Efficient Diversification

79. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. Stock B has a standard deviation of 14%. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -.23. A. 9.7% B. 12.2% C. 14% D. 15.6%

A. 9.7%

2. The _______ decision should take precedence over the _____ decision. A. asset allocation; stock selection B. bond selection; mutual fund selection C. stock selection; asset allocation D. stock selection; mutual fund selection

A. Asset allocation; stock selection

10. Asset A has an expected return of 20% and a standard deviation of 25%. The risk-free rate is 10%. What is the reward-to-variability ratio? A. .40 B. .50 C. .75 D. .80

A. .40 20%-10%/25%

29. A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 24%, while stock B has a standard deviation of return of 18%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is .0380, the correlation coefficient between the returns on A and B is _________. A. .583 B. .225 C. .327 D. .128

A. .583 .0380 = (.62)(.242) + (.42)(.182) + 2(.6)(.4)(.24)(.18) ρ; ρ = .583

34. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The proportion of the optimal risky portfolio that should be invested in stock A is _________. A. 0% B. 40% C. 60% D. 100%

A. 0%

35. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The expected return on the optimal risky portfolio is _________. A. 14% B. 15.6% C. 16.4% D. 18%

A. 14%

46. Stock A has a beta of 1.2, and stock B has a beta of 1. The returns of stock A are ______ sensitive to changes in the market than are the returns of stock B. A. 20% more B. slightly more C. 20% less D. slightly less

A. 20% more

5. Asset A has an expected return of 15% and a reward-to-variability ratio of .4. Asset B has an expected return of 20% and a reward-to-variability ratio of .3. A risk-averse investor would prefer a portfolio using the risk-free asset and ______. A. asset A B. asset B C. no risky asset D. The answer cannot be determined from the data given.

A. asset A

54. A security's beta coefficient will be negative if ____________. A. its returns are negatively correlated with market-index returns B. its returns are positively correlated with market-index returns C. its stock price has historically been very stable D. market demand for the firm's shares is very low

A. its returns are negatively correlated with market-index returns

24. On a standard expected return versus standard deviation graph, investors will prefer portfolios that lie to the _____________ of the current investment opportunity set. A. left and above B. left and below C. right and above D. right and below

A. left and above

59. If an investor does not diversify his portfolio and instead puts all of his money in one stock, the appropriate measure of security risk for that investor is the ________. A. stock's standard deviation B. variance of the market C. stock's beta D. covariance with the market index

A. stock's standard deviation

25. The term complete portfolio refers to a portfolio consisting of _________________. A. the risk-free asset combined with at least one risky asset B. the market portfolio combined with the minimum-variance portfolio C. securities from domestic markets combined with securities from foreign markets D. common stocks combined with bonds

A. the risk-free asset combined with at least one risky asset

32. The standard deviation of return on investment A is .10, while the standard deviation of return on investment B is .04. If the correlation coefficient between the returns on A and B is -.50, the covariance of returns on A and B is _________. A. -.0447 B. -.0020 C. .0020 D. .0447

B. -.0020 Covariance = -.50(.10)(.04)

71. Which of the following correlation coefficients will produce the most diversification benefits? A. -.6 B. -.9 C. 0 D. .4

B. -.9

81. The expected return of a portfolio is 8.9%, and the risk-free rate is 3.5%. If the portfolio standard deviation is 12%, what is the reward-to-variability ratio of the portfolio? A. 0 B. .45 C. .74 D. 1.35

B. .45 Reward-to-variability ratio = (.089 - .035)/.12 = .45

52. A stock has a correlation with the market of .45. The standard deviation of the market is 21%, and the standard deviation of the stock is 35%. What is the stock's beta? A. 1 B. .75 C. .60 D. .55

B. .75

80. What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 30%. Stock B has a standard deviation of 18%. The portfolio contains 60% of stock A, and the correlation coefficient between the two stocks is -1. A. 0% B. 10.8% C. 18% D. 24%

B. 10.8%

41. An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The expected return on the minimum-variance portfolio is approximately _________. A. 10% B. 13.6% C. 15% D. 19.41%

B. 13.6%

38. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The expected return on the optimal risky portfolio is approximately _________. (Hint: Find weights first.) A. 14% B. 16% C. 18% D. 19%

B. 16%

31. A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35%, while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is .45. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is _________. A. 23% B. 19.76% C. 18.45% D. 17.67%

B. 19.76% σ2p = (.402)(.352) + (.602)(.15)2 + (2)(.4)(.6)(.35)(.15)(.45) σ2p = .039046 σp = 19.76%

83. A project has a 50% chance of doubling your investment in 1 year and a 50% chance of losing half your money. What is the expected return on this investment project? A. 0% B. 25% C. 50% D. 75%

