CHAPTER 10: ARBITRAGE PRICING THEORY AND MULTIFACTOR MODELS OF RISK AND RETURN

1. ___________ a relationship between expected return and risk. C. Both CAPM and APT stipulate

2. ___________ a relationship between expected return and risk. D. APT, CAPM, and CCAPM stipulate

3. In a multi-factor APT model, the coefficients on the macro factors are often called ______.
B. factor sensitivities
D. factor betas
E. B and D

4. In a multi-factor APT model, the coefficients on the macro factors are often called ______. D. factor betas

5. In a multi-factor APT model, the coefficients on the macro factors are often called ______. D. factor
loadings

6. Which pricing model provides no guidance concerning the determination of the risk premium on factor
portfolios? B. The multifactor APT

7. An arbitrage opportunity exists if an investor can construct a __________ investment portfolio that will yield
a sure profit. C. zero

8. The APT was developed in 1976 by ____________. C. Ross

9. A _________ portfolio is a well-diversified portfolio constructed to have a beta of 1 on one of the factors and
a beta of 0 on any other factor. A. factor

10. The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called
___________. A. arbitrage

11. In developing the APT, Ross assumed that uncertainty in asset returns was a result of E. both A and B

12. The ____________ provides an unequivocal statement on the expected return-beta relationship for all
assets, whereas the _____________ implies that this relationship holds for all but perhaps a small number of
securities. C. CAPM, APT

13. Consider a single factor APT. Portfolio A has a beta of 1.0 and an expected return of 16%. Portfolio B has
a beta of 0.8 and an expected return of 12%. The risk-free rate of return is 6%. If you wanted to take
advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long
position in portfolio _______.
C. B, A
A: 16% = 1.0F + 6%; F = 10%;
B: 12% = 0.8F + 6%: F = 7.5%;

14. Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B
has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you want to take
advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long
position in portfolio _________.
C. B, A
A: 13% = 10% + 0.2F; F = 15%;
B: 15% = 10% + 0.4F; F = 12.5%;
therefore, short B and take a long position in A.
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15. Consider the one-factor APT. The variance of returns on the factor portfolio is 6%. The beta of a well-
diversified portfolio on the factor is 1.1. The variance of returns on the well-diversified portfolio is approximately
__________. C. 7.3%

16. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The
standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately
__________. B. 1.13

17. Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The
risk-free rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a
beta of __________.
E. none of the above A: 15% = 6% + bF; B: 8% = 6% + 1.0F; F = 12%; thus, beta of A = 9/12 = 0.75.

18. Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on
factor 1 and a beta of .8 on factor 2. The risk premium on the factor 1 portfolio is 3%. The risk-free rate of
return is 6%. What is the risk-premium on factor 2 if no arbitrage opportunities exit?
D. 7.75% 16.4% = 1.4(3%) + .8x + 6%; x = 7.75.

19. Consider the multifactor model APT with two factors. Portfolio A has a beta of 0.75 on factor 1 and a beta
of 1.25 on factor 2. The risk premiums on the factor 1 and factor 2 portfolios are 1% and 7%, respectively. The
risk-free rate of return is 7%. The expected return on portfolio A is __________ if no arbitrage opportunities
exist.
C. 16.5% 7% + 0.75(1%) + 1.25(7%) = 16.5%.

20. Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are
5% and 6%, respectively. Stock A has a beta of 1.2 on factor 1, and a beta of 0.7 on factor 2. The expected
return on stock A is 17%. If no arbitrage opportunities exist, the risk-free rate of return is ___________.
C. 6.8% 17% = x% + 1.2(5%) + 0.7(6%); x = 6.8%.

21. Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor and portfolio B has a beta of 2.0
on the factor. The expected returns on portfolios A and B are 11% and 17%, respectively. Assume that the
risk-free rate is 6% and that arbitrage opportunities exist. Suppose you invested $100,000 in the risk-free
asset, $100,000 in portfolio B, and sold short $200,000 of portfolio A. Your expected profit from this strategy
would be ______________.
C. $1,000
$100,000(0.06) = $6,000 (risk-free position); $100,000(0.17) = $17,000 (portfolio B); -$200,000(0.11) = -
$22,000 (short position, portfolio A); 1,000 profit.

22. Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas of
portfolios A and B are 1.0 and 1.5, respectively. The expected returns on portfolios A and B are 19% and 24%,
respectively. Assuming no arbitrage opportunities exist, the risk-free rate of return must be ____________.
B. 9.0%
A: 19% = rf + 1(F); B:24% = rf + 1.5(F); 5% = .5(F); F = 10%; 24% = rf + 1.5(10); ff = 9%.

23. Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 3%,
respectively. The risk-free rate of return is 10%. Stock A has an expected return of 19% and a beta on factor 1
of 0.8. Stock A has a beta on factor 2 of ________. C. 1.67

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19% = 10% + 5%(0.8) + 3%(x); x = 1.67.

24. Consider the single factor APT. Portfolios A and B have expected returns of 14% and 18%, respectively.
The risk-free rate of return is 7%. Portfolio A has a beta of 0.7. If arbitrage opportunities are ruled out, portfolio
B must have a beta of __________.
C. 1.10
A: 14% = 7% + 0.7F; F = 10; B: 18% = 7% + 10b; b = 1.10.

There are three stocks, A, B, and C. You can either invest in these stocks or short sell them. There are three
possible states of nature for economic growth in the upcoming year; economic growth may be strong,
moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature
are given below:
Stock Strong Growth Moderate Growth Weak Growth
A 39% 17% -5%
B 30% 15% 0%
C 6% 14% 22%

25. If you invested in an equally weighted portfolio of stocks A and B, your portfolio return would be
___________ if economic growth were moderate.
D. 16.0% ​ E(Rp) = 0.5(17%) + 0.5(15%) = 16%.

26. If you invested in an equally weighted portfolio of stocks A and C, your portfolio return would be
____________ if economic growth was strong.
B. 22.5%​ 0.5(39%) + 0.5(6%) = 22.5%.

27. If you invested in an equally weighted portfolio of stocks B and C, your portfolio return would be
_____________ if economic growth was weak.
D. 11.0%​ 0.5(0%) + 0.5(22%) = 11%.

28. If you want to take advantage of a risk-free arbitrage opportunity, you should take a short position in
_________ and a long position in an equally weighted portfolio of _______.
C. C, A and B
E(RA) = (39% + 17% - 5%)/3 = 17%;
E(RB) = (30% + 15% + 0%)/3 = 15%;
E(RC) = (22% + 14% + 6%)/3 = 14%;
E(RP) = -0.5(14%) + 0.5[(17% + 15%)/2]; -7.0% + 8.0% = 1.0%.

Consider the multifactor APT. There are two independent economic factors, F1 and F2. The risk-free rate of
return is 6%. The following information is available about two well-diversified portfolios:
Portfolio β on F1​ β on F2​ Expected Return
A 1 2 19%
B 2 0 12%

29. Assuming no arbitrage opportunities exist, the risk premium on the factor F1 portfolio should be
__________. A. 3%
2A: 38% = 12% + 2.0(RP1) + 4.0(RP2);
B: 12% = 6% + 2.0(RP1) + 0.0(RP2); 26% = 6% + 4.0(RP2); RP2 = 5;
A: 19% = 6% + RP1 + 2.0(5); RP1 = 3%.

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30. Assuming no arbitrage opportunities exist, the risk premium on the factor F2 portfolio should be
___________. C. 5%

31. A zero-investment portfolio with a positive expected return arises when _________.
D. a risk-free arbitrage opportunity exists

32. An investor will take as large a position as possible when an equilibrium price relationship is violated. This
is an example of _________. C. a risk-free arbitrage

33. The APT differs from the CAPM because the APT _________.
D. recognizes multiple systematic risk factors

34. The feature of the APT that offers the greatest potential advantage over the CAPM is the
______________.
A. use of several factors instead of a single market index to explain the risk-return relationship

35. In terms of the risk/return relationship

A. only factor risk commands a risk premium in market equilibrium.
B. only systematic risk is related to expected returns.
C. only nonsystematic risk is related to expected returns.
D. A and B.

36. The following factors might affect stock returns:

A. the business cycle.
B. interest rate fluctuations.
C. inflation rates.
D. all of the above.

37. Advantage(s) of the APT is(are)

B. that the model does not require a specific benchmark market portfolio.

38. Portfolio A has expected return of 10% and standard deviation of 19%. Portfolio B has expected return of
12% and standard deviation of 17%. Rational investors will
B. Sell A short and buy B.

