Deck 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Question 1

Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios

A)The CAPM
B)The multifactor APT
C)Both the CAPM and the multifactor APT
D)Neither the CAPM nor the multifactor APT
E)None of the options is a true statement.

Answer 1

B
Explanation: The multifactor APT provides no guidance as to the determination of the risk premium on the various factors.The CAPM assumes that the excess market return over the risk-free rate is the market premium in the single factor CAPM.

Question 2

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

A)arbitrage.
B)capital asset pricing.
C)factoring.
D)fundamental analysis.
E)None of the options

Answer 2

A
Explanation: Arbitrage is earning of positive profits with a zero (risk-free) investment.

Question 3

In a multifactor APT model, the coefficients on the macro factors are often called

A)systemic risk.
B)factor sensitivities.
C)idiosyncratic risk.
D)factor betas.
E)factor sensitivities and factor betas.

Answer 3

E
Explanation: The coefficients are called factor betas, factor sensitivities, or factor loadings.

Question 4

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.

A)APT, CAPM
B)APT, OPM
C)CAPM, APT
D)CAPM, OPM

Question 5

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 wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long position in portfolio _________.
A)

A)A, A
B)A, B
C)B, A
D)B, B

Question 6

In a multifactor APT model, the coefficients on the macro factors are often called

A)systemic risk.
B)firm-specific risk.
C)idiosyncratic risk.
D)factor betas.

Question 7

In a multifactor APT model, the coefficients on the macro factors are often called

A)systemic risk.
B)firm-specific risk.
C)idiosyncratic risk.
D)factor loadings.

Question 8

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

A)6.0%.
B)6.5%.
C)6.8%.
D)7.4%.

Question 9

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 exist

A)9.26%
B)3%
C)4%
D)7.75%

Question 10

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

A)3.6%.
B)6.0%.
C)7.3%.
D)10.1%.

Question 11

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

A)0.67.
B)1.00.
C)1.30.
D)1.69.
E)0.75.

Question 12

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

A)positive
B)negative
C)zero
D)All of the options
E)None of the options

Question 13

___________ a relationship between expected return and risk.

A)APT stipulates
B)CAPM stipulates
C)Both CAPM and APT stipulate
D)Neither CAPM nor APT stipulate
E)No pricing model has been found.

Question 14

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 _______.

A)A, A
B)A, B
C)B, A
D)B, B
E)A, the riskless asset

Question 15

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

A)0.80.
B)1.13.
C)1.25.
D)1.56.

Question 16

In developing the APT, Ross assumed that uncertainty in asset returns was a result of

A)a common macroeconomic factor.
B)firm-specific factors.
C)pricing error.
D)a common macroeconomic factor and firm-specific factors.

Question 17

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
B)market
C)index
D)factor and market
E)factor, market, and index

Question 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 exist

A)2%
B)3%
C)4%
D)7.75%

Question 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.

A)13.5%
B)15.0%
C)16.5%
D)23.0%

Question 20

The APT was developed in 1976 by

A)Lintner.
B)Modigliani and Miller.
C)Ross.
D)Sharpe.

Question 21

The APT differs from the CAPM because the APT

A)places more emphasis on market risk.
B)minimizes the importance of diversification.
C)recognizes multiple unsystematic risk factors.
D)recognizes multiple systematic risk factors.

Question 22

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

A)borrow at the risk-free rate and buy A.
B)sell A short and buy B.
C)sell B short and buy A.
D)borrow at the risk-free rate and buy B.
E)lend at the risk-free rate and buy B.

Question 23

An investor will take as large a position as possible when an equilibrium price relationship is violated.This is an example of

A)a dominance argument.
B)the mean-variance efficiency frontier.
C)a risk-free arbitrage.
D)the capital asset pricing model.

Question 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

A)0.45.
B)1.00.
C)1.10.
D)1.22.
E)None of the options

Question 25

There are three stocks, A, B, and

A)A, B and C
B)B, A and C
C)C, A and B
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 (each equally likely to occur); 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:
D)A and B, C

Question 26

There are three stocks, A, B, and

A)3.0%
B)14.5%
C)15.5%
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 (each equally likely to occur); 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:
D)16.0%

Question 27

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.
C)implications for prices derived from CAPM arguments are stronger than prices derived from APT arguments.
D)All of the options are true.
E)Both CAPM depends on risk-return dominance; APT depends on a no arbitrage condition and 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.