B. 25% E[rp] = (.5)(100) + (.5)(-50) = 25%

36. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The standard deviation of return on the optimal risky portfolio is _________. A. 0% B. 5% C. 7% D. 20%

B. 5%

45. The part of a stock's return that is systematic is a function of which of the following variables? I. Volatility in excess returns of the stock market II. The sensitivity of the stock's returns to changes in the stock market III. The variance in the stock's returns that is unrelated to the overall stock market A. I only B. I and II only C. II and III only D. I, II, and III

B. I and II only

76. As you lengthen the time horizon of your investment period and decide to invest for multiple years, you will find that: I. The average risk per year may be smaller over longer investment horizons. II. The overall risk of your investment will compound over time. III. Your overall risk on the investment will fall. A. I only B. I and II only C. III only D. I, II, and III

B. I and II only

49. You are constructing a scatter plot of excess returns for stock A versus the market index. If the correlation coefficient between stock A and the index is -1, you will find that the points of the scatter diagram ___________ and the line of best fit has a ______________. A. all fall on the line of best fit; positive slope B. all fall on the line of best fit; negative slope C. are widely scattered around the line; positive slope D. are widely scattered around the line; negative slope

B. all fall on the line of best fit; negative slope

8. The ________ is equal to the square root of the systematic variance divided by the total variance. A. covariance B. correlation coefficient C. standard deviation D. reward-to-variability ratio

B. correlation coefficient

15. The risk that can be diversified away is __________. A. beta B. firm-specific risk C. market risk D. systematic risk

B. firm-specific risk

68. Decreasing the number of stocks in a portfolio from 50 to 10 would likely ________________. A. increase the systematic risk of the portfolio B. increase the unsystematic risk of the portfolio C. increase the return of the portfolio D. decrease the variation in returns the investor faces in any one year

B. increase the unsystematic risk of the portfolio

58. Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is _____________. A. 1 B. less than 1 C. between 0 and 1 D. less than or equal to 0

B. less than 1

26. Rational risk-averse investors will always prefer portfolios _____________. A. located on the efficient frontier to those located on the capital market line B. located on the capital market line to those located on the efficient frontier C. at or near the minimum-variance point on the efficient frontier D. that are risk-free to all other asset choices

B. located on the capital market line to those located on the efficient frontier

12. Diversification is most effective when security returns are _________. A. high B. negatively correlated C. positively correlated D. uncorrelated

B. negatively correlated

43. A measure of the riskiness of an asset held in isolation is ____________. A. beta B. standard deviation C. covariance D. alpha

B. standard deviation

75. A portfolio of stocks fluctuates when the Treasury yields change. Since this risk cannot be eliminated through diversification, it is called __________. A. firm-specific risk B. systematic risk C. unique risk D. none of the options

B. systematic risk

18. Market risk is also called __________ and _________. A. systematic risk; diversifiable risk B. systematic risk; nondiversifiable risk C. unique risk; nondiversifiable risk D. unique risk; diversifiable risk

B. systematic risk; nondiversifiable risk

21. Harry Markowitz is best known for his Nobel Prize-winning work on _____________. A. strategies for active securities trading B. techniques used to identify efficient portfolios of risky assets C. techniques used to measure the systematic risk of securities D. techniques used in valuing securities options

B. techniques used to identify efficient portfolios of risky assets

50. The term excess return refers to ______________. A. returns earned illegally by means of insider trading B. the difference between the rate of return earned and the risk-free rate C. the difference between the rate of return earned on a particular security and the rate of return earned on other securities of equivalent risk D. the portion of the return on a security that represents tax liability and therefore cannot be reinvested

B. the difference between the rate of return earned and the risk-free rate

22. Suppose that a stock portfolio and a bond portfolio have a zero correlation. This means that ______. A. the returns on the stock and bond portfolios tend to move inversely B. the returns on the stock and bond portfolios tend to vary independently of each other C. the returns on the stock and bond portfolios tend to move together D. the covariance of the stock and bond portfolios will be positive

B. the returns on the stock and bond portfolios tend to vary independently of each other

6. Adding additional risky assets to the investment opportunity set will generally move the efficient frontier _____ and to the ______. A. up; right B. up; left C. down; right D. down; left

B. up; left

9. Which of the following statistics cannot be negative? A. Covariance B. Variance C. E(r) D. Correlation coefficient

B. variance

30. The standard deviation of return on investment A is .10, while the standard deviation of return on investment B is .05. If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is _________. A. .12 B. .36 C. .60 D. .77

C. .60

55. The market value weighted-average beta of firms included in the market index will always be _____________. A. 0 B. between 0 and 1 C. 1 D. none of these options (There is no particular rule concerning the average beta of firms included in the market index.)

