Chapter 7.pdf

Chapter 07 - Introduction to Risk and Return

Chapter 07 Introduction to Risk and Return Multiple Choice Questions

1. Which of the following portfolios have the least risk? A. A portfolio of Treasury bills B. A portfolio of long-term United States Government bonds C. Portfolio of U.S. common stocks of small firms D. None of the above

2. Long-term U.S. government bonds have: A. Interest rate risk B. Default risk C. Market risk D. None of the above

3. What has been the average annual real rate of interest on Treasury bills over the past 107 years (from 1900 to 2006)? A. Less than 1% B. Between 1% and 2% C. Between 2% and 3% D. Greater than 3%

4. What has been the average annual nominal rate of interest on Treasury bills over the past 107 years (1900 - 2006)? A. Less than 1% B. Between 1% and 2% C. Between 2% and 3% D. Greater than 3%

7-1

Chapter 07 - Introduction to Risk and Return

5. What has been the average annual nominal rate of return on a portfolio of U.S. common stocks over the past 107 years (from 1900 to 2006)? A. Less than 2% B. Between 2% and 5% C. Between 5% and 11% D. Greater than 11%

6. One dollar invested in a portfolio of U.S. government bonds in 1900 would have grown in nominal value by the end of year 2006 to: A. $719 B. $66 C. $176 D. $2.80

7. One dollar invested in a portfolio of U.S. common stocks in 1900 would have grown in nominal value by the end of year 2006 to: A. $21,536 B. $176 C. $719 D. $6.81

8. What has been the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and 2006? A. Less than 2% B. Between 2% and 5% C. Between 5% and 8% D. Greater than 8%

9. Which portfolio has had the lowest average annual nominal rate of return during the 19002006 periods? A. Portfolio of U.S. Common stocks B. Portfolio of U.S. government bonds C. Portfolio of Treasury bills D. None of the given answers

7-2

Chapter 07 - Introduction to Risk and Return

10. Which portfolio had the highest average annual return in real terms between 1900 and 2006? A. Portfolio of U.S. Common stocks B. Portfolio of U.S. government bonds C. Portfolio of Treasury bills D. None of the given answers

11. Standard error measures: A. Nominal annual rate of return on a portfolio B. Risk of a portfolio Reliability of an estimate C. Reliability of an estimate D. Real annual rate of return on a portfolio

12. Standard error is estimated as: A. Average annual rate of return divided by the square root of the number of observations B. Variance divided by the number of observations C. Standard deviation of returns divided by the square root of the number of observations D. None of the above

13. Which portfolio has had the highest average risk premium during the period 1900-2006? A. Common stocks B. Government bonds C. Treasury bills D. None of the given answers

14. If the standard deviation is 19.8% and the number of observations is 107, what is the standard error? A. 4.23 % B. 1.9% C. 0.47% D. None of the above

7-3

Chapter 07 - Introduction to Risk and Return

15. If the average annual rate of return for common stocks is 11.7%, and for treasury bills it is 4.0%, what is the market risk premium? A. 15.8% B. 4.1% C. 7.7% D. None of the above

16. Spill Oil Company's stocks had -8%, 11% and 24% rates of return during the last three years respectively; calculate the average rate of return for the stock. A. 8% per year B. 9% per year C. 11% per year D. None of the above

17. For log-normally distributed returns the annul compound returns is equal to: A. the arithmetic average returns minus half the variance B. the arithmetic average returns plus half the variance C. the arithmetic average returns minus half the standard deviation D. the arithmetic average returns plus half the standard deviation

18. Which of the following provides a correct measure of the opportunity cost of capital regardless of the timing of the cash flows? A. Arithmetic average B. Geometric average C. Hyperbolic mean D. None of the above

19. Given the following data: risk-free rate = 4%, average risk premium = 7.7%. Calculate the required rate of return: A. 5.6% B. 7.6% C. 11.7% D. None of the given answers