Question 28

In terms of the risk/return relationship in the APT,

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)only factor risk commands a risk premium in market equilibrium and only systematic risk is related to expected returns.
E)only factor risk commands a risk premium in market equilibrium and only nonsystematic risk is related to expected returns.

Question 29

The following factors might affect stock returns

A)the business cycle.
B)interest rate fluctuations.
C)inflation rates.
D)All of the options

Question 30

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)-$1,000.

A)Your expected profit from this strategy would be
B)$0.
C)$1,000.
D)$2,000.

Question 31

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: Assuming no arbitrage opportunities exist, the risk premium on the factor F₂ portfolio should be

A)3%.
B)4%.
C)5%.
D)6%.

Question 32

There are three stocks, A, B, and

A)-2.5%
B)0.5%
C)3.0%
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 (each equally likely to occur); 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:
D)11.0%

Question 33

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

A)pure arbitrage.
B)risk arbitrage.
C)option arbitrage.
D)equilibrium arbitrage.

Question 34

Advantage(s) of the APT is(are)

A)that the model provides specific guidance concerning the determination of the risk premiums on the factor portfolios.
B)that the model does not require a specific benchmark market portfolio.
C)that risk need not be considered.
D)that the model provides specific guidance concerning the determination of the risk premiums on the factor portfolios and that the model does not require a specific benchmark market portfolio.
E)that the model does not require a specific benchmark market portfolio and that risk need not be considered.

Question 35

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

A)4.0%.
B)9.0%.
C)14.0%.
D)16.5%.

Question 36

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.
B)identification of anticipated changes in production, inflation, and term structure as key factors in explaining the risk-return relationship.
C)superior measurement of the risk-free rate of return over historical time periods.
D)variability of coefficients of sensitivity to the APT factors for a given asset over time.
E)None of the options

Question 37

There are three stocks, A, B, and

A)17.0%
B)22.5%
C)30.0%
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 (each equally likely to occur); 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:
D)30.5%

Question 38

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: Assuming no arbitrage opportunities exist, the risk premium on the factor F₁ portfolio should be

A)3%.
B)4%.
C)5%.
D)6%.

Question 39

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

A)1.33.
B)1.50.
C)1.67.
D)2.00.

Question 40

A zero-investment portfolio with a positive expected return arises when

A)an investor has downside risk only.
B)the law of prices is not violated.
C)the opportunity set is not tangent to the capital allocation line.
D)a risk-free arbitrage opportunity exists.

Question 41

The APT requires a benchmark portfolio

A)that is equal to the true market portfolio.
B)that contains all securities in proportion to their market values.
C)that need not be well-diversified.
D)that is well-diversified and lies on the SML.
E)that is unobservable.

Question 42

In a factor model, the return on a stock in a particular period will be related to

A)factor risk.
B)nonfactor risk.
C)standard deviation of returns.
D)factor risk and nonfactor risk.
E)None of the options is true.

Question 43

Which of the following factors did Chen, Roll, and Ross include in their multifactor model

A)Change in industrial waste
B)Change in expected inflation
C)Change in unanticipated inflation
D)Change in expected inflation and unanticipated inflation
E)All of the factors were included in their model.

Question 44

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 18% and 250 securities

A)1.14%
B)625%
C)0.5%
D)3.54%
E)3.16%

Question 45

Which of the following is true 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)The SML is not relevant for the APT.

Question 46

The factor F in the APT model represents

A)firm-specific risk.
B)the sensitivity of the firm to that factor.
C)a factor that affects all security returns.
D)the deviation from its expected value of a factor that affects all security returns.
E)a random amount of return attributable to firm events.

Question 47

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 25% and 50 securities

A)12.5%
B)625%
C)0.5%
D)3.54%
E)14.59%

Question 48

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

A)one.
B)infinity.
C)zero.
D)negative one.

Question 49

A well-diversified portfolio is defined as

A)one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero.
B)one that contains securities from at least three different industry sectors.
C)a portfolio whose factor beta equals 1.0.
D)a portfolio that is equally weighted.

Question 50

If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must be

A)inversely proportional to the risk-free rate.
B)inversely proportional to its standard deviation.
C)proportional to its weight in the market portfolio.
D)proportional to its standard deviation.
E)proportional to its beta coefficient.