C. 1

72. What is the most likely correlation coefficient between a stock-index mutual fund and the S&P 500? A. -1 B. 0 C. 1 D. .5

C. 1

42. An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The standard deviation of return on the minimum-variance portfolio is _________. A. 0% B. 6% C. 12% D. 17%

C. 12%

39. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The standard deviation of the returns on the optimal risky portfolio is _________. A. 25.5% B. 22.3% C. 21.4% D. 20.7%

C. 21.4%

62. You find that the annual Sharpe ratio for stock A returns is equal to 1.8. For a 3-year holding period, the Sharpe ratio would equal _______. A. 1.8 B. 2.48 C. 3.12 D. 5.49

C. 3.12 The Sharpe ration grows at a rate of so the 3-year Sharpe ration would be 1.8 × = 3.12.

33. Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. The weight of security B in the minimum-variance portfolio is _________. A. 10% B. 20% C. 40% D. 60%

C. 40%

44. Semitool Corp. has an expected excess return of 6% for next year. However, for every unexpected 1% change in the market, Semitool's return responds by a factor of 1.2. Suppose it turns out that the economy and the stock market do better than expected by 1.5% and Semitool's products experience more rapid growth than anticipated, pushing up the stock price by another 1%. Based on this information, what was Semitool's actual excess return? A. 7% B. 8.5% C. 8.8% D. 9.25%

C. 8.8% 6% + (1.5%)(1.2) + 1% = 8.8%

40. An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 24%, while the standard deviation on stock B is 14%. The correlation coefficient between the returns on A and B is .35. The expected return on stock A is 25%, while on stock B it is 11%. The proportion of the minimum-variance portfolio that would be invested in stock B is approximately _________. A. 45% B. 67% C. 85% D. 92%

C. 85%

61. Which of the following statements is (are) true regarding time diversification? I. The standard deviation of the average annual rate of return over several years will be smaller than the 1-year standard deviation. II. For a longer time horizon, uncertainty compounds over a greater number of years. III. Time diversification does not reduce risk. A. I only B. II only C. II and III only D. I, II, and III

C. II and III only

27. The optimal risky portfolio can be identified by finding: I. The minimum-variance point on the efficient frontier II. The maximum-return point on the efficient frontier and the minimum-variance point on the efficient frontier III. The tangency point of the capital market line and the efficient frontier IV. The line with the steepest slope that connects the risk-free rate to the efficient frontier A. I and II only B. II and III only C. III and IV only D. I and IV only

C. III and IV only

20. Which one of the following stock return statistics fluctuates the most over time? A. Covariance of returns B. Variance of returns C. Average return D. Correlation coefficient

C. average return

69. If you want to know the portfolio standard deviation for a three-stock portfolio, you will have to ______. A. calculate two covariances and one trivariance B. calculate only two covariances C. calculate three covariances D. average the variances of the individual stocks

C. calculate free coverlances

51. You are recalculating the risk of ACE stock in relation to the market index, and you find that the ratio of the systematic variance to the total variance has risen. You must also find that the ____________. A. covariance between ACE and the market has fallen B. correlation coefficient between ACE and the market has fallen C. correlation coefficient between ACE and the market has risen D. unsystematic risk of ACE has risen

C. correlation coefficient between ACE and the market has risen

17. 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. equal to the sum of the securities' standard deviations B. equal to -1 C. equal to 0 D. greater than 0

C. equal to 0

28. The _________ reward-to-variability ratio is found on the ________ capital market line. A. lowest; steepest B. highest; flattest C. highest; steepest D. lowest; flattest

C. highest; steepest

48. According to Tobin's separation property, portfolio choice can be separated into two independent tasks consisting of __________ and __________. A. identifying all investor imposed constraints; identifying the set of securities that conform to the investor's constraints and offer the best risk-return trade-offs B. identifying the investor's degree of risk aversion; choosing securities from industry groups that are consistent with the investor's risk profile C. identifying the optimal risky portfolio; constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion D. choosing which risky assets an investor prefers according to the investor's risk-aversion level; minimizing the CAL by lending at the risk-free rate

C. identifying the optimal risky portfolio; constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion

14. Beta is a measure of security responsiveness to _________. A. firm-specific risk B. diversifiable risk C. market risk D. unique risk

C. market risk

23. You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolios have a correlation of .55. The standard deviation of the resulting portfolio will be ________________. A. more than 18% but less than 24% B. equal to 18% C. more than 12% but less than 18% D. equal to 12%

