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

Question 1

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.

Answer 1

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

Question 2

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%.

Answer 2

C
Explanation: s ²_P = (1.1)²(6%) = 7.26%.

Question 3

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%

Answer 3

C
Explanation: 7% + 0.75(1%) + 1.25(7%) = 16.5%.

Question 4

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 5

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 6

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 7

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 are correct.

Question 8

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 9

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

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

Question 10

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 11

___________ 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 12

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 13

The APT was developed in 1976 by

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

Question 14

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 15

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 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

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

Question 17

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 18

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 are correct.

Question 19

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 are correct.

Question 20

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 21

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 22

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 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

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 25

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: $$\begin{array} { c c c c } \text { Portfolio } & \beta \text { on } \mathrm { F } _ { 1 } & \beta \text { on } \mathrm { F } _ { 2 } & \begin{array} { c } \text { Expected } \\\text { Return }\end{array} \\\text { A } & 1.0 & 2.0 & 19 \% \\\text { B } & 2.0 & 0.0 & 12 \% \\\hline\end{array}$$ Assuming no arbitrage opportunities exist, the risk premium on the factor F₂ portfolio should be

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

Question 26

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 27

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

A) -$1,000.
B) $0.
C) $1,000.
D) $2,000.

Question 28

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 are correct.

Question 29

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 30

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 31

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 32

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 33

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 are corrct.

Question 34

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 35

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 36

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.
E) All of the options are true.

Question 37

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 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: $$\begin{array} { c c c c } \text { Portfolio } & \beta \text { on } \mathrm { F } _ { 1 } & \beta \text { on } \mathrm { F } _ { 2 } & \begin{array} { c } \text { Expected } \\\text { Return }\end{array} \\\text { A } & 1.0 & 2.0 & 19 \% \\\text { B } & 2.0 & 0.0 & 12 \% \\\hline\end{array}$$ 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

If you invested in an equally-weighted portfolio of stocks B and C, your portfolio return would be _____________ if economic growth was weak. 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 40

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 41

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 42

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

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

Question 43

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 44

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 45

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 46

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 47

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 48

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 49

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 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.
E) The SML is not relevant for the APT.

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 25% and 50 securities?

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

Question 52

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 53

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 54

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 55

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 56

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 57

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 58

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 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 18% and 250 securities?

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

Question 60

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 are true.

Question 61

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.
E) None of the options are correct.

Question 62

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 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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.

Question 71

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 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

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