TRUE/FALSE
1. A good portfolio is a collection of individually good assets.
ANS: F PTS: 1
2. Risk is defined as the uncertainty of future outcomes.
ANS: T PTS: 1
3. Prior to the work of Markowitz in the late 1950's and early 1960's, portfolio managers did not have a well-developed, quantitative means of measuring risk.
ANS: T PTS: 1
4. A basic assumption of the Markowitz model is that investors base decisions solely on expected return and risk.
ANS: T PTS: 1
5. Markowitz assumed that, given an expected return, investors prefer to minimize risk.
ANS: T PTS: 1
6. The correlation coefficient and the covariance are measures of the extent to which two random variables move together.
ANS: T PTS: 1
7. For a two stock portfolio containing Stocks i and j, the correlation coefficient of returns (rij) is equal to the square root of the covariance (covij).
ANS: F PTS: 1
8. If the covariance of two stocks is positive, these stocks tend to move together over time.
ANS: T PTS: 1
9. The expected return and standard deviation of a portfolio of risky assets is equal to the weighted average of the individual asset's expected returns and standard deviation.
ANS: F PTS: 1
10. The combination of two assets that are completely negatively correlated provides maximum returns.
ANS: F PTS: 1
11. Increasing the correlation among assets in a portfolio results in an increase in the standard deviation of the portfolio.
ANS: T PTS: 1
12. Combining assets that are not perfectly correlated does affect both the expected return of the portfolio as well as the risk of the portfolio.
ANS: F PTS: 1
13. In a three asset portfolio the standard deviation of the portfolio is one third of the square root of the sum of the individual standard deviations.
ANS: F PTS: 1
14. As the number of risky assets in a portfolio increases, the total risk of the portfolio decreases.
ANS: T PTS: 1
15. Assuming that everyone agrees on the efficient frontier (given a set of costs), there would be
consensus that the optimal portfolio on the frontier would be where the ratio of return per unit of risk was greatest.
ANS: F PTS: 1
16. An investor is risk neutral if she chooses the asset with lower risk given a choice of several assets with equal returns.
ANS: F PTS: 1
17. A portfolio is efficient if no other asset or portfolios offer higher expected return with the same (or lower) risk or lower risk with the same (or higher) expected return.
ANS: T PTS: 1
18. A measure that only considers deviations above the mean is semi-variance.
ANS: F PTS: 1
19. The set of portfolios with the maximum rate of return for every given risk level is known as the optimal frontier.
ANS: F PTS: 1
20. Investors choose a portfolio on the efficient frontier based on their utility functions that reflect their attitudes towards risk.
ANS: T PTS: 1
MULTIPLE CHOICE
1. When individuals evaluate their portfolios they should evaluate a. All the U.S. and non-U.S. stocks.
b. All marketable securities.
c. All marketable securities and other liquid assets.
d. All assets.
e. All assets and liabilities.
ANS: E PTS: 1 OBJ: Multiple Choice Concept
2. The probability of an adverse outcome is a definition of a. Statistics.
b. Variance.
c. Random.
d. Risk.
e. Semi-variance above the mean.
ANS: D PTS: 1 OBJ: Multiple Choice Concept
3. The Markowitz model is based on several assumptions regarding investor behavior. Which of the following is not such any assumption?
a. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.
b. Investors maximize one-period expected utility.
c. Investors estimate the risk of the portfolio on the basis of the variability of expected returns.
d. Investors base decisions solely on expected return and risk.
e. None of the above (that is, all are assumptions of the Markowitz model)
ANS: E PTS: 1 OBJ: Multiple Choice Concept
4. Markowitz believes that any asset or portfolio of assets can be described by ____ parameter(s).
a. One b. Two c. Three d. Four e. Five
ANS: B PTS: 1 OBJ: Multiple Choice Concept
5. Semivariance, when applied to portfolio theory, is concerned with a. The square root of deviations from the mean.
b. All deviations below the mean.
c. All deviations above the mean.
d. All deviations.
e. The summation of the squared deviations from the mean.