C. more than 12% but less than 18% σ2p = .02592 = (.52)(.242) + (.52)(.122) + 2(.5)(.5)(.24)(.12).55 = .02592; σ = 16.1%

56. Diversification can reduce or eliminate __________ risk. A. all B. systematic C. nonsystematic D. only an insignificant

C. nonsystematic

7. An investor's degree of risk aversion will determine his or her ______. A. optimal risky portfolio B. risk-free rate C. optimal mix of the risk-free asset and risky asset D. capital allocation line

C. optimal mix of the risk-free asset and risky asset

60. Which of the following provides the best example of a systematic-risk event? A. A strike by union workers hurts a firm's quarterly earnings. B. Mad Cow disease in Montana hurts local ranchers and buyers of beef. C. The Federal Reserve increases interest rates 50 basis points. D. A senior executive at a firm embezzles $10 million and escapes to South America.

C. the Federal Reserve increases internet rates 50 basis points

13. The expected rate of return of a portfolio of risky securities is _________. A. the sum of the securities' covariances B. the sum of the securities' variances C. the weighted sum of the securities' expected returns D. the weighted sum of the securities' variances

C. the weighted sum of the securities' expected returns

3. Many current and retired Enron Corp. employees had their 401k retirement accounts wiped out when Enron collapsed because ________. A. they had to pay huge fines for obstruction of justice B. their 401k accounts were held outside the company C. their 401k accounts were not well diversified D. none of these options

C. their 401k accounts were not well diversified

57. To construct a riskless portfolio using two risky stocks, one would need to find two stocks with a correlation coefficient of ________. A. 1 B. .5 C. 0 D. -1

D. -1

70. Which of the following correlation coefficients will produce the least diversification benefit? A. -.6 B. -.3 C. 0 D. .8

D. .8

16. Approximately how many securities does it take to diversify almost all of the unique risk from a portfolio? A. 2 B. 6 C. 8 D. 20

D. 20

37. An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately _________. A. 29% B. 44% C. 56% D. 71%

D. 71%

82. A project has a 60% chance of doubling your investment in 1 year and a 40% chance of losing half your money. What is the standard deviation of this investment? A. 25% B. 50% C. 62% D. 73%

D. 73% E[rp] = (.60)(1) + (.40)(-.5) = .40 σ2rp = (.60)(1 - .40)2 + (.40)(-.5 - .40)2 = .54 σrp = .73

1. Risk that can be eliminated through diversification is called ______ risk. A. unique B. firm-specific C. diversifiable D. all of these options

D. All of these options

47. Which risk can be partially or fully diversified away as additional securities are added to a portfolio? I. Total risk II. Systematic risk III. Firm-specific risk A. I only B. I and II only C. I, II, and III D. I and III

D. I and III

77. You are considering adding a new security to your portfolio. To decide whether you should add the security, you need to know the security's: I. Expected return II. Standard deviation III. Correlation with your portfolio A. I only B. I and II only C. I and III only D. I, II, and III

D. I, II, and III

74. Investing in two assets with a correlation coefficient of 1 will reduce which kind of risk? A. Market risk B. Unique risk C. Unsystematic risk D. None of these options (With a correlation of 1, no risk will be reduced.)

D. None of these options (with a correlation of 1, no risk will be reduced)

11. The correlation coefficient between two assets equals _________. A. their covariance divided by the product of their variances B. the product of their variances divided by their covariance C. the sum of their expected returns divided by their covariance D. their covariance divided by the product of their standard deviations

D. their covariance divided by the product of their standard deviations

73. Investing in two assets with a correlation coefficient of -.5 will reduce what kind of risk? A. Market risk B. Nondiversifiable risk C. Systematic risk D. Unique risk

D. unique risk

19. Firm-specific risk is also called __________ and __________. A. systematic risk; diversifiable risk B. systematic risk; nondiversifiable risk C. unique risk; nondiversifiable risk D. unique risk; diversifiable risk

D. unique risk; diversifiable risk

53. The values of beta coefficients of securities are __________. A. always positive B. always negative C. always between positive 1 and negative 1 D. usually positive but are not restricted in any particular way

D. usually positive but are not restricted in any particular way

78. Which of the following is a correct expression concerning the formula for the standard deviation of returns of a two-asset portfolio where the correlation coefficient is positive? A. σ2rp < (W12σ12 + W22σ22) B. σ2rp = (W12σ12 + W22σ22) C. σ2rp = (W12σ12 - W22σ22) D. σ2rp > (W12σ12 + W22σ22)

D. σ2rp > (W12σ12 + W22σ22)