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

Answer 1

B

Question 2

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.

Answer 2

C

Question 3

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%

Answer 3

D

Question 4

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 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
B)A; B
C)B; A
D)B; B

Question 6

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

Question 7

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 8

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 9

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 10

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 11

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

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

Question 12

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 13

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.

Question 14

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 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

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

Question 16

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

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

Question 17

___________ 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

Question 18

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

Question 19

The APT was developed in 1976 by

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

Question 20

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 21

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.

Question 22

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 23

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.

Question 24

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 25

Consider the multifactor APT.There are two independent economic factors, F₁andF₂.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 factorF₂portfolio should be

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

Question 26

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.

Question 27

Which of the following factors might affect stock returns?

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

Question 28

Consider the multifactor APT.There are two independent economic factors, F₁andF₂.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 factorF₁portfolio should be

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

Question 29

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.

Question 30

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 31

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 32

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.

Question 33

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 34

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

Question 35

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)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 36

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

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

Question 37

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

Question 38

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 39

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.

Question 40

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.

Question 41

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

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

Question 42

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 43

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.

Question 44

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%

Question 45

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

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

Question 46

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 47

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)A; B
C)B; A
D)B; B

Question 48

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 49

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.

Question 50

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.

Question 51

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

Question 52

The no-arbitrage equation of the APT states that

A)the risk premium is equal to zero.
B)Alpha is greater than zero.
C)the risk premium (expected excess return) on a portfolio is the product of its beta and the market-index risk premium
D)Alpha is smaller than zero.

Question 53

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

Question 54

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.

Question 55

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 are correct.

Question 56

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 57

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%

Question 58

The states that

A)assets that are equivalent have the same risk.
B)if two assets are equivalent in all economically relevant respects, then they should have the same market price.
C)risk and return are directly related.
D)there are always arbitrage opportunities.

Question 59

Multifactor model scan 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.

Question 60

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 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 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.