# Arbitrage pricing theory and multifactor models of risk and return –

Multiple Choice Questions

1. ___________ 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 found

2. ___________ a relationship between expected return and risk.

A. APT stipulates

B. CAPM stipulates

C. CCAPM stipulates

D. APT, CAPM, and CCAPM stipulate

E. No pricing model has found

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

A. systemic risk

B. factor sensitivities

C. idiosyncratic risk

D. factor betas

E. B and D

6. 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 above is a true statement.

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 above

E. none of the above

* *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

B. market

C. index

D. A and B

E. A, B, and C

10. 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 above* *

11. 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. neither A nor B

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.

A. APT, CAPM

B. APT, OPM

C. CAPM, APT

D. CAPM, OPM

E. none of the above

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 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. none of the above* *

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%

E. none of the above

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

E. none of the above

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 __________.

A. 0.67

B. 1.00

C. 1.30

D. 1.69

E. none of the above* *

* *

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?

A. 2%

B. 3%

C. 4%

D. 7.75%

E. none of the above* *

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%

E. none of the above

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 ______________.

A. -$1,000

B. $0

C. $1,000

D. $2,000

E. none of the above

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 ____________.

A. 4.0%

B. 9.0%

C. 14.0%

D. 16.5%

E. none of the above

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:

25. If you invested in an equally weighted portfolio of stocks A and B, your portfolio return would be ___________ if economic growth were moderate.

A. 3.0%

B. 14.5%

C. 15.5%

D. 16.0%

E. none of the above

26. If you invested in an equally weighted portfolio of stocks A and C, your portfolio return would be ____________ if economic growth was strong.

A. 17.0%

B. 22.5%

C. 30.0%

D. 30.5%

E. none of the above

* *

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

A. -2.5%

B. 0.5%

C. 3.0%

D. 11.0%

E. none of the above

28. If you wanted 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 _______.

A. A, B and C

B. B, A and C

C. C, A and B

D. A and B, C

E. none of the above

* *

Consider the multifactor APT. There are two independent economic factors, F_{1} and F_{2}. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios:

29. Assuming no arbitrage opportunities exist, the risk premium on the factor F_{1} portfolio should be __________.

A. 3%

B. 4%

C. 5%

D. 6%

E. none of the above

* *

31. 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

E. none of the above* *

32. 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

E. none of the above* *

33. 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

E. none of the above

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

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 above

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.

E. A and C.

36. The following factors might affect stock returns:

A. the business cycle.

B. interest rate fluctuations.

C. inflation rates.

D. all of the above.

E. none of the above

* *

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

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.

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.

C. implications for prices derived from CAPM arguments are stronger than prices derived from APT arguments.

D. all of the above are true.

E. both A and B are true.

* *

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

A. pure arbitrage.

B. risk arbitrage.

C. option arbitrage.

D. equilibrium arbitrage.

E. none of the above.

41. 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.

E. none of the above.

42. 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.

E. all of the above.* *

43. 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.

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.

46. 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.

* *

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.

* *

48. 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.

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

A. 12.5%

B. 625%

C. 0.5%

D. 3.54%

E. 14.59%* *

53. 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.

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

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.

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%.

A. 15.2%

B. 14.1%

C. 13.3%

D. 10.7%

E. 8.4%* *

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

A. factor risk.

B. non-factor risk.

C. standard deviation of returns.

D. both A and B are true.

E. none of the above are true.

59. 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 above factors were included in their model.

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.

E. None of the above factors were included in their model.* *

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

A. uncertainties in labor income.

B. prices of important consumption goods.

C. book-to-market ratios.

D. changes in future investment opportunities.

E. A, B, and D.

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.

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.

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.

E. none 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.

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.