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

Answer: C Difficulty: Easy Rationale: Both models attempt to explain asset pricing based on risk/return relationships.

2. 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.

Answer: B Difficulty: Moderate Rationale: 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.

3. 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

Answer: C Difficulty: Easy Rationale: If the investor can construct a portfolio without the use of the investor's own funds and the portfolio yields a positive profit, arbitrage opportunities exist.

4. The APT was developed in 1976 by ____________. A) Lintner B) Modigliani and Miller C) Ross D) Sharpe E) none of the above

Answer: C Difficulty: Easy Rationale: Ross developed this model in 1976.

5. 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

Answer: A Difficulty: Easy Rationale: A factor model portfolio has a beta of 1 one factor, with zero betas on other factors.

6. 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

Answer: A Difficulty: Easy Rationale: Arbitrage is earning of positive profits with a zero (risk-free) investment.

7. 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

Answer: E Difficulty: Moderate Rationale: Total risk (uncertainty) is assumed to be composed of both macroeconomic and firm-specific factors.

8. 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

Answer: C Difficulty: Moderate Rationale: The CAPM is an asset-pricing model based on the risk/return relationship of all assets. The APT implies that this relationship holds for all well-diversified portfolios, and for all but perhaps a few individual securities.

9. 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

Answer: C Difficulty: Moderate Rationale: A: 16% = 1.0F + 6%; F = 10%; B: 12% = 0.8F + 6%: F = 7.5%; thus, short B and take a long position in A.

10. 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

Answer: C Difficulty: Moderate Rationale: A: 13% = 10% + 0.2F; F = 15%; B: 15% = 10% + 0.4F; F = 12.5%; therefore, short B and take a long position in A.

11. 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

Answer: C Difficulty: Moderate

Rationale: s2P = (1.1)2(6%) = 7.26%.

12. 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

Answer: B Difficulty: Moderate

Rationale: (18%)2 = (16%)2 b2; b = 1.125.

13. 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

Answer: E Difficulty: Moderate Rationale: A: 15% = 6% + bF; B: 8% = 6% + 1.0F; F = 12%; thus, beta of A = 9/12 = 0.75.

14. 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

Answer: D Difficulty: Difficult Rationale: 16.4% = 1.4(3%) + .8x + 6%; x = 7.75.

15. 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

Answer: C Difficulty: Moderate Rationale: 7% + 0.75(1%) + 1.25(7%) = 16.5%.

16. 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) none of the above

Answer: C Difficulty: Moderate Rationale: 17% = x% + 1.2(5%) + 0.7(6%); x = 6.8%.

17. 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

Answer: C Difficulty: Moderate Rationale: $100,000(0.06) = $6,000 (risk-free position); $100,000(0.17) = $17,000 (portfolio B); -$200,000(0.11) = -$22,000 (short position, portfolio A); 1,000 profit.

18. 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

Answer: B Difficulty: Moderate Rationale: A: 19% = rf + 1(F); B:24% = rf + 1.5(F); 5% = .5(F); F = 10%; 24% = rf +

1.5(10); ff = 9%.

19. 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 E) none of the above

Answer: C Difficulty: Moderate Rationale: 19% = 10% + 5%(0.8) + 3%(x); x = 1.67.

20. 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 above

Answer: C Difficulty: Moderate Rationale: A: 14% = 7% + 0.7F; F = 10; B: 18% = 7% + 10b; b = 1.10.

Use the following to answer questions 21-24:

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:

21. 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

Answer: D Difficulty: Easy Rationale: E(Rp) = 0.5(17%) + 0.5(15%) = 16%.

22. 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

Answer: B Difficulty: Easy Rationale: 0.5(39%) + 0.5(6%) = 22.5%.

23. 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

Answer: D Difficulty: Easy Rationale: 0.5(0%) + 0.5(22%) = 11%.

24. 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, none of the above

Answer: C Difficulty: Difficult Rationale: E(RA) = (39% + 17% - 5%)/3 = 17%; E(RB) = (30% + 15% + 0%)/3 =

15%; E(RC) = (22% + 14% + 6%)/3 = 14%; E(RP) = -0.5(14%) + 0.5[(17% + 15%)/

2]; -7.0% + 8.0% = 1.0%.

Use the following to answer questions 25-26:

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:

25. Assuming no arbitrage opportunities exist, the risk premium on the factor F1 portfolio should be __________. A) 3% B) 4% C) 5% D) 6% E) none of the above

Answer: A Difficulty: Difficult Rationale: 2A: 38% = 12% + 2.0(RP1) + 4.0(RP2); B: 12% = 6% + 2.0(RP1) + 0.0(RP2); 26% = 6% + 4.0(RP2); RP2 = 5; A: 19% = 6% + RP1 + 2.0(5); RP1 = 3%.

26. Assuming no arbitrage opportunities exist, the risk premium on the factor F2 portfolio should be ___________. A) 3% B) 4% C) 5% D) 6% E) none of the above

Answer: C Difficulty: Difficult Rationale: See solution to previous problem.

27. 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

Answer: D Difficulty: Easy Rationale: When an investor can create a zero-investment portfolio (by using none of the investor's own funds) with a possibility of a positive profit, a risk-free arbitrage opportunity exists.

