CHAPTER 05: Optimal Risky Portfolios ​

1. Market risk is also referred to as → B. systematic risk, nondiversifiable risk.

2. Systematic risk is also referred to as → A. market risk, nondiversifiable risk.

3. Nondiversifiable risk is also referred to as → B. systematic risk, market risk.

4. Diversifiable risk is also referred to as → D. unique risk, firm-specific risk.

5. Unique risk is also referred to as → D. diversifiable risk, firm-specific risk.

6. Firm-specific risk is also referred to as → D. diversifiable risk, unique risk.

7. Non-systematic risk is also referred to as → D. diversifiable risk, unique risk.

8. The risk that can be diversified away is → A. firm specific risk.

9. The risk that cannot be diversified away is → D. market risk.

10. The variance of a portfolio of risky securities → C. is the weighted sum of the securities'
variances and covariances.

11. The standard deviation of a portfolio of risky securities→ C. the square root of the weighted sum
of the securities' variances and covariances.

12. The expected return of a portfolio of risky securities → A. is a weighted average of the securities'
returns.

13. Other things equal, diversification is most effective when → D. securities' returns are negatively
correlated.

14. The efficient frontier of risky assets is → A. the portion of the investment opportunity set that lies
above the global minimum variance portfolio.

15. The Capital Allocation Line provided by a risk-free security and N risky securities is → C. the
line tangent to the efficient frontier of risky securities drawn from the risk-free rate.

16. 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 → B. equal to zero.

17. Which of the following statements is (are) true regarding the variance of a portfolio of two
risky securities? → C. The degree to which the portfolio variance is reduced depends on the degree of
correlation between securities.

18. Which of the following statements is (are) false 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.

19. Efficient portfolios of N risky securities are portfolios that → B. have the highest rates of return
for a given level of risk.
20. Which of the following statement(s) is (are) true regarding the selection of a portfolio from
those that lie on the Capital Allocation Line? → E. B and C.

21. Which of the following statement(s) is (are) false 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 security and less in the optimal risky portfolio than more risk-averse investors.

Consider the following probability distribution for stocks A and B:

22. The expected rates of return of stocks A and B are _____ and _____ , respectively. → C.
13.2%; 7.7%
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%.

22. The expected rates of return of stocks A and B are _____ and _____ , respectively. → D. 1.5%;
1.1%
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= 1.1%.

24. The variances of stocks A and B are _____ and _____, respectively. B. 2.3%; 1.2%
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] = 2.25%;
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= 1.21%.

25. The coefficient of correlation between A and B is → A. 0.47.

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.

26. 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? → B. 9.9%; 1.1%
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%.

27. Let G be the global minimum variance portfolio. The weights of A and B in G are __________
and __________, respectively. → E. 0.24; 0.76
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.

28. The expected rate of return and standard deviation of the global minimum variance portfolio,
G, are __________ and __________, respectively. D. 9.04%; 1.05%
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%.
29. Which of the following portfolio(s) is (are) on the efficient frontier?→ C. The portfolio with 26
percent in A and 74 percent in B.
The Portfolio's E(Rp), 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. ​
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%.

30. The weights of A and B in the global minimum variance portfolio are _____ and _____,
respectively.
→ D. 0.43; 0.57
wA = 12 /(16 + 12) = 0.4286; wB = 1 - 0.4286 = 0.5714.

31. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
→ C. 8.9%
E(RP) = 0.43(10%) + 0.57(8%) = 8.86%.

32. Which of the following portfolio(s) is (are) most efficient?

→ D. A and B are both efficient
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 a much higher Reward/volatility ratio.

33. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio
on the Capital Allocation Line must:
→ E. B and C
The only way that an investor can create portfolios to the right of the Capital Allocation Line is to create a
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.

34. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?

→ A. Only portfolio W cannot lie on the efficient frontier.

35. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?

D. Only portfolio D cannot lie on the efficient frontier.

36. Portfolio theory as described by Markowitz is most concerned with: → B. the effect of
diversification on portfolio risk..

37. The measure of risk in a Markowitz efficient frontier is:→ B. standard deviation of returns.

38. 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.

39. The unsystematic risk of a specific security → B. results from factors unique to the firm.

40. Which statement about portfolio diversification is correct?→ D. Typically, as more securities are
added to a portfolio, total risk would be expected to decrease at a decreasing rate.

