16、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) $17.67.
B) $1.50.
C) $26.50.
D) $2.47.
17、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) 0.2275.
B) 0.3050.
C) 0.1500.
D) 0.2500.
18、For assets A and B we know the following: E(RA)=0.10, E(RB)=0.10, Var(RA)=0.18, Var(RB)=0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?
A) 0.1102.
B) 0.1500.
C) 0.2114.
D) 0.2275.
19、Use the following probability distribution to calculate the expected return for the portfolio.
State of the Economy | Probability | Return on Portfolio |
Boom | 0.30 | 15% |
Bust | 0.70 | 3% |
A) 8.1%.
B) 6.6%.
C) 9.0%.
D) 11.4%.
20、Use the following probability distribution to calculate the standard deviation for the portfolio.
State of the Economy | Probability | Return on Portfolio |
Boom | 0.30 | 15% |
Bust | 0.70 | 3% |
A) 6.0%.
B) 5.5%.
C) 6.5%.
D) 7.0%.
答案和详解如下：
16、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) $17.67.
B) $1.50.
C) $26.50.
D) $2.47.
The correct answer was D)
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: (.02 x $50) + (0.49 x $1) + (0.49 x $2) = $2.47.
17、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) 0.2275.
B) 0.3050.
C) 0.1500.
D) 0.2500.
The correct answer was C)
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.
18、For assets A and B we know the following: E(RA)=0.10, E(RB)=0.10, Var(RA)=0.18, Var(RB)=0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?
A) 0.1102.
B) 0.1500.
C) 0.2114.
D) 0.2275.
The correct answer was C)
You are not given the covariance in this problem but instead you are given the correlation coefficient and the variances of assets A and B from which you can determine the covariance by Covariance = (correlation of A,B) * (Standard Deviation of A) * (Standard Deviation of B).
Since it is an equally weighted portfolio, the solution is:
[( 0.52 )* 0.18 ] + [(0.52) * 0.36 ] + [ 2 * 0.5 * 0.5 * 0.6 * ( 0.180.5 ) * ( 0.360.5 )]
= 0.045 + 0.09 + 0.0764 = 0.2114
19、Use the following probability distribution to calculate the expected return for the portfolio.
State of the Economy | Probability | Return on Portfolio |
Boom | 0.30 | 15% |
Bust | 0.70 | 3% |
A) 8.1%.
B) 6.6%.
C) 9.0%.
D) 11.4%.
The correct answer was B)
0.30 × 0.15 + 0.70 × 0.03 = 6.6%
20、Use the following probability distribution to calculate the standard deviation for the portfolio.
State of the Economy | Probability | Return on Portfolio |
Boom | 0.30 | 15% |
Bust | 0.70 | 3% |
A) 6.0%.
B) 5.5%.
C) 6.5%.
D) 7.0%.
The correct answer was B)
[0.30 * (0.15 - 0.066)2 + 0.70 * (0.03 - 0.066)2]1/2 = 5.5%
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