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1、Chapter 7 Optimal Risky PortfoliosMultiple Choice Questions1.Market risk is also referred to as A)systematic risk, diversifiable risk. B)systematic risk, nondiversifiable risk. C)unique risk, nondiversifiable risk. D)unique risk, diversifiable risk. E)none of the above. Answer: B Difficulty: Easy Ra
2、tionale: Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be eliminated from the portfolio by diversification.2.The
3、risk that can be diversified away is A)firm specific risk. B)beta. C)systematic risk. D)market risk. E)none of the above. Answer: A Difficulty: Easy Rationale: See explanations for 1 and 2 above.3.The variance of a portfolio of risky securities A)is a weighted sum of the securities variances. B)is t
4、he sum of the securities variances. C)is the weighted sum of the securities variances and covariances. D)is the sum of the securities covariances. E)none of the above. Answer: C Difficulty: Moderate Rationale: The variance of a portfolio of risky securities is a weighted sum taking into account both
5、 the variance of the individual securities and the covariances between securities.4.The expected return of a portfolio of risky securities A)is a weighted average of the securities returns. B)is the sum of the securities returns. C)is the weighted sum of the securities variances and covariances. D)A
6、 and C. E)none of the above. Answer: A Difficulty: Easy 5.Other things equal, diversification is most effective when 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
7、: D Difficulty: Moderate Rationale: Negative correlation among securities results in the greatest reduction of portfolio risk, which is the goal of diversification.6.The efficient frontier of risky assets is A)the portion of the investment opportunity set that lies above the global minimum variance
8、portfolio. B)the portion of the investment opportunity set that represents the highest standard deviations. C)the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation. D)the set of portfolios that have zero standard deviation. E)both A and B are
9、true. Answer: A Difficulty: Moderate Rationale: Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those portfolios above the global minimum variance portfolio meet this criterion.7.The Capital Allocation Line provided by a risk-fre
10、e 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)
11、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 as
12、set and risky securities. Only C meets that definition.8.Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always A)greater than zero. B)equal to zero. C)equal to the sum
13、of the securities standard deviations. D)equal to -1. E)none of the above. Answer: B Difficulty: Difficult Rationale: If two securities were perfectly negatively correlated, the weights for the minimum variance portfolio for those securities could be calculated, and the standard deviation of the res
14、ulting portfolio would be zero.9.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 betwee
15、n 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 th
16、e securities, the more portfolio risk is reduced.10.Efficient portfolios of N risky securities are portfolios that A)are formed with the securities that have the highest rates of return regardless of their standard deviations. B)have the highest rates of return for a given level of risk. C)are selec
17、ted from those securities with the lowest standard deviations regardless of their returns. D)have the highest risk and rates of return and the highest standard deviations. E)have the lowest standard deviations and the lowest rates of return. Answer: B Difficulty: Moderate Rationale: Portfolios that
18、are efficient are those that provide the highest expected return for a given level of risk.11.Which of the following statement(s) is (are) true regarding the selection of a portfolio from those that lie on the Capital Allocation Line? A)Less risk-averse investors will invest more in the risk-free se
19、curity and less in the optimal risky portfolio than more risk-averse investors. B)More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors. C)Investors choose the portfolio that maximizes their expected utility. D)A
20、 and C. E)B and C. Answer: E Difficulty: Moderate Rationale: All rational investors select the portfolio that maximizes their expected utility; for investors who are relatively more risk-averse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset.Use the foll
21、owing to answer questions 12-18:Consider the following probability distribution for stocks A and B:12.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% E)none of the above Answer: C Difficulty: Easy Rationale: E(RA) = 0.1(10
22、%) + 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%.13.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 Ration
23、ale: 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%)21/2 = 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 = 1.1%.14.The coefficient of correlation between A and B is A)0.47. B)0.60. C)0.58 D)1.2
24、0. 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) = 0.47.15.If you invest 40% of your money in
25、A and 60% in B, what would be your portfolios 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
26、.46)1/2 = 1.1%.16.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) =
27、0.23; wB = 1 - 0.23 = 0.77.Note that the above solution assumes the solutions obtained in question 13 and 14.17.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)n
28、one 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%.18.Which of the following portfolio(s) is (are) on the efficient frontier? A)The portfolio with 20 percent in A an
29、d 80 percent in B. B)The portfolio with 15 percent in A and 85 percent in B. C)The portfolio with 26 percent in A and 74 percent in B. D)The portfolio with 10 percent in A and 90 percent in B. E)A and B are both on the efficient frontier. Answer: C Difficulty: Difficult Rationale: The Portfolios E(R
30、p), sp, Reward/volatility ratios are 20A/80B: 8.8%, 1.05%, 8.38; 15A/85B: 8.53%, 1.06%, 8.07; 26A/74B: 9.13%, 1.05%, 8.70; 10A/90B: 8.25%, 1.07%, 7.73. The portfolio with 26% in A and 74% in B dominates all of the other portfolios by the mean-variance criterion.Use the following to answer questions
31、19-21:Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. 19.The weights of A and B in the global minimum variance portfolio are _ and _
32、, respectively. A)0.24; 0.76 B)0.50; 0.50 C)0.57; 0.43 D)0.43; 0.57 E)0.76; 0.24 Answer: D Difficulty: Moderate Rationale: wA = 12 /(16 + 12) = 0.4286; wB = 1 - 0.4286 = 0.5714.20.The risk-free portfolio that can be formed with the two securities will earn _ rate of return. A)8.5% B)9.0% C)8.9% D)9.