41. The individual investor's optimal portfolio is designated by:→ A. The point of tangency with the
indifference curve and the capital allocation line
42. For a two-stock portfolio, what would be the preferred correlation coefficient between the two
stocks? D. -1.00.

42. For a two-stock portfolio, what would be the preferred correlation coefficient between the two
stocks? → D. -1.00

43. In a two-security minimum variance portfolio where the correlation between securities is
greater than -1.0→ B. the security with the higher standard deviation will be weighted less heavily.

44. Which of the following is not a source of systematic risk? → C. personnel changes

45. The global minimum variance portfolio formed from two risky securities will be riskless when
the correlation coefficient between the two securities is → D. -1.0
46. Security X has expected return of 12% and standard deviation of 20%. Security Y has
expected return of 15% and standard deviation of 27%. If the two securities have a correlation
coefficient of 0.7, what is their covariance?
→ A. 0.038
Cov(rX, rY) = (.7)(.20)(.27) = .0378

47. When two risky securities that are positively correlated but not perfectly correlated are held in
a portfolio→ B. the portfolio standard deviation will be less than the weighted average of the individual
security standard deviations.

48. The line representing all combinations of portfolio expected returns and standard deviations
that can be constructed from two available assets is called the→ D. portfolio opportunity set

49. Given an optimal risky portfolio with expected return of 14% and standard deviation of 22%
and a risk free rate of 6%, what is the slope of the best feasible CAL? → E. 0.36
Slope = (14 - 6)/22 = .3636
50. Given an optimal risky portfolio with expected return of 18% and standard deviation of 21%
and a risk free rate of 5%, what is the slope of the best feasible CAL? → C. 0.62

51. The risk that can be diversified away in a portfolio is referred to as_____.
I) diversifiable risk
II) unique risk
III) systematic risk
IV) firm-specific risk
A. I, III, and IV
B. II, III, and IV
C. III and IV
D. I, II, and IV

52. As the number of securities in a portfolio is increased, what happens to the average portfolio
standard deviation? → D. It decreases at a decreasing rate.

53. In words, the covariance considers the probability of each scenario happening and the
interaction between → B. securities' returns relative to their mean returns.

54. The standard deviation of a two-asset portfolio is a linear function of the assets' weights
when → D. the assets have a correlation coefficient equal to one..

55. A two-asset portfolio with a standard deviation of zero can be formed when

→ E. the assets have a correlation coefficient equal to negative one.

56. When borrowing and lending at a risk-free rate are allowed, which Capital Allocation Line
(CAL) should the investor choose to combine with the efficient frontier?
I) with the highest reward-to-variability ratio.
II) that will maximize his utility.
III) with the steepest slope.
IV) with the lowest slope.
E. I, II, and III

57. Which Excel tool can be used to find the points along an efficient frontier? → B. Solver

58. The separation property refers to the conclusion that

→ A. the determination of the best risky portfolio is objective and the choice of the best complete
portfolio is subjective.
Consider the following probability distribution for stocks A and B:
59. The expected rates of return of stocks A and B are _____ and _____, respectively.
→ B. 13%; 8.4%
E(RA) = 0.15(8%) + 0.2(13%) + 0.15(12%) + 0.3(14%) + 0.2(16%) = 13%; E(RB) = 0.15(8%) + 0.2(7%) +
0.15(6%) + 0.3(9%) + 0.2(11%) = 8.4%.
60. The standard deviations of stocks A and B are _____ and _____, respectively.
→ B. 2.45%; 1.68%
sA = [0.15(8% - 13%)2+ 0.2(13% - 13%)2+ 0.15(12% - 13%)2+ 0.3(14% - 13%)2+ 0.2(16% - 13%)2]1/2=
2.449%; sB = [0.15(8% - 8.4%)2+ 0.2(7% - 8.4%)2+ 0.15(6% - 8.4%)2+ 0.3(9% - 8.4%)2+ 0.2(11% -
8.4%)2] 1/2= 1.676%.

61. The coefficient of correlation between A and B is

→ C. 0.583
covA,B = 0.15(8% - 13%)(8% - 8.4%) + 0.2(13% - 13%)(7% - 8.4%) + 0.15(12% - 13%)(6% - 8.4%) +
0.3(14% - 13%)(9% - 8.4%) + 0.2(16% - 13%)(11% - 8.4%) = 2.40; rA,B = 2.40/[(2.45)(1.68)] = 0.583.