7-4

Chapter 07 - Introduction to Risk and Return

20. Which of the following countries had the lowest risk premium? A. U.S.A B. Denmark C. Italy D. none of the above

21. Which of the following countries had the highest risk premium? A. Germany B. Denmark C. Italy D. None of the above

22. Mega Corporation has the following returns for the past three years: 8%, 12% and 10%. Calculate the variance of the return and the standard deviation of the returns. A. 64 and 8% B. 124 and 11.1% C. 4 and 2% D. None of the above

23. Macro Corporation has had the following returns for the past three years, -10%, 10%, and 30%. Calculate the standard deviation of the returns. A. 10% B. 20% C. 30% D. None of the above

24. Sun Corporation has had returns of -6%, 16%, 18%, and 28% for the past four years. Calculate the standard deviation of the returns. A. 11.6% B. 14.3% C. 13.4 % D. None of the above

7-5

Chapter 07 - Introduction to Risk and Return

25. Which portfolio had the highest standard deviation during the period between 1900 and 2006? A. Common stocks B. Government bonds C. Treasury bills D. None of the given answers

26. What has been the standard deviation of returns of common stocks during the period between 1900 and 2006? A. 19.8% B. 33.4% C. 8.1% D. 7.8%

27. The standard deviation of the UK market during the period from 2001 through 2006 was: (Approximately) A. 12.3% B. 14.1% C. 9.8% D. None of the above

28. A statistical measure of the degree to which securities' returns move together is called: A. Variance B. Correlation Coefficient C. Standard Deviation D. None of the above

29. The type of the risk that can be eliminated by diversification is called: A. Market risk B. Unique risk C. Interest rate risk D. Default risk

7-6

Chapter 07 - Introduction to Risk and Return

30. The unique risk is also called the: A. Unsystematic risk B. Diversifiable risk C. Firm specific risk D. All of the above

31. Market risk is also called: I) systematic risk, II) undiversifiable risk, III) firm specific risk. A. I only B. II only C. III only D. I and II only

32. Stock A has an expected return of 10% per year and stock B has an expected return of 20%. If 40% of the funds are invested in stock A, and the rest in stock B, what is the expected return on the portfolio of stock A and stock B? A. 10% B. 20% C. 16% D. None of the above

33. As the number of stocks in a portfolio is increased: A. Unique risk decreases and approaches to zero B. Market risk decreases C. Unique risk decreases and becomes equal to market risk D. Total risk approaches to zero

34. Stock M and Stock N have had the following returns for the past three years of -12%, 10%, 32%; and 15%, 6%, 24% respectively. Calculate the covariance between the two securities. A. -99 B. +99 C. +250 D. None of the above

7-7

Chapter 07 - Introduction to Risk and Return

35. Stock P and stock Q have had annual returns of -10%, 12%, 28% and 8%, 13%, 24% respectively. Calculate the covariance of return between the securities. A. -149 B. +149 C. 100 D. None of the above

36. Stock X has a standard deviation of return of 10%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between stocks is 0.5. If you invest 60% of the funds in stock X and 40% in stock Y, what is the standard deviation of a portfolio? A. 10% B. 20% C. 12.2% D. None of the above

37. If the correlation coefficient between stock C and stock D is +1.0% and the standard deviation of return for stock C is 15% and that for stock D is 30%, calculate the covariance between stock C and stock D. A. +45 B. -450 C. +450 D. None of the above

38. The range of values that correlation coefficients can take can be: A. zero to +1 B. -1 to +1 C. - infinity to +infinity D. zero to + infinity

7-8

Chapter 07 - Introduction to Risk and Return

39. If the covariance between stock A and stock B is 100, the standard deviation of stock A is 10% and that of stock B is 20%, calculate the correlation coefficient between the two securities. A. -0.5 B. +1.0 C. +0.5 D. None of the above

40. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient between the two stocks is: A. +1 B. -0.5 C. -1 D. 0

41. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N variance terms B. N(N - 1)/2 variance terms C. N2 variance terms D. None of the above

42. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N covariance terms B. N(N - 1)/2 covariance terms C. N2 covariance terms D. None of the above

