Ch. 8

c. Suppose you plotted the returns of a given stock against those of the market, and you found that the slope of the regression line was negative. The CAPM would indicate that the required rate of return on the stock should be less than the risk-free rate for a well-diversified investor, assuming investors expect the observed relationship to continue on into the future.

100. Which of the following statements is CORRECT?

a. The y-axis intercept would decline, and the slope would increase.

101. Other things held constant, if the expected inflation rate decreases and investors also become more risk averse, the Security Market Line would be affected as follows:

d. The required return will increase for stocks that have a beta less than 1.0 but decline for stocks that have a beta greater than 1.0.

102. Assume that the risk-free rate, rRF, increases but the market risk premium, (rM − rRF), declines with the net effect being that the overall required return on the market, rM , remains constant. Which of the following statements is CORRECT?

d. The prices of all stocks would decline, but the decline would be greatest for high-beta stocks.

103. Assume that to cool off the economy and decrease expectations for inflation, the Federal Reserve tightened the money supply, causing an increase in the risk-free rate, rRF. Investors also became concerned that the Fed's actions would lead to a recession, and that led to an increase in the market risk premium, (rM − rRF). Under these conditions, with other things held constant, which of the following statements is most correct?

e. If a stock's returns are negatively correlated with returns on most other stocks, the stock's beta will be negative.

104. Which of the following statements is CORRECT?

a. The required rate of return for an average stock will increase by an amount equal to the increase in the market risk premium.

105. Assume that investors have recently become more risk averse, so the market risk premium has increased. Also, assume that the risk-free rate and expected inflation have not changed. Which of the following is most likely to occur?

e. An increase in expected inflation, combined with a constant real risk-free rate and a constant market risk premium, would lead to identical increases in the required returns on a riskless asset and on an average stock, other things held constant.

106. Which of the following statements is CORRECT?

a. The expected rate of return must be equal to the required rate of return; that is,

107. For markets to be in equilibrium, that is, for there to be no strong pressure for prices to depart from their current levels,

d. The SML relates a stock's required return to its market risk. The slope and intercept of this line cannot be controlled by the firms' managers, but managers can influence their firms' positions on the line by such actions as changing the firm's capital structure or the type of assets it employs.

108. Which of the following statements is CORRECT?

b. Company X has a lower coefficient of variation than Company Y.

109. You observe the following information regarding Companies X and Y: • Company X has a higher expected return than Company Y. • Company X has a lower standard deviation of returns than Company Y. • Company X has a higher beta than Company Y. Given this information, which of the following statements is CORRECT?

c. Portfolio P has more market risk than Stock A but less market risk than B.

110. Stocks A and B both have an expected return of 10% and a standard deviation of returns of 25%. Stock A has a beta of 0.8 and Stock B has a beta of 1.2. The correlation coefficient, r, between the two stocks is +0.6. Portfolio P has 50% invested in Stock A and 50% invested in B. Which of the following statements is CORRECT?

d. If the risk-free rate remains unchanged but the market risk premium increases by 2%, your portfolio's required return will increase by more than 2% RATIONALE: d is correct. The portfolio's beta is 1.08. Therefore, if the market risk premium increases by 2.0% the portfolio's required return will increase by 2.16%.

111. The risk-free rate is 6% and the market risk premium is 5%. Your $1 million portfolio consists of $700,000 invested in a stock that has a beta of 1.2 and $300,000 invested in a stock that has a beta of 0.8. Which of the following statements is CORRECT?

e. Assume that the required rate of return on the market, rM , is given and fixed at 10%. If the yield curve were upward sloping, then the Security Market Line (SML) would have a steeper slope if 1-year Treasury securities were used as the risk-free rate than if 30-year Treasury bonds were used for rRF.

114. Which of the following statements is CORRECT?

d. Coefficient of variation; beta.

51. Which is the best measure of risk for a single asset held in isolation, and which is the best measure for an asset held in a diversified portfolio?

c. Stock B.

52. A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?

c. The beta of an "average stock," or "the market," can change over time, sometimes drastically.

53. Which of the following is NOT a potential problem when estimating and using betas, i.e., which statement is FALSE?

c. The beta coefficient of a stock is normally found by regressing past returns on a stock against past market returns. One could also construct a scatter diagram of returns on the stock versus those on the market, estimate the slope of the line of best fit, and use it as beta. However, this historical beta may differ from the beta that exists in the future.

