# Answers to Chapter 7: Introduction to Risk, Return, and the Opportunity Cost of Capital

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**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) Standard and Poor’s composite index

D) Portfolio of common stocks of small firms

2. What has been the average nominal rate of interest on Treasury bills over the past seventy-five years?

A) Less than 1%

B) Between 1% and 2%

C) Between 2% and 3%

D) Between 3% and 4%

3. What has been the average real rate of interest on Treasury bills over the past seventy-five years?

A) Less than 1%

B) Between 1% and 2%

C) Between 2% and 3%

D) Between 3% and 4%

4. Standard and Poor’s 500 Index is a:

A) Portfolio of common stocks

B) Portfolio of corporate bonds

C) Portfolio of government bonds

D) A and B above

5. Long-term government bonds have:

A) Interest rate risk

B) Default risk

C) Market risk

D) None of the above

6. One dollar invested in the S&P index in 1926 would have grown in nominal value by the end of year 2000 to:

A) $6402.2

B) $2586.5

C) $64.1

D) $16.6

7. One dollar invested in the S&P index in 1926 would have grown in real value by the end of year 2000 to:

A) $659.6

B) $266.5

C) $6.6

D) $5.0

8. What has been the average risk premium on common stocks between 1926 and 2000?

A) 13.4%

B) 9.1%

C) 2.2%

D) 1.9%

9. What has been the average annual rate of return (normal value) for small common stocks between 1926 and 2000?

A) 17.3%

B) 13.0%

C) 6.0%

D) 3.9%

10. Which portfolio had the highest average annual (real) return between 1926 and 2000?

A) Small firm common stocks

B) Common stocks

C) Government bonds

D) Treasury bills

11. Which portfolio has had the lowest average annual nominal rate of return during the 1926-2000 period?

A) Small firm common stocks

B) Common stocks

C) Government bonds

D) Treasury bills

12. What has been the average risk premium on small-firm common stocks between 1926 and 2000?

A) More than 10%

B) Between 8% and 10%

C) Between 2% and 5%

D) Less than 2%

13. Which portfolio has had the highest average risk premium during the period 1926-2000?

A) Small firm common stocks

B) Common stocks

C) Government bonds

D) Treasury bills

14. Standard error measures:

A) Nominal annual rate of return on a portfolio

B) Risk of a portfolio

C) Reliability of an estimate

D) Real annual rate of return on a portfolio

15. Standard error is estimated as:

A) Average annual rate of return divided by the square root of the number of observations

B) Standard deviation of returns divided by the square root of the number of observations

C) Variance divided by the number of observations

D) None of the above

16. If the standard deviation is 13.4% and the number of observations is 10, what is the standard error?

A) 4.23 %

B) 2.4%

C) 0.47%

D) None of the above

17. Spill Oil Company’s stocks had -8%, 12% and 26% rates of return during the last three years respectively; calculate the average rate of return for the stock.

A) 10% per year

B) 8% per year

C) 12% per year

D) None of the above

18. If the average annual rate of return for common stocks is 13%, and treasury bills is 3.8%, what is the average market risk premium?

A) 13%

B) 3.8%

C) 9.2%

D) None of the above

19. The discount rate for safe projects is the:

A) Market rate of return

B) Risk-free rate

C) Market risk premium

D) None of the above

20. The discount rate for a project with a risk the same as the market risk is the:

A) Market rate of return

B) Risk-free rate

C) Market risk premium

D) None of the above

21. Mega Corporation has the following returns for the past three years: 8%, 16% and 24%. Calculate the variance of the return and the standard deviation of the returns.

A) 64 and 8%

B) 128 and 11.3%

C) 43 and 6.5%

D) None of the above

22. Macro Corporation has had the following returns for the past three years, -20%, 10%, 40%. Calculate the standard deviation of the returns.

A) 10%

B) 30%

C) 60%

D) None of the above

23. Micro Corporation has had returns of –5%, 15% and 20% for the past three years. Calculate the standard deviation of the returns.

