Chapter 02

© 2009 McGraw-Hill Ryerson Ltd. 2-1

Jordan: Fundamentals of Investments, 2ce Test Bank

CHAPTER 2 DIVERSIFICATION AND ASSET ALLOCATION

I. DEFINITIONS EXPECTED RETURN A 1. The return you anticipate earning in the future on a risky asset is the called the ______ return. A. Expected B. Realized C. Unrealized D. Diversified E. Terminal Level: Easy PORTFOLIO D 2. A combination of assets held by an investor is known as a(n) ________. A. Opportunity set B. Efficient asset C. Markowitz selection D. Portfolio E. Minimum variance option Level: Easy PORTFOLIO WEIGHT B 3. The portfolio weight of an asset is the A. Market value of that asset expressed as a percentage of the asset’s initial cost B. Market value of that asset expressed as a percentage of the total portfolio value C. Cost invested in that asset expressed as a percentage of the total cost of the portfolio D. Number of shares held in that asset divided by the total number of shares owned E. Return on the asset as a fraction of the entire return on the portfolio Level: Medium DIVERSIFICATION B 4. The reduction in risk realized when a portfolio is invested in a variety of assets is called A. Stock selection B. Diversification C. Correlation D. Stock management E. Opportunity investing Level: Easy CORRELATION C 5. ________ is the extent to which the returns on two assets move together. A. Standard deviation B. Variance C. Correlation D. Efficiency

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E. Tangency Level: Easy COVARIANCE

A 6. ________ is a statistical measure of the degree to which two variables (e.g. securities’ returns) move together.

A. Covariance B. Variance C. Skewness D. Coefficient of variation E. Tangency Level: Easy ASSET ALLOCATION D 7. The manner in which an investor spreads his portfolio across a variety of securities is called A. The efficient frontier B. Correlation C. Minimization D. Asset allocation E. The investment opportunity set Level: Easy INVESTMENT OPPORTUNITY SET B 8. All possible risk-return combinations available from portfolios consisting of different group of

assets are the __________. A. efficient frontier B. investment opportunity set C. portfolio set D. correlation E. capital asset pricing model Level; Easy EFFICIENT PORTFOLIO C 9. A(n) _____ portfolio offers the lowest risk for a given level of return or it generates the highest

possible return for a given level of risk A. Diversified B. Market C. Efficient D. Stock E. Opportunity Level: Medium MARKOWITZ EFFICIENT FRONTIER A 10. The Markowitz efficient frontier is defined as the A. Entire set of efficient portfolios given varying levels of risk B. Highest level of return that can be obtained given any combination of tow individual assets C. Single most efficient portfolio that can be generated from two individual assets D. Total possible risk-return combination that can be generated from two individual assets E. Minimum variance portfolio


Level: Medium RISK PREMIUM E 11. The extra compensation paid to an investor who invests in a risky asset rather than in a risk-free

asset is called the A. Inefficient premium B. Diversification benefit C. Expected return D. Portfolio adjustment E. Risk premium Level: Easy II. CONCEPTS ECONOMIC STATES D 12. Which of the following is true given various states of the economy? A. Stock returns are generally not affected by the state of the economy B. The summation of the probabilities of the various economic states must equal to 10 C. The majority of stock returns increase as the state of the economy worsens D. Both the risk and return on a security are affected by the likelihood of various economic states

occurring E. The probabilities of the various economic states affect the expected return on a stock, but not the

level of risk associated with those returns Level: Medium ECONOMIC STATES C 13. Which of the following is true given various states of the economy? A. The various economic states of the economy are generally equally likely to occur in any given

year B. Most stocks tend to have the same return regardless of the economic state C. The expected state of the economy can have a major impact on the expected return on a portfolio D. If the economy moves into a recession period from a normal period, all stocks will have lower

expected returns E. A change in the probability of a state of the economy occurring has no impact on the expected

return on a portfolio of risky assets Level: Medium PORTFOLIO WEIGHTS B 14. Which of the following portfolio values are weighted average? I) Expected return II) Standard deviation III) Correlation IV) Beta A. I and III B. I and IV C. II and III D. II and IV E. I, II and IV Level: Medium

