Chapter 10 Arbitrage Pricing Theory and Multifactor Models of Risk and ReturnMultiple Choice Questions1. ___________ a relationship between expected return and risk.A. APT stipulatesB. CAPM stipulatesC. Both CAPM and APT stipulateD. Neither CAPM nor APT stipulateE. No pricing model has found2. 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 is3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exit?A. 9.26%B. 3%C. 4%D. 7.75%E. 9.75%3. In a multi-factor APT model, the coefficients on the macro factors are often called ______.A. systemic riskB. factor sensitivitiesC. idiosyncratic riskD. factor betasE. both factor sensitivities and factor betas4. In a multi-factor APT model, the coefficients on the macro factors are often called ______.A. systemic riskB. firm-specific riskC. idiosyncratic riskD. factor betasE. unique risk5. In a multi-factor APT model, the coefficients on the macro factors are often called ______.A. systemic riskB. firm-specific riskC. idiosyncratic riskD. factor loadingsE. unique risk6. Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios?A. The CAPMB. The multifactor APTC. Both the CAPM and the multifactor APTD. Neither the CAPM nor the multifactor APTE. No pricing model currently exists that provides guidance concerning the determination of the risk premium on any portfolio7. An arbitrage opportunity exists if an investor can construct a __________ investment portfolio that will yield a sure profit.A. small positiveB. small negativeC. zeroD. large positiveE. large negative8. The APT was developed in 1976 by ____________.A. LintnerB. Modigliani and MillerC. RossD. SharpeE. Fama9. A _________ portfolio is a well-diversified portfolio constructed to havea beta of 1 on one of the factors and a beta of 0 on any other factor.A. factorB. marketC. indexD. factor and marketE. factor, market, and index10. The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called ___________.A. arbitrageB. capital asset pricingC. factoringD. fundamental analysisE. technical analysis11. In developing the APT, Ross assumed that uncertainty in asset returns wasa result ofA. a common macroeconomic factor.B. firm-specific factors.C. pricing error.D. neither common macroeconomic factors nor firm-specific factors.E. both common macroeconomic factors and firm-specific factors.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; CAPMB. APT; OPMC. CAPM; APTD. CAPM; OPME. APT and OPM; CAPM13. 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; AB. A; BC. B; AD. B; BE. A; the riskless asset14. 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; AB. A; BC. B; AD. B; BE. No arbitrage opportunity exists.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. 8.6%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. 0.80B. 1.13C. 1.25D. 1.56E. 0.9317. 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. 0.67B. 1.00C. 1.30D. 1.69E. 0.7518. 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. 6.89%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. 18.7%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 ___________.A. 6.0%B. 6.5%C. 6.8%D. 7.4%E. 7.7%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. −$1,000B. $0C. $1,000D. $2,000E. $1,60022. 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. 8.2%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 ________.A. 1.33B. 1.50C. 1.67D. 2.00E. 1.7324. 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. 0.45B. 1.00C. 1.10D. 1.22E. 1.33There 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. 17.0%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. 25.6%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. 9.0%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 CB. B; A and CC. C; A and BD. A and B; CE. No arbitrage opportunity exists.Consider the multifactor APT. There are two independent economic factors, Fand1. The risk-free rate of return is 6%. The following information is available F2about two well-diversified portfolios:29. Assuming no arbitrage opportunities exist, the risk premium on the factor Fportfolio should be __________.1A. 3%B. 4%C. 5%D. 6%E. 2%30. Assuming no arbitrage opportunities exist, the risk premium on the factor Fportfolio should be ___________.2A. 3%B. 4%C. 5%D. 6%E. 2%31. A zero-investment portfolio with a positive expected return arises when _________.A. an investor has downside risk onlyB. the law of prices is not violatedC. the opportunity set is not tangent to the capital allocation lineD. a risk-free arbitrage opportunity existsE. a risk-free arbitrage opportunity does not exist32. 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 argumentB. the mean-variance efficiency frontierC. a risk-free arbitrageD. the capital asset pricing modelE. the SML33. The APT differs from the CAPM because the APT _________.A. places more emphasis on market riskB. minimizes the importance of diversificationC. recognizes multiple unsystematic risk factorsD. recognizes multiple systematic risk factorsE. places more emphasis on systematic risk34. 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 relationshipB. identification of anticipated changes in production, inflation, and term structure as key factors in explaining the risk-return relationshipC. superior measurement of the risk-free rate of return over historical time periodsD. variability of coefficients of sensitivity to the APT factors for a given asset over timeE. superior measurement of the risk-free rate of return over historical time periods and variability of coefficients of sensitivity to the APT factors for a given asset over time35. In terms of the risk/return relationship in the APTA. 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.36. The following factors might affect stock returns:A. the business cycle.B. interest rate fluctuations.C. inflation rates.D. the business cycle, interest rate fluctuations, and inflation rates.E. the relationship between past FRED spreads.37. 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.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 willA. 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 isA. 