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53. Which of the following is NOT a potential problem when estimating and using betas, i.e., which statement is FALSE?
a. The fact that a security or project may not have a past history that can be used as the basis for calculating beta.
b. Sometimes, during a period when the company is undergoing a change such as toward more leverage or riskier
assets, the calculated beta will be drastically different from the “true” or “expected future” beta.
c. The beta of an “average stock,” or “the market,” can change over time, sometimes drastically.
d. Sometimes the past data used to calculate beta do not reflect the likely risk of the firm for the future because
conditions have changed.
e. The beta coefficient of a stock is normally found by regressing past returns on a stock against past market returns.
This calculated historical beta may differ from the beta that exists in the future.
54. Which of the following statements is CORRECT?
a. The beta of a portfolio of stocks is always smaller than the betas of any of the individual stocks.
b. If you found a stock with a zero historical beta and held it as the only stock in your portfolio, you would by
definition have a riskless portfolio.
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.
d. The beta of a portfolio of stocks is always larger than the betas of any of the individual stocks.
e. It is theoretically possible for a stock to have a beta of 1.0. If a stock did have a beta of 1.0, then, at least in
theory, its required rate of return would be equal to the risk-free (default-free) rate of return, rRF.
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61. Which of the following statements is CORRECT?
a. If you add enough randomly selected stocks to a portfolio, you can completely eliminate all of the market risk
from the portfolio.
b. If you were restricted to investing in publicly traded common stocks, yet you wanted to minimize the riskiness of
your portfolio as measured by its beta, then according to the CAPM theory you should invest an equal amount of money
in each stock in the market. That is, if there were 10,000 traded stocks in the world, the least risky possible portfolio
would include some shares of each one.
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.
d. Market risk can be eliminated by forming a large portfolio, and if some Treasury bonds are held in the portfolio,
the portfolio can be made to be completely riskless.
e. A portfolio that consists of all stocks in the market would have a required return that is equal to the riskless rate.
62. Inflation, recession, and high interest rates are economic events that are best characterized as being
a. systematic risk factors that can be diversified away.
b. company-specific risk factors that can be diversified away.
c. among the factors that are responsible for market risk.
d. risks that are beyond the control of investors and thus should not be considered by security analysts or portfolio
managers.
e. irrelevant except to governmental authorities like the Federal Reserve.
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63. Which of the following statements is CORRECT?
a. A stock’s beta is less relevant as a measure of risk to an investor with a well-diversified portfolio than to an
investor who holds only that one stock.
b. If an investor buys enough stocks, he or she can, through diversification, eliminate all of the diversifiable risk
inherent in owning stocks. Therefore, if a portfolio contained all publicly traded stocks, it would be essentially riskless.
c. The required return on a firm’s common stock is, in theory, determined solely by its market risk. If the market risk
is known, and if that risk is expected to remain constant, then no other information is required to specify the firm’s
required return.
d. Portfolio diversification reduces the variability of returns (as measured by the standard deviation) of each
individual stock held in a portfolio.
e. A security’s beta measures its non-diversifiable, or market, risk relative to that of an average stock.
64. Which of the following statements is CORRECT?
a. A large portfolio of randomly selected stocks will always have a standard deviation of returns that is less than the
standard deviation of a portfolio with fewer stocks, regardless of how the stocks in the smaller portfolio are selected.
b. Diversifiable risk can be reduced by forming a large portfolio, but normally even highly-diversified portfolios are
subject to market (or systematic) risk.
c. A large portfolio of randomly selected stocks will have a standard deviation of returns that is greater than the
standard deviation of a 1-stock portfolio if that one stock has a beta less than 1.0.
d. A large portfolio of stocks whose betas are greater than 1.0 will have less market risk than a single stock with a
beta = 0.8.
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e. If you add enough randomly selected stocks to a portfolio, you can completely eliminate all of the market risk
from the portfolio.
65. Which of the following statements is CORRECT?
a. A two-stock portfolio will always have a lower standard deviation than a one-stock portfolio.
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.
c. A two-stock portfolio will always have a lower beta than a one-stock portfolio.
d. If portfolios are formed by randomly selecting stocks, a 10-stock portfolio will always have a lower beta than a
one-stock portfolio.
e. A stock with an above-average standard deviation must also have an above-average beta.
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.
Stock Expected
Return Standard
Deviation
Beta
A 10% 20% 1.0
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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?
a. Portfolio AB has a standard deviation of 20%.
b. Portfolio AB’s coefficient of variation is greater than 2.0.
c. Portfolio AB’s required return is greater than the required return on Stock A.
d. Portfolio ABC’s expected return is 10.66667%.
e. Portfolio ABC has a standard deviation of 20%.
67. Which of the following statements is CORRECT?
a. If the returns on two stocks are perfectly positively correlated (i.e., the correlation coefficient is +1.0) and these
stocks have identical standard deviations, an equally weighted portfolio of the two stocks will have a standard deviation
that is less than that of the individual stocks.