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PORTFOLIO WEIGHTS C 15. You are computing the expected return on a portfolio of six stocks given three states of the

economy. How will the expected return of the portfolio be computed given an economic state? A. Add up the returns on each stock and divide by 6 B. Sum up the returns on each stock and divide by (6 – 1) C. Multiply the individual returns with the weights based on the market value of each of the stock

position D. Multiply the individual returns with the weights based on the relative prices of each stock

position E. Multiply the individual returns with the weights based on the number of shares of each stock

owned Level: Easy EXPECTED RETURN D 16. You own a stock that is expected to return 125 in a booming economy and 75 in a normal

economy. If the probability of a booming economy increases, your expected return will A. Decrease B. Either remain constant or decrease C. Remain constant D. Increase E. Change but the direction of change is undetermined from the given information Level: Medium EXPECTED RISK PREMIUM C 17. The expected risk premium on a security is computed by A. Subtracting the security’s expected return from the risk-free rate B. Subtracting the expected market return from the security’s expected return C. Subtracting the risk-free rate from the security’s expected return D. Adding the security’s expected return to the risk-free rate E. Adding the security’s expected return to the expected return on the market Level: Easy RISK PREMIUM A 18. If the future return on a security is known with certainty, then the risk premium on that security

should be equal to A. Zero B. The risk-free rate C. The market rate D. The market rate minus the risk-free rate E. The risk-free rate plus one-half of the market rate Level: Medium VARIANCE B 19. Variance is a measure of A. Return B. Risk C. Correlation


D. Diversification E. Efficiency Level: Easy RISK PREMIUM

E 20. All else constant, the risk premium on a security will decrease when the I) security’s expected return increases II) security’s expected return decreases III) risk-free rate increases IV) risk-free rate decreases A. I B. II C. I and III D. I and IV E. II and III Level: Medium DIVERSIFICATION A 21. Which of the following shows how much different an outcome may be from what is anticipated

on the basis of a central tendency measure? A. Standard deviation B. Coefficient of variation C. Standard means D. Covariance E. Histogram Level: Easy DIVERSIFICATION D 22. You own Stock A with a standard deviation of 48% and Stock B with a standard deviation of

35%. As you add more Stock A to your portfolio, the standard deviation of your portfolio will: A. always increase. B. always decrease. C. remain the same. D. It depends on the initial weights and the correlation. E. Insufficient information. Level: Hard PORTFOLIO RETURNS E 23. The expected return on a portfolio is affected by the I) choice of securities held in the portfolio II) return of each security given a particular economic state III) portfolio weight assigned to each security IV) probability of each economic state occurring A. II and III B. II and Iv C. I, II and III D. II, III and Iv E. I, II, III and IV Level: Medium

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PORTFOLIO VARIANCE E 24. A particular portfolio has an expected return that is unaffected by the state of the economy. The

variance of this portfolio must A. Be negative B. Be less than 1 C. Be greater than 1 D. Equal to 1 E. Equal to 0 Level: Medium PORTFOLIO STANDARD DEVIATION C 25. As the number of stocks in a portfolio increases, the portfolio standard deviation A. Increases at a diminishing rate B. Increases at an increasing rate C. Decreases at a diminishing rate D. Remains unchanged E. Decreases at an increasing rate Level: Hard DIVERSIFIABLE RISK B 26. The portfolio risk that decreases as the number of securities in the portfolio increases is referred

to as the _____ risk. A. Market B. Diversifiable C. Non-diversifiable D. Inefficient E. Efficient Level: Easy CORRELATION B 27. The minimum correlation is ___ and the maximum correlation is ____. A. –1; 0 B. –1; +1 C. 0 ; +1 D. –100; +100 E. negative infinity; positive infinity Level: Easy CORRELATION D 28. All else the same, a correlation of _____ will result in the least diversification benefits. A. –100 B. –1 C. 0 D. +1 E. +100 Level: Medium