ANS: B PTS: 1 OBJ: Multiple Choice Concept
6. The purpose of calculating the covariance between two stocks is to provide a(n) ____ measure of their movement together.
a. Absolute b. Relative c. Indexed d. Loglinear e. Squared
ANS: A PTS: 1 OBJ: Multiple Choice Concept
7. In a two stock portfolio, if the correlation coefficient between two stocks were to decrease over time, everything else remaining constant, the portfolio's risk would
a. Decrease.
b. Remain constant.
c. Increase.
d. Fluctuate positively and negatively.
e. Be a negative value.
ANS: A PTS: 1 OBJ: Multiple Choice Concept
8. Which of the following statements about the correlation coefficient is false?
a. The values range between −1 to +1.
b. A value of +1 implies that the returns for the two stocks move together in a completely linear manner.
c. A value of −1 implies that the returns move in a completely opposite direction.
d. A value of zero means that the returns are independent.
e. None of the above (that is, all statements are true)
ANS: D PTS: 1 OBJ: Multiple Choice Concept
9. You are given a two asset portfolio with a fixed correlation coefficient. If the weights of the two assets are varied the expected portfolio return would be ____ and the expected portfolio standard deviation would be ____.
a. Nonlinear, elliptical b. Nonlinear, circular c. Linear, elliptical d. Linear, circular e. Circular, elliptical
ANS: C PTS: 1 OBJ: Multiple Choice Concept
10. Given a portfolio of stocks, the envelope curve containing the set of best possible combinations is known as the
a. Efficient portfolio.
b. Utility curve.
c. Efficient frontier.
d. Last frontier.
e. Capital asset pricing model.
ANS: C PTS: 1 OBJ: Multiple Choice Concept
11. If equal risk is added moving along the envelope curve containing the best possible combinations the return will
a. Decrease at an increasing rate.
b. Decrease at a decreasing rate.
c. Increase at an increasing rate.
d. Increase at a decreasing rate.
e. Remain constant.
ANS: D PTS: 1 OBJ: Multiple Choice Concept
12. A portfolio is considered to be efficient if:
a. No other portfolio offers higher expected returns with the same risk.
b. No other portfolio offers lower risk with the same expected return.
c. There is no portfolio with a higher return.
d. Choices a and b e. All of the above
ANS: D PTS: 1 OBJ: Multiple Choice Concept
13. The optimal portfolio is identified at the point of tangency between the efficient frontier and the a. highest possible utility curve.
b. lowest possible utility curve.
c. middle range utility curve.
d. steepest utility curve.
e. flattest utility curve.
ANS: A PTS: 1 OBJ: Multiple Choice Concept
14. An individual investor's utility curves specify the tradeoffs he or she is willing to make between a. high risk and low risk assets.
b. high return and low return assets.
c. covariance and correlation.
d. return and risk.
e. efficient portfolios.
ANS: D PTS: 1 OBJ: Multiple Choice Concept
15. As the correlation coefficient between two assets decreases, the shape of the efficient frontier a. approaches a horizontal straight line.
b. bends out.
c. bends in.
d. approaches a vertical straight line.
e. none of the above.
ANS: C PTS: 1 OBJ: Multiple Choice Concept
16. A portfolio manager is considering adding another security to his portfolio. The correlations of the 5 alternatives available are listed below. Which security would enable the highest level of risk
diversification?
a. 0.0 b. 0.25 c. −0.25 d. −0.75
e. 1.0
ANS: D PTS: 1 OBJ: Multiple Choice Concept
17. A positive covariance between two variables indicates that a. the two variables move in different directions.
b. the two variables move in the same direction.
c. the two variables are low risk.
d. the two variables are high risk.
e. the two variables are risk free.
ANS: B PTS: 1 OBJ: Multiple Choice Concept
18. A positive relationship between expected return and expected risk is consistent with a. investors being risk seekers.
b. investors being risk avoiders.
c. investors being risk averse.
d. all of the above.
e. none of the above.