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. CAPM depends on risk-return dominance; APT depends on a no arbitrage condition, 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, implications for prices derived from CAPM arguments are stronger than prices derived from APT arguments.E. CAPM depends on risk-return dominance; APT depends on a no arbitrage condition and assumes many small changes are required to bring the market back to equilibrium.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 inA. pure arbitrage.B. risk arbitrage.C. option arbitrage.D. equilibrium arbitrage.E. covered interest arbitrage.41. In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its nonsystematic risk approachesA. one.B. infinity.C. zero.D. negative one.E. None of these is correct.42. A well-diversified portfolio is defined asA. 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. a portfolio that is equally weighted and contains securities from at least three different industry sectors.43. The APT requires a benchmark portfolioA. 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.A. I and III are correct.B. I and IV are correct.C. II and III are correct.D. II and IV are correct.E. Only I is 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?A. 7.0%B. 8.0%C. 9.2%D. 13.0%E. 13.2%46. The term "arbitrage" refers toA. 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 wouldI) 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 IVB. I and IIIC. II and IIID. I, III, and IVE. II, III, and IV48. The factor F in the APT model representsA. 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 σ(e) equal to 25% andi50 securities?A. 12.5%B. 625%C. 0.5%D. 3.54%E. 14.59%50. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has an average value of σ(e) equal to 20% andi20 securities?A. 12.5%B. 625%C. 4.47%D. 3.54%E. 14.59%51. In the APT model, what is the nonsystematic standard deviation of an) equal to 20% and equally-weighted portfolio that has an average value of σ(ei40 securities?A. 12.5%B. 625%C. 0.5%D. 3.54%E. 3.16%52. In the APT model, what is the nonsystematic standard deviation of an) equal to 18% and equally-weighted portfolio that has an average value of (ei250 securities?A. 1.14%B. 625%C. 0.5%D. 3.54%E. 3.16%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. The SML has a downward slope, the SML for the APT shows expected return in relation to portfolio standard deviation, and the SML for the APT has an intercept equal to the expected return on the market portfolio are all false.55. If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must beA. 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%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 IVB. II and IVC. II and IIID. I, II, and IVE. I, II, III, and IV58. In a factor model, the return on a stock in a particular period will be related toA. factor risk.B. non-factor risk.C. standard deviation of returns.D. both factor risk and non-factor risk.E. There is no relationship between factor risk, risk premiums, and returns.59. Which of the following factors did Chen, Roll and Ross not include in their multifactor model?A. Change in industrial productionB. Change in expected inflationC. Change in unanticipated inflationD. Excess return of long-term government bonds over T-billsE. Neither the change in industrial production, change in expected inflation, change in unanticipated inflation, nor excess return of long-term government bonds over T-bills were included in their model.60. Which of the following factors did Chen, Roll and Ross include in their multifactor model?A. Change in industrial wasteB. Change in expected inflationC. Change in unanticipated inflationD. Change in expected inflation and Change in unanticipated inflationE. All of these factors were included in their model61. 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 these factors were included in their model.E. None of these factors were included in their model.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. 0.67B. 0.93C. 1.30D. 1.69E. 1.2763. 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. 1.58B. 1.13C. 1.25D. 0.76E. 1.4264. 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 snoopingB. they are sources of systematic riskC. they can be explained by security characteristic linesD. they are more appropriate for a single-factor modelE. they are macroeconomic factors65. Multifactor models seek to improve the performance of the single-index model byA. 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. modeling the systematic component of firm returns in greater detail, incorporating firm-specific components into the pricing model, and allowing for multiple economic factors to have differential effects.E. none of these statements are true.66. Multifactor models such as the one constructed by Chen, Roll, and Ross, can better describe assets' returns byA. 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.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.A. 13.5%B. 13.4%C. 16.5%D. 23.0%E. 11.6%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 ________.A. 1.33B. 1.05C. 1.67D. 2.00E. .9569. 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%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 wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _______.A. A; AB. A; BC. B; AD. B; BE. A; the riskless asset71. 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; AB. A; BC. B; AD. B; BE. No arbitrage opportunity exists.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%E. 9.7%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%B. 6.0%C. 7.3%D. 14.1%E. 11.4%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 __________.A. 0.80B. 1.13C. 1.25D. 1.57E. 67Short Answer Questions75. Discuss the advantages of arbitrage pricing theory (APT) over the capital asset pricing model (CAPM) relative to diversified portfolios.76. 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?77. Discuss arbitrage opportunities in the context of violations of the law of one price.78. 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.79. Security A has a beta of 1.0 and an expected return of 12%. Security B hasa 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.80. 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.。