CORRELATION C 29. A correlation coefficient of ___ indicates a perfect positive correlation. A. 0 B. 0.5 C. 1 D. 10 E. 100 Level: Easy CORRELATION B 30. Consider the stock returns of Manulife, McDonald’s, and Royal Bank. You would expect the

greatest correlation between the stocks of: A. Manulifeand McDonald’s. B. Royal Bank and Manulife. C. McDonald’s and Royal Bank. D. All correlations would be about the same. E. Insufficient information. Level: Medium CORRELATION B 31. If the correlation between two assets is ____, all risk can be eliminated in a portfolio. A. –100 B. –1 C. 0 D. +1 E. +100 PORTFOLIO VARIANCE A 32. The greater the variance of a portfolio, A. The less certain the actual return B. The lower the level of risk C. The lower the expected return D. The smaller the standard deviation E. The greater the number of individual securities held Level: Medium MARKOWITZ EFFICIENT FRONTIER C 33. Which of the following assets cannot lie on the Markowitz efficient frontier? A. Expected return = 10 percent; Standard deviation = 38 percent B. Expected return = 12 percent; Standard deviation = 49 percent C. Expected return = 9 percent; Standard deviation = 41 percent D. Expected return = 14 percent; Standard deviation = 51 percent E. All of the assets could lie on the Markowitz efficient frontier. Level: Hard

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MARKOWITZ EFFICIENT FRONTIER D 34. Which of the following assets cannot lie on the Markowitz efficient frontier? A. Expected return = 16 percent; Standard deviation = 62 percent B. Expected return = 13 percent; Standard deviation = 45 percent C. Expected return = 9 percent; Standard deviation = 36 percent D. Expected return = 11 percent; Standard deviation = 47 percent E. All of the assets could lie on the Markowitz efficient frontier. Level: Hard MARKOWITZ EFFICIENT FRONTIER B 35. To lie on the Markowitz efficient frontier, an asset must have a ____ expected return than any

other asset with the same standard deviation. The asset must also have a ____ standard deviation than any other asset with the same expected return.

A. higher: higher B. higher; lower C. lower; lower D. lower; higher E. Insufficient information. Level: Medium DIVERSIFICATION C 36. The major benefit of diversification is to: A. increase the expected return. B. decrease the expected return. C. decrease the risk. D. make the stock market more efficient. E. increase investor participation in the market. Level: Medium DIVERSIFICATION D 37. You have a portfolio of two stocks. As you increase the weight of the lowest risk stock, the risk

of your portfolio will: A. increase. B. decrease. C. remain the same. D. increase or decrease depending on the correlation. E. decrease or remain the same. Level: Medium RISK PREMIUM A 38. Which of the following is false about the expected risk premium of an asset? A. The expected risk premium is always positive. B. The risk premium is the expected return of a risky asset minus the risk-free rate. C. The expected risk premium is the reward for bearing risk. D. The risk-free asset has no risk premium. E. All of the above are true. Level: Medium


PORTFOLIO WEIGHT C 39. Which of the following is false regarding portfolio weights? A. Portfolio weights must sum to one. B. The portfolio weight of an asset can be negative. C. Since cash is not a security investment, the portfolio weight of cash is zero. D. A portfolio weight measures the percentage of total assets invested in a single asset. E. All else the same, as the price of a stock increases, its portfolio weight increase. Level: Hard DOMINATED PORTFOLIOS C 40. Which of the following stocks dominates Stock V with an expected return of 12 percent and a

standard deviation of 48 percent? A. Expected return = 14 percent; Standard deviation = 53 percent B. Expected return = 10 percent; Standard deviation = 31 percent C. Expected return = 13 percent; Standard deviation = 45 percent D. Expected return = 11 percent; Standard deviation = 52 percent E. None of these stocks dominate Stock V. Level: Hard DIVERSIFICATION A 41. Which of the following statements is false regarding diversification? A. Adding assets will always reduce risk. B. Diversification works because some risks are not common to all assets. C. Diversification benefits occur most when the assets have a low correlation. D. The market is a completely diversified portfolio. E. A diversified portfolio always has less risk than the highest risk asset assuming the correlation

between the assets is less than one and the standard deviation of the assets is not the same. Level: Medium MINIMUM VARIANCE PORTFOLIO A 42. A stock has an expected return of 14 percent and a standard deviation of 61 percent. What is the

weight of the stock in the minimum variance portfolio consisting of the stock and the risk-free asset?