43. The "beta" is a measure of: A. Unique risk B. Total risk C. Market risk D. None of the above

7-9

Chapter 07 - Introduction to Risk and Return

44. The beta of market portfolio is: A. + 1.0 B. +0.5 C. 0 D. -1.0

45. For each additional 1% change in the market return, Amazon stock return on the average changes by: A. 1.26% B. 1.59% C. 2.2% D. None of the above

46. The beta of Nestle measured relative to its home market is: A. 0.17 B. 1.54 C. 1.01 D. none of the above

47. If the standard deviation of returns of the market is 20% and the beta of a well-diversified portfolio is 1.5, calculate the standard deviation of the portfolio: A. 30% B. 20% C. 10% D. none of the above

48. The correlation coefficient between stock A and the market portfolio is +0.6. The standard deviation of return of the stock is 30% and that of the market portfolio is 20%. Calculate the beta of the stock. A. 1.1 B. 1.0 C. 0.9 D. 0.6

7-10

Chapter 07 - Introduction to Risk and Return

49. Historical nominal return for stock A is -8%, +10% and +22%. The nominal return for the market portfolio is +6%, +18% and 24%. Calculate the beta for stock A. A. 1.64 B. 0.61 C. 1.0 D. None of the above

50. The annual return for three years for stock B comes out to be 0%, 10% and 26%. Annual returns for three years for the market portfolios are +6%, 18%, 24%. Calculate the beta for the stock. A. 0.74 B. 1.36 C. 1.0 D. None of the above

51. The correlation coefficient between stock B and the market portfolio is 0.8. The standard deviation of the stock B is 35% and that of the market is 20%. Calculate the beta of the stock. A. 1.0 B. 1.4 C. 0.8 D. 0.7

52. The covariance between YOHO stock and the S&P 500 is .05. The standard deviation of the stock market is 20%. What is the beta of YOHO? A. 0.00 B. 1.00 C. 1.25 D. 1.42

7-11

Chapter 07 - Introduction to Risk and Return

53. What is the beta of a security where the expected return is double that of the stock market, there is no correlation coefficient relative to the US stock market and the standard deviation of the stock market is .18? A. 0.00 B. 1.00 C. 1.25 D. 2.00

True / False Questions

54. Treasury bills have provided the highest average return, both in nominal terms and in real terms, between 1900-2006. True False

55. Risk premium is the difference between the security return and the Treasury bill return. True False

56. For log-normally distributed returns the annual geometric average return is greater than the arithmetic average return. True False

57. According to the authors, a reasonable range for the risk premium in the United States is 5% to 8%. True False

58. The standard statistical measures of spread are beta and covariance. True False

7-12

Chapter 07 - Introduction to Risk and Return

59. Diversification reduces risk because prices of different securities do not move exactly together. True False

60. The risk that cannot be eliminated by diversification is called unique risk. True False

61. The risk that cannot be eliminated by diversification is called market risk. True False

62. Beta of a well-diversified portfolio is equal to the value weighted average beta of the securities included in the portfolio. True False

63. The average beta of all stocks in the market is zero. True False

64. A portfolio with a beta of one offers an expected return equal to the market risk premium. True False

65. Higher the standard deviation of a stock higher is its beta. True False

66. High standard deviation always translates into high beta. True False

7-13

Chapter 07 - Introduction to Risk and Return

67. A stock with a covariance with the market higher than the variance of the market will always high a beta above 1.0. True False