ANS: C PTS: 1 OBJ: Multiple Choice Concept
19. The slope of the efficient frontier is calculated as follows a. E(Rportfolio)/E(σportfolio)
b. E(σportfolio)/ E(Rportfolio) c. ∆E(Rportfolio)/∆E(σportfolio) d. ∆E(σportfolio)/∆E(Rportfolio) e. None of the above
ANS: C PTS: 1 OBJ: Multiple Choice Concept
20. The slope of the utility curves for a strongly risk-averse investor, relative to the slope of the utility curves for a less risk-averse investor, will
a. Be steeper.
b. Be flatter.
c. Be vertical.
d. Be horizontal.
e. None of the above.
ANS: A PTS: 1 OBJ: Multiple Choice Concept
21. All of the following are assumptions of the Markowitz model except a. Risk is measured based on the variability of returns.
b. Investors maximize one-period expected utility.
c. Investors' utility curves demonstrate properties of diminishing marginal utility of wealth.
d. Investors base decisions solely on expected return and time.
e. All of the above
ANS: D PTS: 1 OBJ: Multiple Choice Concept
22. The most important criteria when adding new investments to a portfolio is the a. Expected return of the new investment.
b. Standard deviation of the new investment.
c. Correlation of the new investment with the portfolio.
d. Both a and b
e. All of the above are equally important
ANS: C PTS: 1 OBJ: Multiple Choice Concept
23. A portfolio of two securities that are perfectly positively correlated has
a. A standard deviation that is the weighted average of the individual securities standard deviations.
b. An expected return that is the weighted average of the individual securities expected returns.
c. No diversification benefit over holding either of the securities independently.
d. Both b and c e. All of the above
ANS: E PTS: 1 OBJ: Multiple Choice Concept
24. All of the following are common risk measurements except a. Standard deviation
b. Variance c. Semivariance d. Covariance e. Range of returns
ANS: D PTS: 1 OBJ: Multiple Choice Concept
25. When assessing the risk impact of adding a new security to a portfolio, it is necessary to consider the a. New securities variance
b. Variance of every security in the portfolio c. Weight of every security in the portfolio
d. Average covariance of the new security with every security in the portfolio e. All of the above
ANS: E PTS: 1 OBJ: Multiple Choice Concept
26. Between 1990 and 2000, the standard deviation of the returns for the NIKKEI and the DJIA indexes were 0.18 and 0.16, respectively, and the covariance of these index returns was 0.003. What was the correlation coefficient between the two market indicators?
a. 9.6 b. 0.0187 c. 0.1042 d. 0.0166 e. 0.343 ANS: C
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.003) ÷ (0.18)(0.16) = .1042 PTS: 1 OBJ: Multiple Choice Problem
27. Between 1994 and 2004, the standard deviation of the returns for the S&P 500 and the NYSE indexes were 0.27 and 0.14, respectively, and the covariance of these index returns was 0.03. What was the correlation coefficient between the two market indicators?
a. 1.26 b. 0.7937 c. 0.2142 d. 0.1111 e. 0.44
ANS: B
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.03) ÷ (0.27)(0.14) = .7937 PTS: 1 OBJ: Multiple Choice Problem
28. Between 1980 and 1990, the standard deviation of the returns for the NIKKEI and the DJIA indexes were 0.19 and 0.06, respectively, and the covariance of these index returns was 0.0014. What was the correlation coefficient between the two market indicators?
a. 8.1428 b. 0.0233 c. 0.0073 d. 0.2514 e. 0.1228 ANS: E
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.0014) ÷ (0.19)(0.06) = .1228 PTS: 1 OBJ: Multiple Choice Problem
29. Between 1975 and 1985, the standard deviation of the returns for the NYSE and the S&P 500 indexes were 0.06 and 0.07, respectively, and the covariance of these index returns was 0.0008. What was the correlation coefficient between the two market indicators?