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.
c. If a stock has a negative beta, its expected return must be negative.
d. A portfolio with a large number of randomly selected stocks would have less market risk than a single stock that
has a beta of 0.5.
e. According to the CAPM, stocks with higher standard deviations of returns must also have higher expected
returns.
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68. For a portfolio of 40 randomly selected stocks, which of the following is most likely to be true?
a. The riskiness of the portfolio is greater than the riskiness of each of the stocks if each was held in isolation.
b. The riskiness of the portfolio is the same as the riskiness of each stock if it was held in isolation.
c. The beta of the portfolio is less than the weighted average of the betas of the individual stocks.
d. The beta of the portfolio is equal to the weighted average of the betas of the individual stocks.
e. The beta of the portfolio is larger than the weighted average of the betas of the individual stocks.
69. Which of the following statements best describes what you should expect if you randomly select stocks and add them
to your portfolio?
a. Adding more such stocks will reduce the portfolio’s unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio’s expected rate of return.
c. Adding more such stocks will reduce the portfolio’s beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio’s risk.
e. Adding more such stocks will reduce the portfolio’s market risk but not its unsystematic risk.
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?
a. The combined portfolio’s expected return will be less than the simple weighted average of the expected returns of
the two individual portfolios, 10.0%.
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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%.
c. The combined portfolio’s expected return will be greater than the simple weighted average of the expected returns
of the two individual portfolios, 10.0%.
d. The combined portfolio’s standard deviation will be greater than the simple average of the two portfolios’ standard
deviations, 25%.
e. The combined portfolio’s standard deviation will be equal to a simple average of the two portfolios’ standard
deviations, 25%.
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. Your portfolio has a standard deviation of 30%, and its expected return is 15%.
b. Your portfolio has a standard deviation less than 30%, and its beta is greater than 1.6.
c. Your portfolio has a beta equal to 1.6, and its expected return is 15%.
d. Your portfolio has a beta greater than 1.6, and its expected return is greater than 15%.
e. Your portfolio has a standard deviation greater than 30% and a beta equal to 1.6.
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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?
a. The diversifiable risk of your portfolio will likely decline, but the expected market risk should not change.
b. The expected return of your portfolio is likely to decline.
c. The diversifiable risk will remain the same, but the market risk will likely decline.
d. Both the diversifiable risk and the market risk of your portfolio are likely to decline.
e. The total risk of your portfolio should decline, and as a result, the expected rate of return on the portfolio should
also decline.
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?
a. Jane’s portfolio will have less diversifiable risk and also less market risk than Dick’s portfolio.
b. The required return on Jane’s portfolio will be lower than that on Dick’s portfolio because Jane’s portfolio will
have less total risk.
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.
d. If the two portfolios have the same beta, their required returns will be the same, but Jane’s portfolio will have less
market risk than Dick’s.
e. The expected return on Jane’s portfolio must be lower than the expected return on Dick’s portfolio because Jane is
more diversified.
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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?
a. Portfolio P has a beta that is greater than 1.2.
b. Portfolio P has a standard deviation that is greater than 25%.
c. Portfolio P has an expected return that is less than 12%.
d. Portfolio P has a standard deviation that is less than 25%.
e. Portfolio P has a beta that is less than 1.2.
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?
a. Portfolio AC has an expected return that is less than 10%.
b. Portfolio AC has an expected return that is greater than 25%.
c. Portfolio AB has a standard deviation that is greater than 25%.
d. Portfolio AB has a standard deviation that is equal to 25%.
e. Portfolio AC has a standard deviation that is less than 25%.
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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?
a. The portfolio’s beta is less than 1.2.
b. The portfolio’s expected return is 15%.
c. The portfolio’s standard deviation is greater than 20%.
d. The portfolio’s beta is greater than 1.2.
e. The portfolio’s standard deviation is 20%.
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?
a. Portfolio P’s expected return is greater than the expected return on Stock B.
b. Portfolio P’s expected return is equal to the expected return on Stock A.
c. Portfolio P’s expected return is less than the expected return on Stock B.
d. Portfolio P’s expected return is equal to the expected return on Stock B.
e. Portfolio P’s expected return is greater than the expected return on Stock C.
78. In a portfolio of three randomly selected stocks, which of the following could NOT be true, i.e., which statement is
false?
a. The riskiness of the portfolio is less than the riskiness of each of the stocks if they were held in isolation.
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b. The riskiness of the portfolio is greater than the riskiness of one or two of the stocks.
c. The beta of the portfolio is lower than the lowest of the three betas.
d. The beta of the portfolio is higher than the beta of one or two of the stocks in the portfolio.
e. The beta of the portfolio is calculated as a weighted average of the individual stocks’ betas.
79. Stock A has a beta = 0.8, while Stock B has a beta = 1.6. Which of the following statements is CORRECT?
a. Stock B’s required return is double that of Stock A’s.
