47.
Correct answer is C)
Since the probability of the coin landing on its edge is 0.02, the probability of each of the other two events is 0.49. The expected payoff is: (0.02 × $50) + (0.49 × $1) + (0.49 × $2) = $2.47.
Q14. The following information is available concerning expected return and standard deviation of Pluto and Neptune Corporations:
| Expected Return | Standard Deviation |
Pluto Corporation | 11% | 0.22 |
Neptune Corporation | 9% | 0.13 |
If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.
A) 10.3% expected return and 2.58% standard deviation.
B) 10.3% expected return and 16.05% standard deviation.
C) 10.0% expected return and 16.05% standard deviation.
Correct answer is B)
ERPort | = (WPluto)(ERPluto) + (WNeptune)(ERNeptune) |
| = (0.65)(0.11) + (0.35)(0.09) = 10.3% |
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σp | = [(w1)2(σ1)2 + (w2)2(σ2)2 + 2w1w2σ1σ2 r1,2]1/2 |
| = [(0.65)2(22)2 + (0.35)2(13)2 + 2(0.65)(0.35)(22)(13)(0.25)]1/2 |
| = [(0.4225)(484) + (0.1225)(169) + 2(0.65)(0.35)(22)(13)(0.25)]1/2 |
| = (257.725)1/2 = 16.0538% |
Q15. Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?
A) 4.18%.
B) 0.00%.
C) 0.17%.
Correct answer is A)
The standard deviation of the portfolio is found by:
[W12 σ12 + W22 σ22 + 2W1W2σ1σ2r1,2]0.5, or [(0.75)2(0.102)2 + (0.25)2(0.139)2 + (2)(0.75)(0.25)(0.102)(0.139)(–1.0)]0.5 = 0.0418, or 4.18%.
看答案，谢谢LZ
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