Short Answer Questions

68. Define the term risk premium.

69. Briefly explain the term "variance" of the returns.

70. Briefly explain how diversification reduces risk.

7-14

Chapter 07 - Introduction to Risk and Return

71. In the formula for calculating the variance of N-stock portfolio, how many covariance and variance terms are there?

72. Briefly explain how "beta" of a stock is estimated.

73. Briefly explain what "beta" of a stock means.

74. Discuss the importance of "beta" as a measure of risk.

7-15

Chapter 07 - Introduction to Risk and Return

75. Briefly explain the difference between beta as a measure of risk and variance as a measure of risk.

76. Briefly explain how individual securities affect portfolio risk.

77. What is the beta of a portfolio with a large number of randomly selected stocks?

78. How can individual investors diversify?

7-16

Chapter 07 - Introduction to Risk and Return

79. Briefly explain the concept of value additivity.

80. Explain why international stock may have high standard deviation but low betas.

7-17

Chapter 07 - Introduction to Risk and Return

Chapter 07 Introduction to Risk and Return Answer Key

Multiple Choice Questions

1. Which of the following portfolios have the least risk? A. A portfolio of Treasury bills B. A portfolio of long-term United States Government bonds C. Portfolio of U.S. common stocks of small firms D. None of the above

Type: Easy

2. Long-term U.S. government bonds have: A. Interest rate risk B. Default risk C. Market risk D. None of the above

Type: Medium

3. What has been the average annual real rate of interest on Treasury bills over the past 107 years (from 1900 to 2006)? A. Less than 1% B. Between 1% and 2% C. Between 2% and 3% D. Greater than 3%

Type: Easy

7-18

Chapter 07 - Introduction to Risk and Return

4. What has been the average annual nominal rate of interest on Treasury bills over the past 107 years (1900 - 2006)? A. Less than 1% B. Between 1% and 2% C. Between 2% and 3% D. Greater than 3%

Type: Easy

5. What has been the average annual nominal rate of return on a portfolio of U.S. common stocks over the past 107 years (from 1900 to 2006)? A. Less than 2% B. Between 2% and 5% C. Between 5% and 11% D. Greater than 11%

Type: Easy

6. One dollar invested in a portfolio of U.S. government bonds in 1900 would have grown in nominal value by the end of year 2006 to: A. $719 B. $66 C. $176 D. $2.80

Type: Medium

7. One dollar invested in a portfolio of U.S. common stocks in 1900 would have grown in nominal value by the end of year 2006 to: A. $21,536 B. $176 C. $719 D. $6.81

Type: Medium

7-19

Chapter 07 - Introduction to Risk and Return

8. What has been the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and 2006? A. Less than 2% B. Between 2% and 5% C. Between 5% and 8% D. Greater than 8%

Type: Medium

9. Which portfolio has had the lowest average annual nominal rate of return during the 19002006 periods? A. Portfolio of U.S. Common stocks B. Portfolio of U.S. government bonds C. Portfolio of Treasury bills D. None of the given answers

Type: Medium

10. Which portfolio had the highest average annual return in real terms between 1900 and 2006? A. Portfolio of U.S. Common stocks B. Portfolio of U.S. government bonds C. Portfolio of Treasury bills D. None of the given answers

Type: Medium

11. Standard error measures: A. Nominal annual rate of return on a portfolio B. Risk of a portfolio Reliability of an estimate C. Reliability of an estimate D. Real annual rate of return on a portfolio

Type: Difficult

7-20

Chapter 07 - Introduction to Risk and Return

12. Standard error is estimated as: A. Average annual rate of return divided by the square root of the number of observations B. Variance divided by the number of observations C. Standard deviation of returns divided by the square root of the number of observations D. None of the above

Type: Medium

13. Which portfolio has had the highest average risk premium during the period 1900-2006? A. Common stocks B. Government bonds C. Treasury bills D. None of the given answers

Type: Medium

14. If the standard deviation is 19.8% and the number of observations is 107, what is the standard error? A. 4.23 % B. 1.9% C. 0.47% D. None of the above Standard error = 19.8/√107 = 1.9%

Type: Difficult

7-21

Chapter 07 - Introduction to Risk and Return

15. If the average annual rate of return for common stocks is 11.7%, and for treasury bills it is 4.0%, what is the market risk premium? A. 15.8% B. 4.1% C. 7.7% D. None of the above Average risk premium: 11.7 - 4.0 = 7.7%