a. .1525 b. .1388 c. .1458 d. .1622 e. .1064 ANS: C
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.0008) ÷ (0.06)(0.07) = .1458 PTS: 1 OBJ: Multiple Choice Problem
30. Between 1986 and 1996, the standard deviation of the returns for the NYSE and the DJIA indexes were 0.10 and 0.09, respectively, and the covariance of these index returns was 0.0009. What was the correlation coefficient between the two market indicators?
a. .1000 b. .1100 c. .1258 d. .1322 e. .1164 ANS: A
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.0009) ÷ (0.10)(0.09) = .1000 PTS: 1 OBJ: Multiple Choice Problem
31. Between 1980 and 2000, the standard deviation of the returns for the NIKKEI and the DJIA indexes were 0.08 and 0.10, respectively, and the covariance of these index returns was 0.0007. What was the correlation coefficient between the two market indicators?
a. .0906 b. .0985 c. .0796 d. .0875
e. .0654 ANS: D
rA,B = (σA,B) ÷ [(σA)(σ B)] = (0.0007) ÷ (0.08)(0.10) = .0875 PTS: 1 OBJ: Multiple Choice Problem
32. What is the expected return of the three stock portfolio described below?
Common Stock Market Value Expected Return
Ando Inc. 95,000 12.0%
Bee Co. 32,000 8.75%
Cool Inc. 65,000 17.7%
a. 18.45%
b. 12.82%
c. 13.38%
d. 15.27%
e. 16.67%
ANS: C
WA = 95,000 ÷ 192,000 = 0.4947 WB = 32,000 ÷ 192,000 = 0.1667 WC = 65,000 ÷ 192,000 = 0.3385
0.1338 = (0.4947)(0.12) + (0.1667)(0.0875) + (0.3385)(0.177) PTS: 1 OBJ: Multiple Choice Problem
33. What is the expected return of the three stock portfolio described below?
Common Stock Market Value Expected Return
Xerox 125,000 8%
Yelcon 250,000 25%
Zwiebal 175,000 16%
a. 18.27%
b. 14.33%
c. 16.33%
d. 12.72%
e. 16.45%
ANS: A
WX = 125,000 ÷ 550,000 = 0.2273 WY = 250,000 ÷ 550,000 = 0.4545 WZ = 175,000 ÷ 550,000 = 0.3182
0.1827 = (0.2273)(0.08) + (0.4545)(0.25) + (0.3182)(0.16) PTS: 1 OBJ: Multiple Choice Problem
34. What is the expected return of the three stock portfolio described below?
Common Stock Market Value Expected Return
Alko Inc. 25,000 38%
Belmont Co. 100,000 10%
Cardo Inc. 75,000 16%
a. 21.33%
b. 12.50%
c. 32.00%
d. 15.75%
e. 16.80%
ANS: D
WA = 25,000 ÷ 200,000 = 0.125 WB = 100,000 ÷ 200,000 = 0.50 WC = 75,000 ÷ 200,000 = 0.375
0.1575 = (0.125)(0.38) + (0.5)(0.1) + (0.375)(0.16) PTS: 1 OBJ: Multiple Choice Problem