33、9% E)none of the above Answer: C Difficulty: Difficult Rationale: E(RP) = 0.43(10%) + 0.57(8%) = 8.86%.21.Which of the following portfolio(s) is (are) most efficient? A)45 percent in A and 55 percent in B. B)65 percent in A and 35 percent in B. C)35 percent in A and 65 percent in B. D)A and B are bo
34、th efficient. E)A and C are both efficient. Answer: D Difficulty: Difficult Rationale: The Portfolio E(Rp), sp, and Reward/volatility ratios are 45A/55B: 8.9%, 0.6%, 14.83; 65A/35B: 9.3%, 6.2%, 1.5; 35A/65B: 8.7%, 2.2%, 3.95. Both A and B are efficient according to the mean-variance criterion. A has
35、 a much higher Reward/volatility ratio.22.An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation Line must: A)lend some of her money at the risk-free rate and invest the remainder in the optimal risky portfolio. B)borrow some money
36、at the risk-free rate and invest in the optimal risky portfolio. C)invest only in risky securities. D)such a portfolio cannot be formed. E)B and C Answer: E Difficulty: Moderate Rationale: The only way that an investor can create portfolios to the right of the Capital Allocation Line is to create a
37、borrowing portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free security, but will hold only risky securities.23.Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?A)Only portfolio W cannot lie on the efficie
38、nt frontier. B)Only portfolio X cannot lie on the efficient frontier. C)Only portfolio Y cannot lie on the efficient frontier. D)Only portfolio Z cannot lie on the efficient frontier. E)Cannot tell from the information given. Answer: A Difficulty: Moderate Rationale: When plotting the above portfoli
39、os, only W lies below the efficient frontier as described by Markowitz. It has a higher standard deviation than Z with a lower expected return.24.Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?A)Only portfolio A cannot lie on the efficient fronti
40、er. B)Only portfolio B cannot lie on the efficient frontier. C)Only portfolio C cannot lie on the efficient frontier. D)Only portfolio D cannot lie on the efficient frontier. E)Cannot tell from the information given. Answer: D Difficulty: Moderate Rationale: When plotting the above portfolios, only
41、W lies below the efficient frontier as described by Markowitz. It has a higher standard deviation than Z with a lower expected return.25.Portfolio theory as described by Markowitz is most concerned with: A)the elimination of systematic risk. B)the effect of diversification on portfolio risk. C)the i
42、dentification of unsystematic risk. D)active portfolio management to enhance returns. E)none of the above. Answer: B Difficulty: Moderate Rationale: Markowitz was concerned with reducing portfolio risk by combining risky securities with differing return patterns.26.The measure of risk in a Markowitz
43、 efficient frontier is: A)specific risk. B)standard deviation of returns. C)reinvestment risk. D)beta. E)none of the above. Answer: B Difficulty: Moderate Rationale: Markowitz was interested in eliminating diversifiable risk (and thus lessening total risk) and thus was interested in decreasing the s
44、tandard deviation of the returns of the portfolio.27.A statistic that measures how the returns of two risky assets move together is: A)variance. B)standard deviation. C)covariance. D)correlation. E)C and D. Answer: E Difficulty: Moderate Rationale: Covariance measures whether security returns move t
45、ogether or in opposition; however, only the sign, not the magnitude, of covariance may be interpreted. Correlation, which is covariance standardized by the product of the standard deviations of the two securities, may assume values only between +1 and -1; thus, both the sign and the magnitude may be
46、 interpreted regarding the movement of one securitys return relative to that of another security.28.The unsystematic risk of a specific security A)is likely to be higher in an increasing market. B)results from factors unique to the firm. C)depends on market volatility. D)cannot be diversified away. E)n