Type: Easy

16. Spill Oil Company's stocks had -8%, 11% and 24% rates of return during the last three years respectively; calculate the average rate of return for the stock. A. 8% per year B. 9% per year C. 11% per year D. None of the above Average rate of return = (-8 + 11 + 24)/3 = 9%

Type: Easy

17. For log-normally distributed returns the annul compound returns is equal to: A. the arithmetic average returns minus half the variance B. the arithmetic average returns plus half the variance C. the arithmetic average returns minus half the standard deviation D. the arithmetic average returns plus half the standard deviation

Type: Difficult

7-22

Chapter 07 - Introduction to Risk and Return

18. Which of the following provides a correct measure of the opportunity cost of capital regardless of the timing of the cash flows? A. Arithmetic average B. Geometric average C. Hyperbolic mean D. None of the above

Type: Difficult

19. Given the following data: risk-free rate = 4%, average risk premium = 7.7%. Calculate the required rate of return: A. 5.6% B. 7.6% C. 11.7% D. None of the given answers Required rate of return = 4 + 7.7 = 11.7 %

Type: Easy

20. Which of the following countries had the lowest risk premium? A. U.S.A B. Denmark C. Italy D. none of the above

Type: Easy

21. Which of the following countries had the highest risk premium? A. Germany B. Denmark C. Italy D. None of the above

Type: Easy

7-23

Chapter 07 - Introduction to Risk and Return

22. Mega Corporation has the following returns for the past three years: 8%, 12% and 10%. Calculate the variance of the return and the standard deviation of the returns. A. 64 and 8% B. 124 and 11.1% C. 4 and 2% D. None of the above Mean = (8 + 12 + 10)/3 = 10%; Variance = [(8 - 10)^2 + (12 - 10)^2 + (10 - 10)^2]/(3 - 1) = 4; Standard deviation = 4^(1/2) = 2%

Type: Difficult

23. Macro Corporation has had the following returns for the past three years, -10%, 10%, and 30%. Calculate the standard deviation of the returns. A. 10% B. 20% C. 30% D. None of the above Mean = (-10 + 10 + 30)/3 = 10%; Variance = [(-10 - 10)^2 + (10 - 10)^2 + (30 - 10)^2]/2 = 400; Standard deviation = 20%

Type: Difficult

24. Sun Corporation has had returns of -6%, 16%, 18%, and 28% for the past four years. Calculate the standard deviation of the returns. A. 11.6% B. 14.3% C. 13.4 % D. None of the above (-6 + 16 + 18 + 28)/4 = 14%; Variance = [(-6 - 14)^2 + (16 - 14)^2 + (18 - 14)^2 + (28 - 14)^2]/(4 - 1) = 205.33; Standard deviation = 180.7^(1/2) = 14.3%

Type: Difficult

7-24

Chapter 07 - Introduction to Risk and Return

25. Which portfolio had the highest standard deviation during the period between 1900 and 2006? A. Common stocks B. Government bonds C. Treasury bills D. None of the given answers

Type: Easy

26. What has been the standard deviation of returns of common stocks during the period between 1900 and 2006? A. 19.8% B. 33.4% C. 8.1% D. 7.8%

Type: Medium

27. The standard deviation of the UK market during the period from 2001 through 2006 was: (Approximately) A. 12.3% B. 14.1% C. 9.8% D. None of the above

Type: Medium

28. A statistical measure of the degree to which securities' returns move together is called: A. Variance B. Correlation Coefficient C. Standard Deviation D. None of the above

Type: Medium

7-25

Chapter 07 - Introduction to Risk and Return

29. The type of the risk that can be eliminated by diversification is called: A. Market risk B. Unique risk C. Interest rate risk D. Default risk

Type: Medium

30. The unique risk is also called the: A. Unsystematic risk B. Diversifiable risk C. Firm specific risk D. All of the above

Type: Easy

31. Market risk is also called: I) systematic risk, II) undiversifiable risk, III) firm specific risk. A. I only B. II only C. III only D. I and II only