35. What is the expected return of the three stock portfolio described below?
Common Stock Market Value Expected Return
Delton Inc. 50,000 10%
Efley Co. 40,000 11%
Grippon Inc. 60,000 16%
a. 14.89%
b. 16.22%
c. 12.66%
d. 13.85%
e. 16.99%
ANS: C
WD = 50,000 ÷ 150,000 = 0.33 (0.33)(10) = 3.33
WE = 40,000 ÷ 150,000 = 0.27 (0.27)(11) = 2.93
WG = 60,000 ÷ 150,000 = 0.40 (0.40)(16) = 6.40
3.33 + 2.93 + 6.4 = 12.66%
PTS: 1 OBJ: Multiple Choice Problem
36. What is the expected return of the three stock portfolio described below?
Common Stock Market Value Expected Return
Lupko Inc. 50,000 13%
Mackey Co. 25,000 9%
Nippon Inc. 75,000 14%
a. 12.04%
b. 12.83%
c. 13.07%
d. 15.89%
e. 17.91%
ANS: B
WL = 50,000 ÷ 150,000 = 0.33 (0.33)(13) = 4.33
WM = 25,000 ÷ 150,000 = 0.167 (0.167)(9) = 1.50
WN = 75,000 ÷ 150,000 = 0.50 (0.50)(14) = 7.0
4.33 + 1.50 + 7.0 = 12.83%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.1
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 10% E(RB) = 15%
(σA) = 8% (σB) = 9.5%
WA = 0.25 WB = 0.75 CovA,B = 0.006
37. Refer to Exhibit 7.1. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 8.79%
b. 12.5%
c. 13.75%
d. 7.72%
e. 12%
ANS: C
E(Rp) = WAE(RA) + WBE(RB)
= (0.25)(10) + (0.75)(15) = 13.75%
PTS: 1 OBJ: Multiple Choice Problem
38. Refer to Exhibit 7.1. What is the standard deviation of this portfolio?
a. 8.79%
b. 13.75%
c. 12.5%
d. 7.72%
e. 5.64%
ANS: A
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.25)2(0.08)2 + (0.75)2(0.095)2 + (2)(0.25)(0.75)(0.006)]1/2
= 8.79%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.2
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 25% E(RB) = 15%
(σA) = 18% (σB) = 11%
WA = 0.75 WB = 0.25 COVA,B = −0.0009
39. Refer to Exhibit 7.2. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 18.64%
b. 20.0%
c. 22.5%
d. 13.65%
e. 11%
ANS: C
E(Rp) = WAE(RA) + WBE(RB)
= (0.75)(25) + (0.25)(15) = 22.5%
PTS: 1 OBJ: Multiple Choice Problem
40. Refer to Exhibit 7.2. What is the standard deviation of this portfolio?
a. 5.45%
b. 18.64%
c. 20.0%
d. 22.5%
e. 13.65%
ANS: E
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.75)2(0.18)2 + (0.25)2(0.11)2 + (2)(0.75)(0.25)(−0.0009]1/2
= 13.65%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.3
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 9% E(RB) = 11%
(σA) = 4% (σB) = 6%
WA = 0.4 WB = 0.6 COVA,B = 0.0011
41. Refer to Exhibit 7.3. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 8.95%
b. 9.30%
c. 9.95%
d. 10.20%
e. 10.70%
ANS: D
E(Rp) = WAE(RA) + WBE(RB)
= (0.4)(9) + (0.6)(11) = 10.20%
PTS: 1 OBJ: Multiple Choice Problem
42. Refer to Exhibit 7.3. What is the standard deviation of this portfolio?
a. 3.68%
b. 4.56%
c. 4.99%
d. 5.16%
e. 6.02%
ANS: B
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.4)2 (0.04)2 + (0.6)2(0.06)2 + (2)(0.4)(0.6)(0.0011)]1/2
= (0.002080)1/2 = 4.56%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.4
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 10% E(RB) = 8%
(σA) = 6% (σB) = 5%
WA = 0.3 WB = 0.7 COVA,B = 0.0008
43. Refer to Exhibit 7.4. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 8.6%
b. 8.1%
c. 9.3%
d. 10.2%
e. 11.6%
ANS: A
E(Rp) = WAE(RA) + WBE(RB)