54. Which of the following statements is CORRECT?

b. Suppose the returns on two stocks are negatively correlated. One has a beta of 1.2 as determined in a regression analysis using data for the last 5 years, while the other has a beta of −0.6. The returns on the stock with the negative beta must have been negatively correlated with returns on most other stocks during that 5-year period.

55. Which of the following statements is CORRECT?

e. During a period when a company is undergoing a change such as increasing its use of leverage or taking on riskier projects, the calculated historical beta may be drastically different from the beta that will exist in the future.

56. Which of the following statements is CORRECT?

e. In equilibrium, the expected return on Stock A will be greater than that on B.

57. Stock A's beta is 1.5 and Stock B's beta is 0.5. Which of the following statements must be true, assuming the CAPM is correct.

c. If the expected rate of inflation increases but the market risk premium is unchanged, the required returns on the two stocks should increase by the same amount.

58. Stock X has a beta of 0.5 and Stock Y has a beta of 1.5. Which of the following statements must be true, according to the CAPM?

d. bA < 0; bB = 0.

59. You have the following data on (1) the average annual returns of the market for the past 5 years and (2) similar information on Stocks A and B. Which of the possible answers best describes the historical betas for A and B? Years Market Stock A Stock B 1 0.03 0.16 0.05 2 −0.05 0.20 0.05 3 0.01 0.18 0.05 4 −0.10 0.25 0.05 5 0.06 0.14 0.05

e. An investor can eliminate virtually all diversifiable risk if he or she holds a very large, well-diversified portfolio of stocks.

60. Which of the following statements is CORRECT?

c. If you formed a portfolio that consisted of all stocks with betas less than 1.0, which is about half of all stocks, the portfolio would itself have a beta coefficient that is equal to the weighted average beta of the stocks in the portfolio, and that portfolio would have less risk than a portfolio that consisted of all stocks in the market.

61. Which of the following statements is CORRECT?

c. among the factors that are responsible for market risk.

62. Inflation, recession, and high interest rates are economic events that are best characterized as being

e. A security's beta measures its non-diversifiable, or market, risk relative to that of an average stock.

63. Which of the following statements is CORRECT?

b. Diversifiable risk can be reduced by forming a large portfolio, but normally even highly-diversified portfolios are subject to market (or systematic) risk.

64. Which of the following statements is CORRECT?

b. A portfolio that consists of 40 stocks that are not highly correlated with "the market" will probably be less risky than a portfolio of 40 stocks that are highly correlated with the market, assuming the stocks all have the same standard deviations.

65. Which of the following statements is CORRECT?

d. Portfolio ABC's expected return is 10.66667%.

66. Consider the following information for three stocks, A, B, and C. The stocks' returns are positively but not perfectly positively correlated with one another, i.e., the correlations are all between 0 and 1. Expected Standard Stock Return Deviation Beta A 10% 20% 1.0 B 10% 10% 1.0 C 12% 12% 1.4 Portfolio AB has half of its funds invested in Stock A and half in Stock B. Portfolio ABC has one third of its funds invested in each of the three stocks. The risk-free rate is 5%, and the market is in equilibrium, so required returns equal expected returns. Which of the following statements is CORRECT?

b. A portfolio with a large number of randomly selected stocks would have more market risk than a single stock that has a beta of 0.5, assuming that the stock's beta was correctly calculated and is stable.

67. Which of the following statements is CORRECT?

d. The beta of the portfolio is equal to the weighted average of the betas of the individual stocks.

68. For a portfolio of 40 randomly selected stocks, which of the following is most likely to be true?

a. Adding more such stocks will reduce the portfolio's unsystematic, or diversifiable, risk.

69. Which of the following statements best describes what you should expect if you randomly select stocks and add them to your portfolio?

b. The combined portfolio's beta will be equal to a simple weighted average of the betas of the two individual portfolios, 1.0; its expected return will be equal to a simple weighted average of the expected returns of the two individual portfolios, 10.0%; and its standard deviation will be less than the simple average of the two portfolios' standard deviations, 25%.