Type: Easy

32. Stock A has an expected return of 10% per year and stock B has an expected return of 20%. If 40% of the funds are invested in stock A, and the rest in stock B, what is the expected return on the portfolio of stock A and stock B? A. 10% B. 20% C. 16% D. None of the above 0.40(10) + 0.60(20) = 16%

Type: Easy

7-26

Chapter 07 - Introduction to Risk and Return

33. As the number of stocks in a portfolio is increased: A. Unique risk decreases and approaches to zero B. Market risk decreases C. Unique risk decreases and becomes equal to market risk D. Total risk approaches to zero

Type: Medium

34. Stock M and Stock N have had the following returns for the past three years of -12%, 10%, 32%; and 15%, 6%, 24% respectively. Calculate the covariance between the two securities. A. -99 B. +99 C. +250 D. None of the above E(RM ) = (-12 + 10 + 32)/3 = 10% E(RN) = (6 + 15 + 24)/3 = 15% Cov(RM, RN) = [(-12 - 10)(15 - 15) + (10 - 10)(6 - 15) + (32 - 10)(24 - 15)]/(3 - 1) = 99

Type: Difficult

35. Stock P and stock Q have had annual returns of -10%, 12%, 28% and 8%, 13%, 24% respectively. Calculate the covariance of return between the securities. A. -149 B. +149 C. 100 D. None of the above E(P) = (-10 + 12 + 28)/3 = 10%; E(Q) = (8 + 13 + 24)/3 = 15% Cov(P,Q) = [(-10 - 10)(8 - 15) + (12 - 10) (13 - 15) + (28 - 10)(24 - 15)]/2 = 149

Type: Difficult

7-27

Chapter 07 - Introduction to Risk and Return

36. Stock X has a standard deviation of return of 10%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between stocks is 0.5. If you invest 60% of the funds in stock X and 40% in stock Y, what is the standard deviation of a portfolio? A. 10% B. 20% C. 12.2% D. None of the above (0.6^2)(10^2) + (0.4^2) (20^2) + (2)(0.6)(0.4)(0.5)(10)(20) = 148; Standard deviation = (148^0.5) = 12.2%

Type: Difficult

37. If the correlation coefficient between stock C and stock D is +1.0% and the standard deviation of return for stock C is 15% and that for stock D is 30%, calculate the covariance between stock C and stock D. A. +45 B. -450 C. +450 D. None of the above Cov(RC, RD) = (+1)(30)(15) = +450

Type: Medium

38. The range of values that correlation coefficients can take can be: A. zero to +1 B. -1 to +1 C. - infinity to +infinity D. zero to + infinity

Type: Medium

7-28

Chapter 07 - Introduction to Risk and Return

39. If the covariance between stock A and stock B is 100, the standard deviation of stock A is 10% and that of stock B is 20%, calculate the correlation coefficient between the two securities. A. -0.5 B. +1.0 C. +0.5 D. None of the above Corr(RA, RB) = 100/(10 * 20) = +0.5

Type: Medium

40. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient between the two stocks is: A. +1 B. -0.5 C. -1 D. 0

Type: Medium

41. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N variance terms B. N(N - 1)/2 variance terms C. N2 variance terms D. None of the above

Type: Medium

42. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N covariance terms B. N(N - 1)/2 covariance terms C. N2 covariance terms D. None of the above

Type: Medium

7-29

Chapter 07 - Introduction to Risk and Return

43. The "beta" is a measure of: A. Unique risk B. Total risk C. Market risk D. None of the above

Type: Medium

44. The beta of market portfolio is: A. + 1.0 B. +0.5 C. 0 D. -1.0

Type: Easy

45. For each additional 1% change in the market return, Amazon stock return on the average changes by: A. 1.26% B. 1.59% C. 2.2% D. None of the above

Type: Medium

46. The beta of Nestle measured relative to its home market is: A. 0.17 B. 1.54 C. 1.01 D. none of the above

Type: Easy

7-30

Chapter 07 - Introduction to Risk and Return

47. If the standard deviation of returns of the market is 20% and the beta of a well-diversified portfolio is 1.5, calculate the standard deviation of the portfolio: A. 30% B. 20% C. 10% D. none of the above Standard deviation of the portfolio = (1.5) * (20) = 30%