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.
c. An equally weighted portfolio of Stocks A and B will have a beta lower than 1.2.
d. If the marginal investor becomes more risk averse, the required return on Stock A will increase by more than the
required return on Stock B.
e. If the risk-free rate increases but the market risk premium remains constant, the required return on Stock A will
increase by more than that on Stock B.
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?
a. Portfolio AB’s standard deviation is 17.5%.
b. The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is overvalued.
c. The stocks are not in equilibrium based on the CAPM; if A is valued correctly, then B is undervalued.
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d. Portfolio AB’s expected return is 11.0%.
e. Portfolio AB’s beta is less than 1.2.
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?
a. Portfolio P has a standard deviation of 20%.
b. The required return on Portfolio P is equal to the market risk premium (rM – rRF).
c. Portfolio P has a beta of 0.7.
d. Portfolio P has a beta of 1.0 and a required return that is equal to the riskless rate, rRF.
e. Portfolio P has the same required return as the market (rM).
82. Which of the following statements is CORRECT? (Assume that the risk-free rate is a constant.)
a. If the market risk premium increases by 1%, then the required return will increase for stocks that have a beta
greater than 1.0, but it will decrease for stocks that have a beta less than 1.0.
b. The effect of a change in the market risk premium depends on the slope of the yield curve.
c. If the market risk premium increases by 1%, then the required return on all stocks will rise by 1%.
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.
e. The effect of a change in the market risk premium depends on the level of the risk-free rate.
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d. The required return for all stocks will fall by the same amount.
e. The required return will fall for all stocks, but it will fall less for stocks with higher betas.
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?
a. If the risk-free rate increases but the market risk premium stays unchanged, Stock B’s required return will increase
by more than Stock A’s.
b. Stock B’s required rate of return is twice that of Stock A.
c. If Stock A’s required return is 11%, then the market risk premium is 5%.
d. If Stock B’s required return is 11%, then the market risk premium is 5%.
e. If the risk-free rate remains constant but the market risk premium increases, Stock A’s required return will
increase by more than Stock B’s.
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. The required returns on all stocks have fallen, but the decline has been greater for stocks with lower betas.
b. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.
c. The average required return on the market, rM, has remained constant, but the required returns have fallen for
stocks that have betas greater than 1.0.
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d. Required returns have increased for stocks with betas greater than 1.0 but have declined for stocks with betas less
than 1.0.
e. The required returns on all stocks have fallen by the same amount.
87. Assume that the risk-free rate is 5%. Which of the following statements is CORRECT?
a. If a stock has a negative beta, its required return under the CAPM would be less than 5%.
b. If a stock’s beta doubled, its required return under the CAPM would also double.
c. If a stock’s beta doubled, its required return under the CAPM would more than double.
d. If a stock’s beta were 1.0, its required return under the CAPM would be 5%.
e. If a stock’s beta were less than 1.0, its required return under the CAPM would be less than 5%.
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?
a. If expected inflation remains constant but the market risk premium (rM – rRF) declines, the required return of
Stock LB will decline but the required return of Stock HB will increase.
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.
c. If both expected inflation and the market risk premium (rM – rRF) increase, the required returns of both stocks will
increase by the same amount.
d. Since the market is in equilibrium, the required returns of the two stocks should be the same.
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e. If expected inflation remains constant but the market risk premium (rM – rRF) declines, the required return of
Stock HB will decline but the required return of Stock LB will increase.
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?
a. The required return of all stocks will remain unchanged since there was no change in their betas.
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.
c. The required return on the average stock will remain unchanged, but the returns of riskier stocks (such as Stock
C) will increase while the returns of safer stocks (such as Stock A) will decrease.
d. The required returns on all three stocks will increase by the amount of the increase in the market risk premium.
e. The required return on the average stock will remain unchanged, but the returns on riskier stocks (such as Stock
C) will decrease while the returns on safer stocks (such as Stock A) will increase.
90. Which of the following statements is CORRECT?
a. If a company’s beta doubles, then its required rate of return will also double.
b. Other things held constant, if investors suddenly become convinced that there will be deflation in the economy,
then the required returns on all stocks should increase.
c. If a company’s beta were cut in half, then its required rate of return would also be halved.
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d. If the risk-free rate rises by 0.5% but the market risk premium declines by that same amount, then the required
rates of return on stocks with betas less than 1.0 will decline while returns on stocks with betas above 1.0 will increase.
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.
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. An index fund with beta = 1.0 should have a required return of 11%.
b. If a stock has a negative beta, its required return must also be negative.
c. An index fund with beta = 1.0 should have a required return less than 11%.
d. If a stock’s beta doubles, its required return must also double.
e. An index fund with beta = 1.0 should have a required return greater than 11%.
92. Which of the following statements is CORRECT?
a. The slope of the security market line is equal to the market risk premium.
b. Lower beta stocks have higher required returns.
c. A stock’s beta indicates its diversifiable risk.
d. Diversifiable risk cannot be completely diversified away.
e. Two securities with the same stand-alone risk must have the same betas.