A. .00 B. .18 C. .06 D. .21 E. .32 Level: Hard NONDIVERSIFIABLE RISK D 43. The reason why a fully-diversified portfolio does not have zero risk is that some risk is: A. diversifiable. B. unrelated. C. not correlated. D. nondiversifiable. E. intrinsic. Level: Easy

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ASSET STANDARD DEVIATION D 44. As the probabilities associated with the expected returns of an asset change, the standard

deviation of the asset will: A. increase. B. decrease. C. remain the same. D. increase or decrease. E. decrease if the expected return decreases. Level: Medium INVESTMENT OPPORTUNITY SET E 45. Which of the following statements is false regarding the investment opportunity set of two

assets? A. If the correlation is +1, it is a straight line. B. It graphically illustrates all possible portfolio combinations between the two assets. C. It is a straight line if one of the assets is risk-free. D. Assuming positive portfolio weights, it can never plot below the lowest expected return asset. E. It is not applicable when the assets have a zero correlation. Level: Medium INEFFICIENT PORTFOLIOS B 46. A portfolio that plots below the minimum variance portfolio is _____. A. dominant B. inefficient C. correlated D. optimal E. redundant Level: Easy MINIMUM VARIANCE PORTFOLIO A 47. Stock X has an expected return of 10 percent and a standard deviation of 38 percent. Stock Y has

an expected return of 13 percent and a standard deviation of 48 percent. The weight of Stock X in the minimum variance portfolio of the two assets is ____ than the weight of Stock Y.

A. greater B. less C. the same D. less only if the correlation is negative E. greater only if the correlation is positive Level: Medium EFFICIENT FRONTIER A 48. An asset on the Markowitz efficient frontier has: A. the greatest return for a given level of risk. B. less risk than the market. C. the greatest risk for a given level of return. D. a return greater than the market. E. A single asset cannot lie on the efficient frontier, only portfolios. Level: Easy


MARKOWITZ ANALYSIS B 49. In the analysis of the Markowitz efficient frontier, which of the following information is not

needed? A. The correlation between every possible pair of assets. B. The weight of every asset. C. The expected rerun of every asset. D. The standard deviation of every asset. E. All of the above are needed. Level: Hard EFFICIENT FRONTIER A 50. Which of the following is false regarding the efficient frontier? A. A stock that lies above the efficient frontier is overvalued. B. The efficient frontier includes stocks, bonds, and all other assets. C. The efficient frontier may include individual stocks as well as portfolios. D. A bond can lie on the efficient frontier. E. All of the above are true. Level: Hard DIVERSIFICATION E 51. The correlation between Stock A and Stock B is 0.40. The correlation between Stock A and

Stock C is 0.20, and the correlation between Stock B and Stock C is 0.25. All else the same, which of the following portfolios will have the least risk?

A. All invested in Stock A. B. All invested in Stock C. C. Equally invested in Stock A and Stock B. D. Equally invested in Stock B and Stock C. E. Equally invested in Stock A and Stock C. Level: Hard EFFICIENT FRONTIER C 52. The market consists of two stocks. Stock F has an expected return of 9 percent and a standard

deviation of 32 percent. Stock G has an expected return of 13 percent and a standard deviation of 50 percent. The correlation between the two stocks is –0.10. The efficient frontier is:

A. the line between Stock F and Stock G. B. the line between the minimum variance portfolio and Stock F. C. the line between the minimum variance portfolio and Stock G. D. all to the right of Stock F on the risk/return graph. E. all to the right of Stock G on the risk/return graph. Level: Hard PORTFOLIO STANDARD DEVIATION E 53. Which of the following is true regarding the standard deviation for a portfolio? A. The portfolio’s standard deviation must be less than the individual standard deviations. B. The standard deviation of the portfolio falls continuously as more assets are added. C. The standard deviation for a portfolio is a weighted average of individual standard deviations. D. All of the above. E. None of the above.

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Level: Hard CORRELATION

C 54. What is the possible correlation between a Bombardier stock with a standard deviation of 50 percent and a Treasury bill issued by Government of Canada?