Type: Medium

48. The correlation coefficient between stock A and the market portfolio is +0.6. The standard deviation of return of the stock is 30% and that of the market portfolio is 20%. Calculate the beta of the stock. A. 1.1 B. 1.0 C. 0.9 D. 0.6 Cov (Rs, Rm) = (0.6)(20)(30) = 360; var(Rm) = 20^2 = 400 Beta = [Cov(Rs, Rm)]/var(Rm) = 360/400 = 0.9

Type: Difficult

49. Historical nominal return for stock A is -8%, +10% and +22%. The nominal return for the market portfolio is +6%, +18% and 24%. Calculate the beta for stock A. A. 1.64 B. 0.61 C. 1.0 D. None of the above Mean A = 8%; Mean M = 16%; Cov(Ra, Rm) = 138; Var(Rm) = 84; Beta = 138/84 = 1.64

Type: Difficult

7-31

Chapter 07 - Introduction to Risk and Return

50. The annual return for three years for stock B comes out to be 0%, 10% and 26%. Annual returns for three years for the market portfolios are +6%, 18%, 24%. Calculate the beta for the stock. A. 0.74 B. 1.36 C. 1.0 D. None of the above Mean B = 12%, Mean M = 16%, Cov(Ra, Rm) = 114; Va (Rm) = 84; Beta = 114/84 = 1.36

Type: Difficult

51. The correlation coefficient between stock B and the market portfolio is 0.8. The standard deviation of the stock B is 35% and that of the market is 20%. Calculate the beta of the stock. A. 1.0 B. 1.4 C. 0.8 D. 0.7 Cov(Rb,Rm) = (0.8)(20)(35) = 560; Beta = 560/400 = 1.4

Type: Difficult

52. The covariance between YOHO stock and the S&P 500 is .05. The standard deviation of the stock market is 20%. What is the beta of YOHO? A. 0.00 B. 1.00 C. 1.25 D. 1.42 Beta = .05/(.2 × .2) = 1.25

Type: Difficult

7-32

Chapter 07 - Introduction to Risk and Return

53. What is the beta of a security where the expected return is double that of the stock market, there is no correlation coefficient relative to the US stock market and the standard deviation of the stock market is .18? A. 0.00 B. 1.00 C. 1.25 D. 2.00 No correlation means no covariance, thus no beta.

Type: Difficult

True / False Questions

54. Treasury bills have provided the highest average return, both in nominal terms and in real terms, between 1900-2006. FALSE

Type: Easy

55. Risk premium is the difference between the security return and the Treasury bill return. TRUE

Type: Easy

56. For log-normally distributed returns the annual geometric average return is greater than the arithmetic average return. FALSE

Type: Difficult

7-33

Chapter 07 - Introduction to Risk and Return

57. According to the authors, a reasonable range for the risk premium in the United States is 5% to 8%. TRUE

Type: Medium

58. The standard statistical measures of spread are beta and covariance. FALSE

Type: Easy

59. Diversification reduces risk because prices of different securities do not move exactly together. TRUE

Type: Easy

60. The risk that cannot be eliminated by diversification is called unique risk. FALSE

Type: Medium

61. The risk that cannot be eliminated by diversification is called market risk. TRUE

Type: Medium

7-34

Chapter 07 - Introduction to Risk and Return

62. Beta of a well-diversified portfolio is equal to the value weighted average beta of the securities included in the portfolio. TRUE

Type: Medium

63. The average beta of all stocks in the market is zero. FALSE

Type: Medium

64. A portfolio with a beta of one offers an expected return equal to the market risk premium. FALSE

Type: Medium

65. Higher the standard deviation of a stock higher is its beta. FALSE

Type: Difficult

66. High standard deviation always translates into high beta. FALSE

Type: Medium

67. A stock with a covariance with the market higher than the variance of the market will always high a beta above 1.0. TRUE

Type: Medium

7-35

Chapter 07 - Introduction to Risk and Return

Short Answer Questions

68. Define the term risk premium. The difference between the security return and the risk free rate, such as a Treasury bill return, is called the risk premium. This denotes the additional return on the security because of additional risk.