39. An important difference between CAPM and APT is

A. CAPM depends on risk-return dominance; APT depends on a no arbitrage condition.
B. CAPM assumes many small changes are required to bring the market back to equilibrium; APT assumes a
few large changes are required to bring the market back to equilibrium.
E. both A and B are true.
Under the risk-return dominance argument of CAPM, when an equilibrium price is

40. A professional who searches for mispriced securities in specific areas such as merger-target stocks, rather
than one who seeks strict (risk-free) arbitrage opportunities is engaged in B. risk arbitrage.

41. In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its
nonsystematic risk approaches C. zero.

42. A well-diversified portfolio is defined as

A. one that is diversified over a large enough number of securities that the non - systematic variance is
essentially zero.

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43. The APT requires a benchmark portfolio
D. that is well-diversified and lies on the SML.

44. Imposing the no-arbitrage condition on a single-factor security market implies which of the following
statements?
I) the expected return-beta relationship is maintained for all but a small number of well-diversified portfolios.
II) the expected return-beta relationship is maintained for all well-diversified portfolios.
III) the expected return-beta relationship is maintained for all but a small number of individual securities.
IV) the expected return-beta relationship is maintained for all individual securities.
C. II and III are correct.

45. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium
on the first factor portfolio is 4% and the risk premium on the second factor portfolio is 3%. If portfolio A has a
beta of 1.2 on the first factor and .8 on the second factor, what is its expected return?
E. 13.2% ​ 6%+ 1.2 x 4% + .8 (.03) = .132

46. The term "arbitrage" refers to ​ C. earning risk-free economic profits.

47. To take advantage of an arbitrage opportunity, an investor would

I) construct a zero investment portfolio that will yield a sure profit.
II) construct a zero beta investment portfolio that will yield a sure profit.
III) make simultaneous trades in two markets without any net investment.
IV) short sell the asset in the low-priced market and buy it in the high-priced market.
B. I and III

48. The factor F in the APT model represents

D. the deviation from its expected value of a factor that affects all security returns.

49. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has
an average value of (ei) equal to 25% and 50 securities? D. 3.54%

50. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has
an average value of (ei) equal to 20% and 20 securities? C. 4.47%

51. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has
an average value of (ei) equal to 20% and 40 securities? E. 3.16%

52. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has
an average value of (ei) equal to 18% and 250 securities? A. 1.14%

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53. Which of the following is true about the security market line (SML) derived from the APT?
D. The benchmark portfolio for the SML may be any well-diversified portfolio.

54. Which of the following is false about the security market line (SML) derived from the APT?
A. The SML has a downward slope.
B. The SML for the APT shows expected return in relation to portfolio standard deviation.
C. The SML for the APT has an intercept equal to the expected return on the market portfolio.
D. The benchmark portfolio for the SML may be any well-diversified portfolio.
E. A, B, and C are false.

55. If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must
be E. proportional to its beta coefficient.

56. Suppose you are working with two factor portfolios, Portfolio 1 and Portfolio 2. The portfolios have
expected returns of 15% and 6%, respectively. Based on this information, what would be the expected return
on well-diversified portfolio A, if A has a beta of 0.80 on the first factor and 0.50 on the second factor? The
risk-free rate is 3%.
B. 14.1% ​ E(RA) = 3 +0.8 * (15 - 3) + 0.5 * (6 - 3) = 14.1

57. Which of the following is (are) true regarding the APT?

I) The Security Market Line does not apply to the APT.
II) More than one factor can be important in determining returns.
III) Almost all individual securities satisfy the APT relationship.
IV) It doesn't rely on the market portfolio that contains all assets.
A. II, III, and IV

58. In a factor model, the return on a stock in a particular period will be related to
A. factor risk. C. standard deviation of returns.
B. non-factor risk. D. both A and B are true.