A. –100 B. –1 C. 0 D. +1 E. +100 Level: Medium MINIMUM VARIANCE PORTFOLIO B 55. For the standard deviation of a minimum variance portfolio of two assets to be zero, the

correlation between the assets must be ____. A. –100 B. –1 C. 0 D. +1 E. +100 Level: Medium VARIANCE E 56. What is the typical range of the variance of return for a stock portfolio? A. 0 to 1 B. –1 to +1 C. 0 to +100 D. Between the high and low values for the individual returns being used E. No precise range exists Level: Medium III. PROBLEMS RISK PREMIUM E 57. What is the risk premium of a stock that has an expected return of 14.2 percent if the risk-free

rate is 5.7 percent? A. 9.4% B. 19.9% C. 7.5% D. 7.9% E. 8.5% Level: Easy Solution: Risk premium = 14.2% - 5.7% = 8.5%


RISK PREMIUM B 58. What is the risk-free rate if there is a stock with a risk premium of 7.3 percent and the return of

the stock is 13.2 percent? A. 6.4% B. 5.9% C. 6.1% D. 5.7% E. 20.5% Level: Easy Solution: Risk-free rate = 13.2% - 7.3% = 5.9% RISK PREMIUM A 59. What is the expected return of a stock with a risk premium of 7.6 percent if the risk-free rate is

4.8 percent? A. 12.4% B. 13.1% C. 11.3% D. 2.8% E. 11.7% Level: Easy Solution: Expected return = 4.8% + 7.6% = 12.4% PORTFOLIO WEIGHTS E 60. An investor has $800 invested in Stock X and $1,300 invested in Stock Y. What is the portfolio

weight of Stock Y? A. 41% B. 38% C. 27% D. 33% E. 62% Level: Easy Solution: WY = $1,300 / ($800 + $1,300) = $1,300 / $2,100 = 0.61905 PORTFOLIO WEIGHTS C 61. You have a portfolio with 200 shares of Stock A at a price of $34 and 300 shares of Stock B at a

price of $28. What is the weight of Stock A in your portfolio? A. 55% B. 41% C. 45% D. 51% E. 37% Level: Easy Solution: ($34)(200) / [ ($34)(200) + ($28)(300)] = $6,800 / $15,200 = 0.447368 Use the following information for Problems 62 – 64. State of the economy Probability Stock R Boom .4 32%

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Normal .3 10% Recession .3 –9% EXPECTED RETURN

D 62. What is the expected return of Stock R? A. 12.42% B. 14.11% C. 10.05% D. 13.10% E. 11.65% Level: Medium Solution: (0.4)(32%) + (0.3)(10%) + (0.3)(-9%) = 12.8% + 3% - 2.7% = 13.1% VARIANCE C 63. What is the variance of Stock R? A. 0.0328 B. 0.0416 C. 0.0292 D. 0.0375 E. 0.0253 Level: Medium Solution: E(R) = (.4 × .32) + (.3 × .10) + (.3 × -.09) = .128 + .03 − .027 = .131 Var = .4(.32 − .131)2 + .30(.10 − .131)2 + .3(-.09 − .131)2 = .0142884 + .0002883 + .0146523 = .029229 STANDARD DEVIATION A 64. What is the standard deviation of Stock R? A. 17.10% B. 26.82% C. 21.85% D. 14.28% E. 23.43% Level: Medium Solution: E(R) = (.4 × .32) + (.3 × .10) + (.3 × -.09) = .128 + .03 − .027 = .131 Var = .4(.32 − .131)2 + .30(.10 − .131)2 + .3(-.09 − .131)2 = .0142884 + .0002883 + .0146523 = 0.029229 Std. Dev. = (0.029229)0.5 = 0.170965 Use the following information for Problems 65 – 68. State of the economy Probability Stock F Boom .3 65% Normal .4 14% Recession .3 –50% EXPECTED RETURN C 65. What is the expected return of Stock F? A. 10.67% B. 11.15% C. 10.10% D. 11.76% E. 10.86%