28. 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

Answer: C Difficulty: Moderate Rationale: When the equilibrium price is violated, the investor will buy the lower priced asset and simultaneously place an order to sell the higher priced asset. Such transactions result in risk-free arbitrage. The larger the positions, the greater the risk-free arbitrage profits.

29. 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

Answer: D Difficulty: Moderate Rationale: The CAPM assumes that market returns represent systematic risk. The APT recognizes that other macroeconomic factors may be systematic risk factors.

30. 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

Answer: A Difficulty: Easy Rationale: The advantage of the APT is the use of multiple factors, rather than a single market index, to explain the risk-return relationship. However, APT does not identify the specific factors.

31. 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.

Answer: D Difficulty: Easy Rationale: Nonfactor risk may be diversified away; thus, only factor risk commands a risk premium in market equilibrium. Nonsystematic risk across firms cancels out in well-diversified portfolios; thus, only systematic risk is related to expected returns.

32. 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.

Answer: D Difficulty: Easy Rationale: A, B, and C all are likely to affect stock returns.

33. 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) A and B. E) B and C.

Answer: B Difficulty: Easy Rationale: The APT provides no guidance concerning the determination of the risk premiums on the factor portfolios. Risk must considered in both the CAPM and APT. A major advantage of APT over the CAPM is that a specific benchmark market portfolio is not required.

34. 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.

Answer: B Difficulty: Easy Rationale: Rational investors will arbitrage by selling A and buying B.

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) all of the above are true. E) both A and B are true.

Answer: E Difficulty: Difficult Rationale: Under the risk-return dominance argument of CAPM, when an equilibrium price is violated many investors will make small portfolio changes, depending on their risk tolerance, until equilibrium is restored. Under the no-arbitrage argument of APT, each investor will take as large a position as possible so only a few investors must act to restore equilibrium. Implications derived from APT are much stronger than those derived from CAPM, making C an incorrect statement.

36. 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.

Answer: B Difficulty: Moderate Rationale: Risk arbitrage involves searching for mispricings based on speculative information that may or may not materialize.

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. E) none of the above.

Answer: C Difficulty: Easy Rationale: As the number of securities, n, increases, the nonsystematic risk of a well-diversified portfolio approaches zero.

38. 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.

Answer: A Difficulty: Moderate Rationale: A well-diversified portfolio is one that contains a large number of securities, each having a small (but not necessarily equal) weight, so that nonsystematic variance is negligible.

39. 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.

Answer: D Difficulty: Moderate Rationale: Any well-diversified portfolio lying on the SML can serve as the benchmark portfolio for the APT. The true (and unobservable) market portfolio is only a requirement for the CAPM.

40. 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.

Answer: C Difficulty: Moderate Rationale: The expected return-beta relationship must hold for all well-diversified portfolios and for all but a few individual securities; otherwise arbitrage opportunities will be available.

41. 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%

Answer: E Difficulty: Moderate Rationale: .06 + 1.2 (.04) + .8 (.03) = .132

42. 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.

Answer: C Difficulty: Easy Rationale: Arbitrage is exploiting security mispricings by the simultaneous purchase and sale to gain economic profits without taking any risk. A capital market in equilibrium rules out arbitrage opportunities.

43. 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

Answer: B Difficulty: Difficult Rationale: Only I and III are correct. II is incorrect because the beta of the portfolio does not need to be zero. IV is incorrect because the opposite is true.

44. 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.

Answer: D Difficulty: Moderate Rationale: F measures the unanticipated portion of a factor that is common to all security returns.

45. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has an average value of ó(ei) equal to 25% and 50 securities? A) 12.5% B) 625% C) 0.5% D) 3.54% E) 14.59%

Answer: D Difficulty: Moderate Rationale:

46. 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.

Answer: D Difficulty: Moderate Rationale: The benchmark portfolio does not need to be the (unobservable) market portfolio under the APT, but can be any well-diversified portfolio. The intercept still equals the risk-free rate.

47. 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.

Answer: E Difficulty: Moderate Rationale: For each well-diversified portfolio (P and Q, for example), it must be true that [E(rp)-rf]/βp = [E(rQ)-rf]/ βQ.

48. 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%

Answer: B Difficulty: Moderate Rationale: E(RA) = 3 +0.8*(15-3) + 0.5*(6-3) = 14.1.

49. 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

Answer: A Difficulty: Moderate Rationale: All except the first item are true. There is a Security Market Line associated with the APT.

50. 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 is true.

Answer: D Difficulty: Moderate Rationale: Factor models explain firm returns based on both factor risk and non-factor risk.

51. 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.

Answer: E Difficulty: Moderate Rationale: Chen, Roll and Ross included the four listed factors as well as the excess return of long-term corporate bonds over long-term government bonds in their model.

52. 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 was included in their model.

Answer: D Difficulty: Moderate Rationale: Fama and French included all three of the factors listed.

53. Which of the following factors did Merton not 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) All of the above are sources of uncertainty affecting security returns.