62. If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected
rate of return and standard deviation?
→ C. 10%; 1.7%
E(RP) = 0.35(13%) + 0.65(8.4%) = 10.01%; sP = [(0.35)2(2.45%)2+ (0.65)2(1.68)2+
2(0.35)(0.65)(2.45)(1.68) (0.583)]1/2 = 1.7%.

63. The weights of A and B in the global minimum variance portfolio are _____ and _____,
respectively.
→ D. 0.45; 0.55
wA = 14 /(17 + 14) = 0.45; wB = 1 - 0.45 = 0.55.

64. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
→ C. 10.9%

E(RP) = 0.45(12%) + 0.55(9%) = 10.35%.

65. Security X has expected return of 14% and standard deviation of 22%. Security Y has
expected return of 16% and standard deviation of 28%. If the two securities have a correlation
coefficient of 0.8, what is their covariance?
→ B. 0.049
Cov(rX, rY) = (.8)(.22)(.28) = .04928

66. Security X has expected return of 9% and standard deviation of 18%. Security Y has expected
return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of
-0.4, what is their covariance?
→ E. -0.1512
Cov(rX, rY) = (-.4)(.18)(.21) = -.01512
67. Given an optimal risky portfolio with expected return of 16% and standard deviation of 20%
and a risk free rate of 4%, what is the slope of the best feasible CAL?→ A. 0.60
Slope = (16 - 4)/20 = .6
68. Given an optimal risky portfolio with expected return of 12% and standard deviation of 26%
and a risk free rate of 3%, what is the slope of the best feasible CAL?→ D. 0.35
Slope = (12 - 3)/26 = .346

Consider the following probability distribution for stocks C and D:

69. The expected rates of return of stocks C and D are __ and __, respectively. A. 4.4%; 9.5%.
E(RC) = 0.30(7%) + 0.5(11%) + 0.20(-16%) = 4.4%; E(RD) = 0.30(-9%) + 0.5(14%) + 0.20(26%) = 9.5%.
70. The standard deviations of stocks C and D are _____ and _____, respectively.
→ C. 9.34%; 12.93%
sC = [0.30(7% - 4.4%)2+ 0.5(11% - 4.4%)2+ 0.20(-16% - 4.4%)2]1/2= 9.34%; sD = [0.30(-9% - 9.5%)2+
0.50(14% - 9.5%)2+0.20(26% - 9.5%)2]1/2= 12.93%.
71. The coefficient of correlation between C and D is → C. -0.554
covC,D = 0.30(7% - 4.4%)(-9% - 9.5%) + 0.50(11% - 4.4%)(14% - 9.5%) + 0.20(-16% - 4.4%)(26% -
9.5%) = 2.40; rA,B = -66.90/[(9.34)(12.93)] = -0.554
72. If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected
rate of return and standard deviation?→ C. 10.425%; 8.63%
E(RP) = 0.25(4.4%) + 0.75(9.5%) = 10.425%; sP = [(0.25)2(9.34%)2+ (0.75)2(12.93)2+ 2(0.25)(0.75)(9.34)
(12.93)(-0.554)]1/2 = 8.63%.

Consider two perfectly negatively correlated risky securities K and L. K has an expected rate of
return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a
standard deviation of 16%.
73. The weights of K and L in the global minimum variance portfolio are _____ and _____,
respectively. → C. 0.54; 0.46
wA = 19 /(19 + 16) = 0.54; wB = 1 - 0.54 = 0.46.
74. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
→ E. none of the above
E(RP) = 0.54(13%) + 0.46(10%) = 11.62%.
75. Security M has expected return of 17% and standard deviation of 32%. Security S has
expected return of 13% and standard deviation of 19%. If the two securities have a correlation
coefficient of 0.78, what is their covariance?→ C. 0.047
Cov(rX, rY) = (.78)(.32)(.19) = .0474
76. Security X has expected return of 7% and standard deviation of 12%. Security Y has expected
return of 11% and standard deviation of 20%. If the two securities have a correlation coefficient of
-0.45, what is their covariance?→ B. -0.0108
Cov(rX, rY) = (-.45)(.12)(.20) = -.0108
77. Given an optimal risky portfolio with expected return of 13% and standard deviation of 26%
and a risk free rate of 5%, what is the slope of the best feasible CAL?→ E. 0.31
Slope = (13 - 5)/26 = .31
78. Given an optimal risky portfolio with expected return of 12% and standard deviation of 23%
and a risk free rate of 3%, what is the slope of the best feasible CAL?→ B. 0.39Slope = (12 - 3)/23 =
.391