= (0.3)(10) + (0.7)(8) = 8.6%
PTS: 1 OBJ: Multiple Choice Problem
44. Refer to Exhibit 7.4. What is the standard deviation of this portfolio?
a. 5.02%
b. 3.88%
c. 6.21%
d. 4.04%
e. 4.34%
ANS: E
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.3)2(0.06)2 + (0.7)2(0.05)2 + (2)(0.3)(0.7)(0.0008)]1/2
= (0.001885)1/2 = 4.34%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.5
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 8% E(RB) = 15%
(σA) = 7% (σB) = 10%
WA = 0.4 WB = 0.6 COVA,B = 0.0006
45. Refer to Exhibit 7.5. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 8.0%
b. 12.2%
c. 7.4%
d. 9.1%
e. 11.6%
ANS: B
E(Rp) = WAE(RA) + WBE(RB)
= (0.4)(8) + (0.6)(15) = 12.2%
PTS: 1 OBJ: Multiple Choice Problem
46. Refer to Exhibit 7.5. What is the standard deviation of this portfolio?
a. 3.89%
b. 4.61%
c. 5.02%
d. 6.83%
e. 6.09%
ANS: D
σp = [(WA)2 (σA)2 + (WB)2 (σB)2+ (2)(WA)(WB)(COVA,B)]1/2
= [(0.4)2(0.07)2 + (0.6)2(0.10)2 + (2)(0.6)(0.4)(0.0006)]1/2
= (0.004672)1/2 = 6.83%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.6
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Asset (A) Asset (B) E(RA) = 16% E(RB) = 10%
(σA) = 9% (σB) = 7%
WA = 0.5 WB = 0.5 COVA,B = 0.0009
47. Refer to Exhibit 7.6. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 10.6 % b. 10.2%
c. 13.0%
d. 11.9%
e. 14.0%
ANS: C
E(Rp) = WAE(RA) + WBE(RB)
= (0.5)(16) + (0.5)(10) = 13%
PTS: 1 OBJ: Multiple Choice Problem
48. Refer to Exhibit 7.6. What is the standard deviation of this portfolio?
a. 6.08%
b. 5.89%
c. 7.06%
d. 6.54%
e. 7.26%
ANS: A
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.5)2(0.09)2 + (0.5)2(0.07)2 + (2)(0.5)(0.5)(0.0009)]1/2
= (0.0037)1/2 = 6.08%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.7
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 7% E(RB) = 9%
(σA) = 6% (σB) = 5%
WA = 0.6 WB = 0.4 COVA,B = 0.0014
49. Refer to Exhibit 7.7. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 5.8%
b. 6.1%
c. 6.9%
d. 7.8%
e. 8.9%
ANS: D
E(Rp) = WAE(RA) + WBE(RB)
= (0.6)(7) + (0.4)(9) = 7.8%
PTS: 1 OBJ: Multiple Choice Problem
50. Refer to Exhibit 7.7. What is the standard deviation of this portfolio?
a. 4.87%
b. 3.62%
c. 4.13%
d. 5.76%
e. 6.02%
ANS: A
σp = [(WA)2 (σA)2 + (WB)2(σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.6)2(0.06)2 + (0.4)2(0.05)2 + (2)(0.6)(0.4)(0.0014)]1/2
= (0.002368)1/2 = 4.87%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.8
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 10% E(RB) = 14%
(σA) = 7% (σB) = 8%
WA = 0.7 WB = 0.3 COVA,B = 0.0013
51. Refer to Exhibit 7.8. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 6.4%
b. 9.1%
c. 10.2%
d. 10.8%
e. 11.2%
ANS: E
E(Rp) = WAE(RA) + WBE(RB)
= (0.7)(10) + (0.3)(14) = 11.2%
PTS: 1 OBJ: Multiple Choice Problem
52. Refer to Exhibit 7.8. What is the standard deviation of this portfolio?
a. 4.51%
b. 5.94%
c. 6.75%
d. 7.09%
e. 8.62%
ANS: B
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.7)2(0.07)2 + (0.3)2(0.08)2 + (2)(0.7)(0.3)(0.0013)]1/2
= (0.003523)1/2 = 5.94%
PTS: 1 OBJ: Multiple Choice Problem
Exhibit 7.9
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 18% E(RB) = 13%
(σA) = 7% (σB) = 6%
WA = 0.3 WB = 0.7 COVA,B = 0.0011
53. Refer to Exhibit 7.9. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 10.10%
b. 11.60%
c. 13.88%
d. 14.50%
e. 15.37%
ANS: D
E(Rp) = WAE(RA) + WBE(RB)