Level: Medium Solution: E(R) = (.30 × .65) + (.40 × .14) + (.30 × -.50) = .195 + .056 − .15 = .101 VARIANCE A 66. What is the variance of Stock F? A. 0.1994 B. 0.1741 C. 0.2217 D. 0.1823 E. 0.2074 Level: Medium Solution: Given E(R ) = 0.101, Var = .30(.65 − .101)2 + .40(.14 − .101)2 + .30(-.50 − .101)2 = .0904203 + .0006084 + .1083603 = .199389 STANDARD DEVIATION B 67. What is the standard deviation of Stock F? A. 50.86% B. 44.65% C. 41.37% D. 35.21% E. 23.06% Level: Medium Solution: Std Dev = √.199389 = .44653 = 44.65 percent RISK PREMIUM D 68. If the risk-rate is 5.8 percent, what is the risk premium of Stock F? A. 15.9% B. 5.25% C. 4.87% D. 4.30% E. 5.06% Level: Easy Solution: Risk premium = 10.1% - 5.8% = 4.3% Use the following information for Problems 69 – 72. State of the economy Probability Stock P Stock Q Boom .3 20% 14% Recession .7 12% 8% EXPECTED RETURN D 69. What is the expected return of Stock P? A. 15.3% B. 10.9% C. 17.1% D. 14.4% E. 15.8% Level: Easy Solution: (0.3)(20%) + (0.7)(12%) = 6% + 8.4% = 14.4%

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EXPECTED RETURN B 70. What is the expected return of Stock Q? A. 12.3% B. 9.8% C. 10.9% D. 11.2% E. 8.5% Level: Easy Solution: (0.3)(14%) + (0.7)(8%) = 4.2% + 5.6% = 9.8% PORTFOLIO EXPECTED RETURN D 71. What is the expected return of a portfolio 60 percent invested in Stock P and the remainder in

Stock Q? A. 14.30% B. 13.19% C. 15.17% D. 12.56% E. 10.66% Level: Medium Solution: E(RBoom) = (.60 × .20) + (.40 × .14) = .12 + .056 = .176

E(Rrecession) = (.60 × .12) + (.40 × .08) = .072 + .032 = .104 E(RPort) = (.30 × .176) + (.70 × .104) = .0528 + .0728 = .1256 = 12.56 percent

PORTFOLIO STANDARD DEVIATION E 72. What is the standard deviation of a portfolio 60 percent invested in Stock P and the remainder in

Stock Q? A. 5.88% B. 1.46% C. 4.27% D. 2.63% E. 3.30% Level: Hard Solution: E(RBoom) = (.60 × .20) + (.40 × .14) = .12 + .056 = .176

E(RRecession) = (.60 × .12) + (.40 × .08) = .072 + .032 = .104 E(RPort) = (.3 × .176) + (.7 × .104) = .0528 + .0728 = .1256

VarPort = .3(.176 − .1256)2 + .7(.104 − .1256)2 = .000762048 + .000326592 = .00108864 Std DevPort = √.00108864 = .0329945 = 3.30 percent PORTFOLIO VARIANCE A 73. A portfolio is equally invested in two stocks. The standard deviations are 58%and 46%,

respectively. If the correlation between the stocks is 0.24, what is the variance of the portfolio? A. 0.1690 B. 0.2382 C. 0.1813 D. 0.2489 E. 0.2046 Level: Medium


Solution:

PORTFOLIO VARIANCE D 74. Stock J has a standard deviation of 67 percent, and Stock K has a standard deviation of 51

percent. The correlation between the two stocks is –0.10. What is the variance of a portfolio of the two assets with 35 percent invested in Stock J?

A. 0.1026 B. 0.2318 C. 0.1653 D. 0.1493 E. 0.1986 Level: Medium Solution:

PORTFOLIO STANDARD DEVIATION B 75. Stock J has a standard deviation of 67 percent and Stock K has a standard deviation of 51

percent. The correlation between the two stocks is –0.10. What is the standard deviation of a portfolio of the two assets with 35 percent invested in Stock J?

A. 46.23% B. 38.64% C. 41.07% D. 35.19% E. 43.82% Level: Medium Solution:

PORTFOLIO STANDARD DEVIATION C 76. Suppose a portfolio has 55 percent of its assets invested in Stock S with a standard deviation of

40 percent and the remainder in Stock T with a standard deviation of 12 percent. If the correlation between the two stocks is 0.22, what is the standard deviation of the portfolio?