59. Which of the following factors did Chen, Roll and Ross not include in their multifactor model?
A. Change in industrial production D. Excess return of long-term government bonds over T-bills
B. Change in expected inflation E. All of the above factors were included in their model.
C. Change in unanticipated inflation

60. Which of the following factors did Chen, Roll and Ross include in their multifactor model?
B. Change in expected inflation C. Change in unanticipated inflation D. B and C

61. Which of the following factors were used by Fama and French in their multi-factor model?
A. Return on the market index
B. Excess return of small stocks over large stocks.
C. Excess return of high book-to-market stocks over low book-to-market stocks.
D. All of the above factors were included in their model.

62. Which of the following factors did Merton not suggest as a likely source of uncertainty that might affect
security returns? C. book-to-market ratios.

63. Which of the following factors did Merton suggest as a likely source of uncertainty that might affect security
returns?

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 A. uncertainties in labor income. C. book-to-market ratios. E. A, B, and D
B. prices of important consumption goods D. changes in future investment opportunities

64. Black argues that past risk premiums on firm-characteristic variables, such as those described by Fama
and French, are problematic because ________. A. they may result from data snooping.

65. Multifactor models seek to improve the performance of the single-index model by
A. modeling the systematic component of firm returns in greater detail.
B. incorporating firm-specific components into the pricing model.
C. allowing for multiple economic factors to have differential effects
D. all of the above are true.

66. Multifactor models such as the one constructed by Chen, Roll, and Ross, can better describe assets'
returns by A. expanding beyond one factor to represent sources of systematic risk.

67. Consider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of
1.1 on factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%,
5% and 2%, respectively. The risk-free rate of return is 3%. The expected return on portfolio A is __________
if no arbitrage opportunities exist. B. 13.4% ​3% + 0.8(3%) + 1.1(5%) + 1.25(2%) = 13.4%.

68. Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 6% and 4%,
respectively. The risk-free rate of return is 4%. Stock A has an expected return of 16% and a beta on factor 1
of 1.3. Stock A has a beta on factor 2 of ________. B. 1.05 16% = 4% + 6%(1.3) + 4%(x); x = 1.05.

69. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 5%, the risk premium
on the first factor portfolio is 4% and the risk premium on the second factor portfolio is 6%. If portfolio A has a
beta of 0.6 on the first factor and 1.8 on the second factor, what is its expected return?
C. 18.2% ​ 00.05 + .6 (.04) + 1.8 (.06) = .182

70. Consider a single factor APT. Portfolio A has a beta of 2.0 and an expected return of 22%. Portfolio B has
a beta of 1.5 and an expected return of 17%. The risk-free rate of return is 4%. If you want to take advantage
of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in
portfolio _______. C. B, A
A: 22% = 2.0F + 4%; F = 9%;
B: 17% = 1.5F + 4%: F = 8.67%;
thus, short B and take a long position in A.

71. Consider the single factor APT. Portfolio A has a beta of 0.5 and an expected return of 12%. Portfolio B
has a beta of 0.4 and an expected return of 13%. The risk-free rate of return is 5%. If you want to take
advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long
position in portfolio _________. B. A, B
A: 12% = 5% + 0.5F; F = 14%;
B: 13% = 5% + 0.4F; F = 20%;
therefore, short A and take a long position in B.

72. Consider the one-factor APT. The variance of returns on the factor portfolio is 9%. The beta of a well-
diversified portfolio on the factor is 1.25. The variance of returns on the well-diversified portfolio is
approximately __________.
D. 14.1%

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73. Consider the one-factor APT. The variance of returns on the factor portfolio is 11%. The beta of a
well-diversified portfolio on the factor is 1.45. The variance of returns on the well-diversified portfolio is
approximately __________.
A. 23.1%

74. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 22%. The
standard deviation on the factor portfolio is 14%. The beta of the well-diversified portfolio is approximately
__________.
D. 1.57

75. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 19%.
The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately
__________.
A. 1.58

76. Consider the single-factor APT. Stocks A and B have expected returns of 12% and 14%, respectively. The
risk-free rate of return is 5%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a
beta of __________.
B. 0.93 ​ A: 12% = 5% + bF; B: 14% = 5% + 1.2F; F = 7.5%; Thus, beta of A = 7/7.5 = 0.93.

77. Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on
factor 1 and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of
return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exit?
A. 9.26%​ 17.6% = 1.45(3.2%) + .86x + 5%; x = 9.26.