= (0.3)(18) + (0.7)(13) = 14.5%
PTS: 1 OBJ: Multiple Choice Problem
54. Refer to Exhibit 7.9. What is the standard deviation of this portfolio?
a. 5.16%
b. 5.89%
c. 6.11%
d. 6.57%
e. 7.02%
ANS: A
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.3)2(0.07)2 + (0.7)2(0.06)2 + (2)(0.3)(0.7)(0.0011)]1/2
= (0.002667)1/2 = 5.16%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.10
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) Asset (A) Asset (B)
E(RA) = 16% E(RB) = 14%
(σA) = 3% (σB) = 8%
WA = 0.5 WB = 0.5 COVA,B = 0.0014
55. Refer to Exhibit 7.10. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (σi), covariance (COVi,j), and asset weight (Wi) are as shown above?
a. 11%
b. 12%
c. 13%
d. 14%
e. 15%
ANS: E
E(Rp) = WAE(RA) + WBE(RB)
= (0.5)(16) + (0.5)(14) = 15%
PTS: 1 OBJ: Multiple Choice Problem
56. Refer to Exhibit 7.10. What is the standard deviation of this portfolio?
a. 3.02%
b. 4.88%
c. 5.24%
d. 5.98%
e. 6.52%
ANS: C
σp = [(WA)2 (σA)2 + (WB)2 (σB)2 + (2)(WA)(WB)(COVA,B)]1/2
= [(0.5)2(0.03)2 + (0.5)2(0.08)2 + (2)(0.5)(0.5)(0.0014)]1/2
= (0.002750)1/2 = 5.24%
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.11
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Asset 1 Asset 2
E(R1) = 0.28 E(R2) = 0.12 E(σ1) = 0.15 E(σ2) = 0.11 W1 = 0.42 W2 = 0.58
r1,2 = 0.7
57. Refer to Exhibit 7.11. Calculate the expected return of the two stock portfolio.
a. 0.107 b. 0.1367 c. 0.1169 d. 0.1872 e. 0.20 ANS: D
Rp = (0.42)(0.28) + (0.58)(0.12) = 0.1872
PTS: 1 OBJ: Multiple Choice Problem
58. Refer to Exhibit 7.11. Calculate the expected standard deviation of the two stock portfolio.
a. 0.1367 b. 0.1872 c. 0.1169 d. 0.20 e. 0.3950 ANS: C
σp = [(0.42)2 (0.15)2 + (0.58)2 (0.11)2 + (2)(0.42)(0.58)(0.15)(0.11)(0.7)]1/2
= 0.1169
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.12
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Asset 1 Asset 2
E(R1) = .12 E(R2) = .16 E(σ1) = .04 E(σ2) = .06
59. Refer to Exhibit 7.12. Calculate the expected return and expected standard deviation of a two stock portfolio when r1,2 = −.60 and w1 = .75.
a. .13 and .0024 b. .13 and .0455 c. .12 and .0585 d. .12 and .5585 e. .13 and .6758 ANS: A
Rp = (0.75)(0.12) + (0.25)(0.16) = 0.13
σp = [(0.75)2 (0.04)2 + (0.25)2(0.06)2 + (2)(0.75)(0.25)(0.04)(0.06) − 0.6]1/2
= [0.0009 + 0.000225 − 0.00054]1/2 = [0.000585]1/2 = 0.024 PTS: 1 OBJ: Multiple Choice Problem
60. Refer to Exhibit 7.12. Calculate the expected returns and expected standard deviations of a two stock portfolio when r1,2 = .80 and w1 = .60.
a. .144 and .0002 b. .144 and .0018 c. .136 and .0045 d. .136 and .0455 e. .136 and .4554 ANS: D
Rp = (0.60)(0.12) + (0.40)(0.16) = 0.136
σp = [(0.60)2 (0.04)2 + (0.40)2(0.06)2 + (2)(0.60)(0.40)(0.04)(0.06)(0.8)]1/2
= [0.000576 + 0.000576 + 0.000922]1/2 = [0.002074]1/2 = 0.0455 PTS: 1 OBJ: Multiple Choice Problem
61. Consider two securities, A and B. Security A and B have a correlation coefficient of 0.65. Security A has standard deviation of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities.