A. 21.05% B. 22.94% C. 23.78% D. 24.68% E. 25.56% Level: Medium Solution: VarPort = [.552 × .402] + [(1 − .55)2 × .122] + [2 × .55 × (1 − .55) × .40 × .12 × .22] = [.3025 × .16] + [.2025 × .0144] + .0052272 = .0484 + .002916 + .0052272 = .0565432 Std DevPort = √.0565432 =.23779 = 23.78 percent

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PORTFOLIO VARIANCE D 77. Stock G has a standard deviation of 49 percent, and Stock H has a standard deviation of 56

percent. The covariance between the two assets is 0.046. What is the variance of a portfolio with 40 percent of its assets invested in Stock G?

A. 0.1686 B. 0.1247 C. 0.1096 D. 0.1734 E. 0.1535 Level: Medium Solution:

PORTFOLIO STANDARD DEVIATION A 78. Stock G has a standard deviation of 49 percent, and Stock H has a standard deviation of 56

percent. The covariance between the two assets is 0.046. What is the standard deviation of a portfolio with 40 percent of its assets invested in Stock G?

A. 41.64% B. 33.35% C. 44.07% D. 39.52% E. 35.31% Level: Medium Solution:

THREE-ASSET PORTFOLIO STANDARD DEVIATION A 79. Stocks D, E and F have standard deviations of 2 percent, 10 percent and 40 percent, respectively.

The correlation coefficients between the stocks are as follows: 0.4 for D and E, -0.4 for D and F, and –0.2 E and F. What is the standard deviation of a portfolio with a mix of 30-30-40 percent in D, E and F?

A. 15.49% B. 13.35% C. 14.07% D. 19.52% Level: Hard Solution:


THREE-ASSET PORTFOLIO STANDARD DEVIATION E 80. You have a three-stock portfolio. Stock A has an expected return of 12% and a standard

deviations of 41%. Stock B has an expected return of 16% and a standard deviation of 58%. Stock C has an expected return of 13% and a standard deviation of 48%. The correlation coefficient between the Stocks A and B is 0.3, between Stocks A and C is 0.2, and between Stocks B and C is 0.05. Your portfolio consists of 30% Stock A, 50% Stock B and 20% Stock C. What is the standard deviation of this portfolio?

A. 35.97% B. 36.52% C. 34.75% D. 37.06% Level: Hard Solution:

MINIMUM VARIANCE PORTFOLIO WEIGHTS D 81. Stock S has an expected return of 8 percent and a standard deviation of 20 percent. Stock B has

an expected return of 3 percent and a standard deviation of 12 percent. If the correlation of the two stocks is 0.15, what is the weight of Stock S in the minimum variance portfolio?

A. 0.287 B. 0.236 C. 0.368 D. 0.229 E. 0.410 Level: Medium Solution: XS = [(0.12)2 – (0.2 × 0.12 × 0.15)] / [ (0.2)2 + (0.12)2 – (2 × 0.2 × 0.12 × 0.15)] = (0.0144 – 0.0036) / (0.04 + 0.0144 – 0.0072) = 0.0108 / 0.0472 = 0.22881 MINIMUM VARIANCE PORTFOLIO EXPECTED RETURN C 82. Stock S has an expected return of 8 percent and a standard deviation of 20 percent. Stock B has

an expected return of 3 percent and a standard deviation of 12 percent. If the correlation of the two stocks is 0.15, what is the expected return of the minimum variance portfolio?

A. 15.40% B. 17.71% C. 4.15% D. 10.37% E. 6.91% Level: Hard Solution: XS = [(0.12)2 – (0.2 × 0.12 × 0.15)] / [ (0.2)2 + (0.12)2 – (2 × 0.2 × 0.12 × 0.15)] = (0.0144 – 0.0036) / (0.04 + 0.0144 – 0.0072) = 0.0108 / 0.0472 = 0.22881 = 23% as the weight assigned to Stock S. The weight for Stock B becomes 77%. E(R) = 0.23 × 8% + 0.77 × 3% = 4.15%

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MINIMUM VARIANCE PORTFOLIO WEIGHTS B 83. The correlation between two stocks is –0.25. The standard deviation of Stock I is 48 percent, and

the standard deviation of Stock J is 34 percent. What is the weight of Stock I in the minimum variance portfolio?