Type: Medium

69. Briefly explain the term "variance" of the returns. Variance is a standard statistical measure of spread. The variance is the expected squared deviation from the expected return. From a finance point of view this measures the total risk of a security: higher the variance, higher the risk. This is also called the measure of total risk.

Type: Medium

70. Briefly explain how diversification reduces risk. Diversification reduces risk because prices of different securities do not move exactly together. When you form portfolios using a large number of stocks the variability of the portfolio is much less than average variability of individual stocks.

Type: Medium

71. In the formula for calculating the variance of N-stock portfolio, how many covariance and variance terms are there? In the formula for calculating the variance of N-asset portfolio, there are [N(N - 1)]/2 covariance terms and N variance terms.

Type: Easy

7-36

Chapter 07 - Introduction to Risk and Return

72. Briefly explain how "beta" of a stock is estimated. "Beta" of a stock can be estimated graphically by plotting the market returns on the x-axis and the corresponding stock returns on the y-axis. The slope of the resulting linear graph is the "beta" estimate for the stock. [βi = Cov(Ri, Rm)/Var(Rm)]

Type: Medium

73. Briefly explain what "beta" of a stock means. For each additional 1% change in the market return, the return on the stock on the average changes by "beta" times 1%. For example the beta of IBM is 1.59, then for additional 1% change in the market return is expected change the returns on the IBM stock by 1.59%.

Type: Difficult

74. Discuss the importance of "beta" as a measure of risk. "Beta" is a measure of market risk. It is also called relative measure of risk as it measures risk relative to the market risk. Beta is useful as a measure of risk in the context of well-diversified portfolios. It measures the risk contribution of a single security to the portfolio risk.

Type: Medium

75. Briefly explain the difference between beta as a measure of risk and variance as a measure of risk. Variance measures the total risk of a security and is a measure of stand-alone risk. Total risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to cancel each other out and only the market risk is remaining. Beta is a measure of market risk and is useful in the context of a well-diversified portfolio. Beta measures the sensitivity of the security returns to changes in market returns. Market portfolio has a beta of one and is considered the average risk.

Type: Medium

7-37

Chapter 07 - Introduction to Risk and Return

76. Briefly explain how individual securities affect portfolio risk. The risk of a well-diversified portfolio depends on the market risk of the securities included in the portfolio. Portfolio beta is the weighted average of individual security betas included in the portfolio.

Type: Medium

77. What is the beta of a portfolio with a large number of randomly selected stocks? The beta of a portfolio with a large number of randomly selected stocks is equal to one. The standard deviation of such a portfolio is equal to the standard deviation of the market.

Type: Medium

78. How can individual investors diversify? One of the simplest ways for individual investor to diversify is to buy shares in a mutual fund that holds a diversified portfolio.

Type: Medium

79. Briefly explain the concept of value additivity. If the capital market establishes a value PV(A) for asset A and PV(B) for asset B the market value of the firm that holds both these assets is: PV(AB) = PV(A) + PV(B). This logic can be extended for any number of assets. Value additivity is also applicable to cash flows. We can add the present values of two cash flows and get the present value of the combined cash flows. It can be stated as follows: PV(A + B) = PV(A) + PV(B) and PV(A + B + C) = PV(A) + PV(B) + PV(C) This idea can be extended for any number of cash flows.

Type: Medium

7-38

Chapter 07 - Introduction to Risk and Return

80. Explain why international stock may have high standard deviation but low betas. Beta is traditionally measured relative to the S&P 500 index. As such, there may be very little statistical relationship between the S&P 500 and an international stock. If these two assets are independent of one another there is little chance they will have a statistically significant covariance. With a low covariance, by definition, the stock will have a low beta. This could occur even if the standard deviation of the beta is very high.

Type: Difficult

7-39