a. 300 b. 461.54 c. 261.54 d. 195 e. 200 ANS: D
Cov(A, B) = (0.65)(12)(25) = 195
PTS: 1 OBJ: Multiple Choice Problem
62. Calculate the expected return for a three asset portfolio with the following
Asset Exp. Ret. Std. Dev Weight
A 0.0675 0.12 0.25
B 0.1235 0.1675 0.35
C 0.1425 0.1835 0.40
a. 11.71%
b. 11.12%
c. 15.70%
d. 14.25%
e. 6.75%.
ANS: A
Expected Return = 11.71% = (0.25)(0.0675) + (0.35)(0.1235) + (0.40)(0.1425) PTS: 1 OBJ: Multiple Choice Problem
63. Given the following weights and expected security returns, calculate the expected return for the portfolio.
Weight Expected Return
.20 .06
.25 .08
.30 .10
.25 .12
a. 0.085 b. 0.090 c. 0.092 d. 0.097
e. None of the above ANS: C
Weight Expected Return WiRi
.20 .06 .012
.25 .08 .020
.30 .10 .030
.25 .12 .030
.092 PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.13
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period.
Probability Return
0.10 −.20
0.25 −.05
0.40 0.15
0.25 0.30
64. Refer to Exhibit 7.13. Calculate the expected return for Magnum Oil.
a. 5.0 b. 10.3%
c. 13.7%
d. 17.5%
e. 20.0%
ANS: B
Expected Return for Magnum Oil = 0.1(−0.20) + 0.25(−0.05) + 0.40(0.15) + (0.25)(0.30)
= −0.02 − 0.0125 + 0.06 + 0.075 = 0.1025 PTS: 1 OBJ: Multiple Choice Problem
65. Refer to Exhibit 7.13. Calculate the standard deviation for Magnum Oil.
a. 0%
b. 11%
c. 16%
d. 20%
e. 26%
ANS: C
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.14
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Stocks A and B have a correlation coefficient of −0.8. The stocks' expected returns and standard deviations are in the table below. A portfolio consisting of 40% of stock A and 60% of stock B is constructed.
Stock Expected Return Standard Deviation
A 20% 25%
B 15% 19%
66. Refer to Exhibit 7.14. What is the expected return of the stock A and B portfolio?
a. 17.0%
b. 17.5%
c. 18.0%
d. 18.5%
e. 19.0%
ANS: A
Expected return = 0.40(0.20) + 0.60(0.15) = 0.08 + 0.09 = 0.17
PTS: 1 OBJ: Multiple Choice Problem
67. Refer to Exhibit 7.14. What is the standard deviation of the stock A and B portfolio?
a. 0.0%
b. 0.5%
c. 4.1%
d. 6.9%
e. 20.3%
ANS: D
The portfolio of stocks A and B has a standard deviation of
PTS: 1 OBJ: Multiple Choice Problem
68. Refer to Exhibit 7.14. What percentage of stock A should be invested to obtain the minimum risk portfolio that contains stock A and B?
a. 35%
b. 42%
c. 58%
d. 65%
e. 72%
ANS: B
PTS: 1 OBJ: Multiple Choice Problem
69. What is the standard deviation of an equally weighted portfolio of two stocks with a covariance of 0.009, if the standard deviation of the first stock is 15% and the standard deviation of the second stock is 20%?
a. 2.0%
b. 2.1%
c. 7.8%
d. 14.2%
e. 14.7%
ANS: D
The correlation coefficient is 0.3 calculated as follows .009/(.15)(.2). The portfolio s.d. =
PTS: 1 OBJ: Multiple Choice Problem Exhibit 7.15
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)