A. 0.486 B. 0.366 C. 0.410 D. 0.532 E. 0.461 Level: Medium Solution: XSI = [(0.34)2 – (0.48 × 0.34 × -0.25)] / [ (0.48)2 + (0.34)2 – (2 × 0.48 × 0.34 × -0.25)] = (0.1156 + 0.0408) / (0.2304 + 0.1156 + 0.0816) = 0.1564 / 0.4276 = 0.36576 COVARIANCE B 84. While Stock A has a standard deviation of 37percent, Stock B has a standard deviation of 46

percent. If the correlation between the stocks is 0.1528, what is the covariance? A. 0.1702 B. 0.0260 C. 0.2875 D. 0.1270 E. 0.0565 Level: Medium Solution: Cov = (0.1528)(0.37)(0.46) = 0.02600656 COVARIANCE C 85. While Stock A has a standard deviation of 37percent, Stock B has a standard deviation of 46

percent. Given the covariance between the two stocks is –0.0255, determine the correlation coefficient.

A. -0.25 B. 0.60 C. -0.15 D. 0.30 E. 0.15 Level: Medium Solution: ρ = -0.0255/(0.37)(0.46) = -0.1498 COVARIANCE D 86. While the covariance between the two stocks, G and H, is 0.0357, the correlation coefficient is

0.17. Given Stock G has a standard deviation of 50 percent, what is the standard deviation of Stock H?

A. 49% B. 56% C. 24% D. 42% E. 61%


Level: Medium Solution: Std. Dev. = 0.0357 / (0.5) × 0.17 = 0.42 CORRELATION A 87. Consider the following correlation coefficient for stocks M, N, P and Q. Which portfolio will

have the least diversification benefit? Stock M Stock N Stock P Stock Q Stock M 1.000 Stock N 0.911 1.000 Stock P 0.543 -0.123 1.000 Stock Q -0.321 0.411 0.000 1.000

A. M and N B. N and P C. P and Q D. M and P E. N and Q Level: Easy Solution: They have the largest correlation coefficient of 0.911 IV. ESSAY 88. Why are some risks diversifiable and others nondiversifiable? Give an example of each. Answer: Some risks (diversifiable) affect only one asset or at most a small group of assets. When you create a portfolio, these risks tend to offset. When bad news is announced for one asset, if the risks are not related, we would expect that on average good news would be announced for another asset. An important assumption is that the risks are not related, in other words, the assets have a low correlation. Nondiversifiable risk affects a large number of assets or the entire market and cannot be eliminated through diversification. 89. What is the importance of the minimum variance portfolio? All else the same, what effect does the correlation between two risky assets have on the minimum variance portfolio? Answer: The minimum variance portfolio is important since it defines the efficient frontier. The possible combinations of the two assets below the minimum variance portfolio are dominated by portfolios above the minimum variance portfolio, and are thus inefficient. Correlation is important in calculating the minimum variance portfolio since all else the same, a lower correlation between the two assets will result in a lower variance for the minimum variance portfolio. 90. In basic terms, what is the major benefit of diversification? How does diversification work? Answer: Diversification permits an investor to reduce risk. The reduction in risk does reduce potential return, but the risk reduction is much greater than the loss in return. Diversification works when the assets in a portfolio have a low correlation. If the assets do have a low correlation, as one asset has a lower than average return, another asset will have a greater than average return, offsetting each other. 91. Why is Markowitz portfolio analysis most commonly used to make asset allocation decisions? Answer: An investor’s optimal portfolio is the portfolio that maximizes the expected utility given the risk preference. The model is helpful for asset reallocation decision. Once the risk tolerance is established, investor subscribes securities to hold. The current choice of the proportion of the overall portfolio invested in broad general asset categories will be compared with an optimal portfolio having the same risk but with a much better return. The model also provides information about return and volatility of the current and optimal portfolios. 92. Explain why changes in economic outlook may cause an investor to change his asset allocation. Answer: Most securities perform differently given different economic states of the economy. If the economic outlook is leaning heavily towards a boom, an investor may prefer to increase the portfolio weight of the higher-risk

CHAPTER 2


securities. On the other hand, if the possibility of an economic recession is strong, an investor may wish to reduce the portfolio weighting of high-risk securities and increase the weighting of low-risk securities.

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Chapter 02