A) securities' returns are uncorrelated. B) securities' returns are positively correlated. C) securities' returns are high. D) securities' returns are negatively correlated. E) B and C.
Answer: D Difficulty: Moderate
Rationale: Negative correlation among securities results in the greatest reduction of portfolio
risk, which is the goal of diversification.
4. The Capital Allocation Line provided by a risk-free security and N risky securities is A) the line that connects the risk-free rate and the global minimum-variance portfolio
of the risky securities.
B) the line that connects the risk-free rate and the portfolio of the risky securities that
has the highest expected return on the efficient frontier.
C) the line tangent to the efficient frontier of risky securities drawn from the risk-free
rate.
D) the horizontal line drawn from the risk-free rate. E) none of the above.
Answer: C Difficulty: Moderate
Rationale: The Capital Allocation Line represents the most efficient combinations of the risk-free asset and risky securities. Only C meets that definition.
5. Which of the following statements is (are) true regarding the variance of a portfolio of
two risky securities? A) The higher the coefficient of correlation between securities, the greater the
reduction in the portfolio variance.
B) There is a linear relationship between the securities' coefficient of correlation and
the portfolio variance.
C) The degree to which the portfolio variance is reduced depends on the degree of
correlation between securities.
D) A and B. E) A and C.
Answer: C Difficulty: Moderate
Rationale: The lower the correlation between the returns of the securities, the more portfolio r
isk is reduced.
Use the following to answer questions 6-11:
Consider the following probability distribution for stocks A and B:
6.
The expected rates of return of stocks A and B are _____ and _____ , respectively. A) 13.2%; 9% B) 14%; 10% C) 13.2%; 7.7% D) 7.7%; 13.2%
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E) none of the above Answer: C Difficulty: Easy
Rationale: E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2%; E(RB) = 0.1(8%) + 0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.
7. The standard deviations of stocks A and B are _____ and _____, respectively. A) 1.5%; 1.9% B) 2.5%; 1.1% C) 3.2%; 2.0% D) 1.5%; 1.1% E) none of the above
Answer: D Difficulty: Moderate
Rationale: sA = [0.1(10% - 13.2%)2 + 0.2(13% - 13.2%)2 + 0.2(12% - 13.2%)2 + 0.3(14% - 13.2%)2 + 0.2(15% - 13.2%)2]1/2 = 1.5%; sB = [0.1(8% - 7.7%)2 + 0.2(7% - 7.7%)2 + 0.2(6% - 7.7%)2 + 0.3(9% - 7.7%)2 + 0.2(8% - 7.7%)2]1/2 = 1.1%.
8. The coefficient of correlation between A and B is A) 0.47. B) 0.60. C) 0.58 D) 1.20. E) none of the above.
Answer: A Difficulty: Difficult
Rationale: covA,B = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% - 7.7%) + 0.2(12% - 13.2%)(6% - 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) + 0.2(15% - 13.2%)(8% - 7.7%) = 0.76; rA,B = 0.76/[(1.1)(1.5)] = 0.47.
9. If you invest 40% of your money in A and 60% in B, what would be your portfolio's
expected rate of return and standard deviation? A) 9.9%; 3% B) 9.9%; 1.1% C) 11%; 1.1% D) 11%; 3% E) none of the above
Answer: B Difficulty: Difficult
Rationale: E(RP) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; sP = [(0.4)2(1.5)2 + (0.6)2(1.1)2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]1/2 = 1.1%.
10. Let G be the global minimum variance portfolio. The weights of A and B in G are
__________ and __________, respectively. A) 0.40; 0.60 B) 0.66; 0.34 C) 0.34; 0.66 D) 0.76; 0.24 E) 0.24; 0.76
Answer: E Difficulty: Difficult
Rationale: wA = [(1.1)2 - (1.5)(1.1)(0.46)]/[(1.5)2 + (1.1)2 - (2)(1.5)(1.1)(0.46) = 0.23; wB = 1-0.23 = 0.77.Note that the above solution assumes the solutions obtained in question 13 and 14.
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11. The expected rate of return and standard deviation of the global minimum variance
portfolio, G, are __________ and __________, respectively. A) 10.07%; 1.05% B) 9.04%; 2.03% C) 10.07%; 3.01% D) 9.04%; 1.05% E) none of the above
Answer: D Difficulty: Moderate
Rationale: E(RG) = 0.23(13.2%) + 0.77(7.7%) = 8.97% . 9%; sG = [(0.23)2(1.5)2 + (0.77)2(1.1)2 + (2)(0.23)(0.77)(1.5)(1.1)(0.46)]1/2 = 1.05%.
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