Question 51

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 20 securities

A)12.5%
B)625%
C)4.47%
D)3.54%
E)14.59%

Question 52

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%.

A)15.2%
B)14.1%
C)13.3%
D)10.7%
E)8.4%

Question 53

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.

A)I and IV
B)I and III
C)II and III
D)I, III, and IV
E)II, III, and IV

Question 54

Which of the following factors did Chen, Roll, and Ross not include in their multifactor model

A)Change in industrial production
B)Change in expected inflation
C)Change in unanticipated inflation
D)Excess return of long-term government bonds over T-bills
E)All of the factors are included in the Chen, Roll, and Ross multifactor model.

Question 55

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.

A)I and III
B)I and IV
C)II and III
D)II and IV
E)Only I is correct.

Question 56

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)The SML has a downward slope, shows expected return in relation to portfolio standard deviation, and has an intercept equal to the expected return on the market portfolio.

Question 57

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

A)7.0%
B)8.0%
C)9.2%
D)13.0%
E)13.2%

Question 58

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
B)II and IV
C)II and III
D)I, II, and IV
E)I, II, III, and IV

Question 59

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 40 securities

A)12.5%
B)625%
C)0.5%
D)3.54%
E)3.16%

Question 60

The term "arbitrage" refers to

A)buying low and selling high.
B)short selling high and buying low.
C)earning risk-free economic profits.
D)negotiating for favorable brokerage fees.
E)hedging your portfolio through the use of options.

Question 61

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%.
B)6.0%.
C)7.3%.
D)14.1%.

Question 62

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

A)0.67.
B)0.93.
C)1.30.
D)1.69.

Question 63

Name three variables that Chen, Roll, and Ross used to measure the impact of macroeconomic factors on security returns.Briefly explain the reasoning behind their model.

Question 64

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.

A)13.5%
B)13.4%
C)16.5%
D)23.0%

Question 65

Discuss the similarities and the differences between the CAPM and the APT with regard to the following factors: capital market equilibrium, assumptions about risk aversion, risk-return dominance, and the number of investors required to restore equilibrium.

Question 66

Discuss arbitrage opportunities in the context of violations of the law of one price.

Question 67

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 options.
E)None of the options is true.

Question 68

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 wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _______.

A)A, A
B)A, B
C)B, A
D)B, B
E)A, the riskless asset

Question 69

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

A)1.33.
B)1.05.
C)1.67.
D)2.00.

Question 70

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

A)0.80.
B)1.13.
C)1.25.
D)1.57.

Question 71

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.
B)1.13.
C)1.25.
D)0.76.

Question 72

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 wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long position in portfolio _________.

A)A, A
B)
B)A, B
C)B, A
D)B, B

Question 73

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

A)3.6%.
B)6.0%.
C)7.3%.
D)14.1%.

Question 74

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

A)7.0%
B)8.0%
C)18.2%
D)13.0%
E)13.2%

Question 75

Discuss the advantages of arbitrage pricing theory (APT) over the capital asset pricing model (CAPM) relative to diversified portfolios.

Question 76

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.
B)they are sources of systematic risk.
C)they can be explained by security characteristic lines.
D)they are more appropriate for a single-factor model.
E)they are macroeconomic factors.

Question 77

Discuss the advantages of the multifactor APT over the single factor APT and the CAPM.What is one shortcoming of the multifactor APT and how does this shortcoming compare to CAPM implications

Question 78

Security A has a beta of 1.0 and an expected return of 12%.Security B has a beta of 0.75 and an expected return of 11%.The risk-free rate is 6%.Explain the arbitrage opportunity that exists; explain how an investor can take advantage of it.Give specific details about how to form the portfolio, what to buy and what to sell.
B.The investor can accomplish this by choosing .75 as the weight in A and .25 in the risk-free asset.This portfolio would have E(r_p) = 0.75(12%) + 0.25(6%) = 10.5%, which is less than B's 11% expected return.The investor should buy B and finance the purchase by short selling A and borrowing at the risk-free asset.Feedback: The student can apply arbitrage principles.

Question 79

Which of the following factors were used by Fama and French in their multifactor 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 factors were included in their model.
E)None of the factors were included in their model.

Question 80

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.
B)using variables that are easier to forecast ex ante.
C)calculating beta coefficients by an alternative method.
D)using only stocks with relatively stable returns.
E)ignoring firm-specific risk.