70. Bob has a $50,000 stock portfolio with a beta of 1.2, an expected return of 10.8%, and a standard deviation of 25%. Becky also has a $50,000 portfolio, but it has a beta of 0.8, an expected return of 9.2%, and a standard deviation that is also 25%. The correlation coefficient, r, between Bob's and Becky's portfolios is zero. If Bob and Becky marry and combine their portfolios, which of the following best describes their combined $100,000 portfolio?

c. Your portfolio has a beta equal to 1.6, and its expected return is 15%.

71. Your portfolio consists of $50,000 invested in Stock X and $50,000 invested in Stock Y. Both stocks have an expected return of 15%, betas of 1.6, and standard deviations of 30%. The returns of the two stocks are independent, so the correlation coefficient between them, rXY, is zero. Which of the following statements best describes the characteristics of your 2-stock portfolio?

a. The diversifiable risk of your portfolio will likely decline, but the expected market risk should not change.

72. Which of the following is most likely to occur as you add randomly selected stocks to your portfolio, which currently consists of 3 average stocks?

c. Dick's portfolio will have more diversifiable risk, the same market risk, and thus more total risk than Jane's portfolio, but the required (and expected) returns will be the same on both portfolios.

73. Jane has a portfolio of 20 average stocks, and Dick has a portfolio of 2 average stocks. Assuming the market is in equilibrium, which of the following statements is CORRECT?

d. Portfolio P has a standard deviation that is less than 25%.

74. Stocks A and B each have an expected return of 12%, a beta of 1.2, and a standard deviation of 25%. The returns on the two stocks have a correlation of +0.6. Portfolio P has 50% in Stock A and 50% in Stock B. Which of the following statements is CORRECT?

e. Portfolio AC has a standard deviation that is less than 25%.

75. Stocks A, B, and C all have an expected return of 10% and a standard deviation of 25%. Stocks A and B have returns that are independent of one another, i.e., their correlation coefficient, r, equals zero. Stocks A and C have returns that are negatively correlated with one another, i.e., r is less than 0. Portfolio AB is a portfolio with half of its money invested in Stock A and half in Stock B. Portfolio AC is a portfolio with half of its money invested in Stock A and half invested in Stock C. Which of the following statements is CORRECT?

b. The portfolio's expected return is 15%.

76. Stocks A and B each have an expected return of 15%, a standard deviation of 20%, and a beta of 1.2. The returns on the two stocks have a correlation coefficient of +0.6. You have a portfolio that consists of 50% A and 50% B. Which of the following statements is CORRECT?

d. Portfolio P's expected return is equal to the expected return on Stock B.

77. Stock A has a beta of 0.8, Stock B has a beta of 1.0, and Stock C has a beta of 1.2. Portfolio P has 1/3 of its value invested in each stock. Each stock has a standard deviation of 25%, and their returns are independent of one another, i.e., the correlation coefficients between each pair of stocks is zero. Assuming the market is in equilibrium, which of the following statements is CORRECT?

c. The beta of the portfolio is lower than the lowest of the three betas.

78. In a portfolio of three randomly selected stocks, which of the following could NOT be true, i.e., which statement is false?

b. If the marginal investor becomes more risk averse, the required return on Stock B will increase by more than the required return on Stock A.

79. Stock A has a beta = 0.8, while Stock B has a beta = 1.6. Which of the following statements is CORRECT?

b. The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is overvalued.

80. Stock A has an expected return of 12%, a beta of 1.2, and a standard deviation of 20%. Stock B also has a beta of 1.2, but its expected return is 10% and its standard deviation is 15%. Portfolio AB has $900,000 invested in Stock A and $300,000 invested in Stock B. The correlation between the two stocks' returns is zero (that is, rA,B = 0). Which of the following statements is CORRECT?

e. Portfolio P has the same required return as the market (rM ).

81. Stock X has a beta of 0.7 and Stock Y has a beta of 1.3. The standard deviation of each stock's returns is 20%. The stocks' returns are independent of each other, i.e., the correlation coefficient, r, between them is zero. Portfolio P consists of 50% X and 50% Y. Given this information, which of the following statements is CORRECT?

d. If the market risk premium increases by 1%, then the required return will increase by 1% for a stock that has a beta of 1.0.

82. Which of the following statements is CORRECT? (Assume that the risk-free rate is a constant.)

c. Small-company stocks, large-company stocks, long-term corporate bonds, long-term government bonds, U.S. Treasury bills.