A) 10%

B) 22.9%

C) 30%

D) None of the above

24. What has been the standard deviation of returns of common stocks during the period between 1926 and 2000?

A) 20.2%

B) 33.4%

C) 8.7%

D) 9.4%

25. Which portfolio had the highest standard deviation during the period between 1926 and 2000?

A) Small firm common stocks

B) Common stocks

C) Government bonds

D) Treasury bills

26. The standard deviation of the UK market during the period from 1996 through 2001 was:

A) 24.1%

B) 20.7%

C) 14.5%

D) None of the above

27. The portion of the risk that can be eliminated by diversification is called:

A) Unique risk

B) Market risk

C) Interest rate risk

D) Default risk

28. The unique risk is also called the:

A) Unsystematic risk

B) Diversifiable risk

C) Firm specific risk

D) Residual risk

E) All of the above

29. Stock A has an expected return of 10% per year and stock B has an expected return of 20%. If 55% of the funds are invested in stock B, what is the expected return on the portfolio of stock A and stock B?

A) 10%

B) 20%

C) 15.5%

D) None of the above

30. As the number of stocks in a portfolio is increased:

A) Unique risk decreases and approaches to zero

B) Market risk decrease

C) Unique risk decreases and becomes equal to market risk

D) total risk approaches to zero

31. 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) 22%

E) None of the above

32. Stock M and Stock N have had returns for the past three years of –12%. 10%, 32% and 6%, 15%, 24% respectively. Calculate the covariance between the two securities.

A) +198

B) –198

C) +132

D) None of the above

33. 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

34. 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

35. 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) –45

D) None of the above

36. The range of values that correlation coefficients can take can be:

A) –1 to +1

B) zero to +1

C) –infinity to +infinity

D) zero to +infinity

37. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient between the two stocks is:

A) +1

B) 0

C) –0.5

D) –1

38. The “beta” is a measure of:

A) Unique risk

B) Market risk

C) Total risk

D) None of the above

39. The variance or standard deviation is a measure of:

A) Total risk

B) Unique risk

C) Market risk

D) None of the above

40. The beta of market portfolio is:

A) 0

B) +0.5

C) +1.0

D) –1.0

41. The beta of a risk-free portfolio is:

A) 0

B) +0.5

C) +1.0

D) –1.0

42. 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) 10%

B) 20%

C) 30%

D) 40%

E) none of the above

43. 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) 0.9

B) 1.0

C) 1.1

D) 0.6

44. 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

45. 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

46. The three year annual return for stock B comes out to be 0%, 10% and 26%. Three year annual returns for the market portfolios are +6%, 18%, 24%. Calculate the beta for the stock.

A) 1.36

B) 0.74

C) 0

D) None of the above

**True/False Questions**

T F 47. Treasury bills have provided the lowest average return between 1926-1997.

T F 48. Risk premium is the difference between the security return and the Treasury bill return.

T F 49. The standard statistical measures of spread are variance and standard deviation.

T F 50. Diversification reduces risk because prices of different securities do not move exactly together.

T F 51. The risk that cannot be eliminated by diversification is called market risk.

T F 52. The risk that cannot be eliminated by diversification is called unique risk.

T F 53. The average beta of all stocks is zero.

T F 54. A portfolio with a beta of zero offers an expected return of zero.

T F 55. Beta of a well-diversified portfolio is equal to the value weighted average beta of the securities included in the portfolio.

**Short Answer Questions**

56. Define the term risk premium.

57. Briefly explain the term “variance” of the returns.

58. Briefly explain how diversification reduces risk.

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

60. Discuss the importance of “beta” as a measure of risk.

61. Briefly explain how “beta” of a stock is estimated.

62. What is the statistical definition of “beta”?

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

64. Briefly explain how individual securities affect portfolio risk.

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

66. How can individual investors diversify?