83. Over the past 87 years, we have observed that investments with the highest average annual returns also tend to have the highest standard deviations of annual returns. This observation supports the notion that there is a positive correlation between risk and return. Which of the following answers correctly ranks investments from highest to lowest risk (and return), where the security with the highest risk is shown first, the one with the lowest risk last?

c. The required return will fall for all stocks, but it will fall more for stocks with higher betas.

84. During the coming year, the market risk premium (rM − rRF), is expected to fall, while the risk-free rate, rRF, is expected to remain the same. Given this forecast, which of the following statements is CORRECT?

c. If Stock A's required return is 11%, then the market risk premium is 5%.

85. The risk-free rate is 6%; Stock A has a beta of 1.0; Stock B has a beta of 2.0; and the market risk premium, rM − rRF, is positive. Which of the following statements is CORRECT?

b. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

86. Assume that in recent years both expected inflation and the market risk premium (rM − rRF) have declined. Assume also that all stocks have positive betas. Which of the following would be most likely to have occurred as a result of these changes?

a. If a stock has a negative beta, its required return under the CAPM would be less than 5%.

87. Assume that the risk-free rate is 5%. Which of the following statements is CORRECT?

b. If both expected inflation and the market risk premium (rM − rRF) increase, the required return on Stock HB will increase by more than that on Stock LB.

88. Stock HB has a beta of 1.5 and Stock LB has a beta of 0.5. The market is in equilibrium, with required returns equaling expected returns. Which of the following statements is CORRECT?

b. The required return on Stock A will increase by less than the increase in the market risk premium, while the required return on Stock C will increase by more than the increase in the market risk premium.

89. Stock A has a beta of 0.8, Stock B has a beta of 1.0, and Stock C has a beta of 1.2. Portfolio P has equal amounts invested in each of the three stocks. Each of the stocks has a standard deviation of 25%. The returns on the three stocks are independent of one another (i.e., the correlation coefficients all equal zero). Assume that there is an increase in the market risk premium, but the risk-free rate remains unchanged. Which of the following statements is CORRECT?

e. If the risk-free rate rises by 0.5% but the market risk premium declines by that same amount, then the required rate of return on an average stock will remain unchanged, but required returns on stocks with betas less than 1.0 will rise.

90. Which of the following statements is CORRECT?

a. An index fund with beta = 1.0 should have a required return of 11%.

91. Assume that the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?

a. The slope of the security market line is equal to the market risk premium.

92. Which of the following statements is CORRECT?

e. The slope of the security market line is equal to the market risk premium, (rM − rRF).

93. Which of the following statements is CORRECT?

e. Portfolio P has a beta of 1.0.

94. Stock A has a beta of 1.2 and a standard deviation of 20%. Stock B has a beta of 0.8 and a standard deviation of 25%. Portfolio P has $200,000 consisting of $100,000 invested in Stock A and $100,000 in Stock B. Which of the following statements is CORRECT? (Assume that the stocks are in equilibrium.)

d. If the risk-free rate increases while the market risk premium remains constant, then the required return on an average stock will increase.

95. Nile Food's stock has a beta of 1.4, while Elba Eateries' stock has a beta of 0.7. Assume that the risk-free rate, rRF, is 5.5% and the market risk premium, (rM − rRF), equals 4%. Which of the following statements is CORRECT?

d. If the market risk premium declines but expected inflation is unchanged, the required return on both stocks will decrease, but the decrease will be greater for Stock Y.

96. Stock X has a beta of 0.6, while Stock Y has a beta of 1.4. Which of the following statements is CORRECT?

a. The required return would increase for both stocks but the increase would be greater for Stock B than for Stock A.

97. Stock A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P is invested in Stock A and 50% is invested in Stock B. If the market risk premium (rM − rRF) were to increase but the risk-free rate (rRF) remained constant, which of the following would occur?

a. The required return on Portfolio P would increase by 1%.

98. Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P has 50% invested in both A and B. Which of the following would occur if the market risk premium increased by 1% but the risk-free rate remained constant?

e. The required return on a stock with a positive beta < 1.0 will decline.

99. Assume that the risk-free rate remains constant, but the market risk premium declines. Which of the following is most likely to occur?