Answer: C Difficulty: Moderate Rationale: Merton did not suggest book-to-market ratios as an ICAPM pricing factor; the other three were suggested.

54. 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.

Answer: A Difficulty: Moderate

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 above are true. E) none of the above is true.

Answer: D Difficulty: Easy

56. 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.

Answer: A Difficulty: Moderate Rationale: The study used five different factors to explain security returns, allowing for several sources of risk to affect the returns.

57. 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) none of the above

Answer: B Difficulty: Moderate Rationale: 3% + 0.8(3%) + 1.1(5%) + 1.25(2%) = 13.4%.

58. 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 E) none of the above

Answer: B Difficulty: Moderate Rationale: 16% = 4% + 6%(1.3) + 4%(x); x = 1.05.

59. 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%

Answer: C Difficulty: Moderate Rationale: .05 + .6 (.04) + 1.8 (.06) = .182

60. 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

Answer: C Difficulty: Moderate Rationale: A: 22% = 2.0F + 4%; F = 9%; B: 17% = 1.5F + 4%: F = 8.67%; thus, short B and take a long position in A.

61. 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 E) none of the above

Answer: B Difficulty: Moderate Rationale: A: 12% = 5% + 0.5F; F = 14%; B: 13% = 5% + 0.4F; F = 20%; therefore, short A and take a long position in B.

62. 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) none of the above

Answer: D Difficulty: Moderate

Rationale: s2P = (1.25)2(9%) = 14.06%.

63. 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 E) none of the above

Answer: D Difficulty: Moderate

Rationale: (22%)2 = (14%)2b2; b = 1.57.

64. 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 E) none of the above

Answer: B Difficulty: Moderate Rationale: A: 12% = 5% + bF; B: 14% = 5% + 1.2F; F = 7.5%; Thus, beta of A = 7/7.5 = 0.93.

65. 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 exit? A) 9.26% B) 3% C) 4% D) 7.75% E) none of the above

Answer: A Difficulty: Difficult Rationale: 17.6% = 1.45(3.2%) + .86x + 5%; x = 9.26.

Essay Questions

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

Difficulty: Moderate

Answer: The APT does not require that the benchmark portfolio in the SML relationship be the true market portfolio. Any well-diversified portfolio lying on the SML may serve as a benchmark portfolio. Thus, the APT has more flexibility than the CAPM, as problems associated with an unobservable market portfolio are not a concern with APT. In addition, the APT provides further justification for the use of the index model for practical implementation of the SML relationship. That is, if the index portfolio is not a precise proxy for the true market portfolio, which is a cause of considerable concern in the context of the CAPM, if an index portfolio is sufficiently diversified, the SML relationship holds, according to APT.

This question is designed to determine if the student understands the basic advantages of APT over the CAPM.

67. 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?

Difficulty: Moderate

Answer: The single factor APT and the CAPM assume that there is only one systematic risk factor affecting stock returns. However, obviously several factors may affect stock returns. Some of these factors are: business cycles, interest rate fluctuations, inflation rates, oil prices, etc. A multifactor model can accommodate these multiple sources of risk.

One shortcoming of the multifactor APT is that the model provides no guidance concerning the risk premiums on the factor portfolios. The CAPM implies that the risk premium on the market is determined by the market's variance and the average degree of risk aversion across investors.

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

Difficulty: Easy

Answer: The law of one price is violated when an asset is trading at different prices in two markets. If the price differential exceeds the transactions costs, a simultaneous trade in the two markets can produce a sure profit with a zero investment. That is, the investor can sell short the asset in the high-priced market and buy the asset in the low-priced market. The investor has been able to assume these positions with a zero investment (using the proceeds of the short transaction to finance the long position). However, it should be remembered that individual investors do not have access to the proceeds of a short transaction until the position has been covered.

69. 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.

Difficulty: Difficult

Answer: Both the CAPM and the APT are market equilibrium models, which examine the factors that affect securities' prices. In equilibrium, there are no overpriced or underpriced securities. In both models, mispriced securities can be identified and purchased or sold as appropriate to earn excess profits.

The CAPM is based on the idea that there are large numbers of investors who are focused on risk-return dominance. Under the CAPM, when a mispricing occurs, many individual investors make small changes in their portfolios, guided by their degrees of risk aversion. The aggregate effect of their actions brings the market back into equilibrium. Under the APT, each investor wants an infinite arbitrage position in the mispriced asset. Therefore, it would not take many investors to identify the arbitrage opportunity and act to bring the market back to equilibrium.

The student can compare the two models by focusing on the specific items.

70. 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.

Difficulty: Moderate

Answer: An arbitrage opportunity exists because it is possible to form a portfolio of security A and the risk-free asset that has a beta of 0.75 and a different expected return than security 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(rp) = 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.

71. 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.

Difficulty: Difficult

Answer: The factors they considered were IP (the % change in industrial production), EI (the % change in expected inflation), UI (the % change in unanticipated inflation), CG (excess return of long-term corporate bonds over long-term government bonds), and GB (excess return of long-term government bonds over T-bills). The rational for their model is that many different economic factors can combine to affect securities' returns. Also, by including factors that are related to the business cycle, the estimation of beta coefficients should be improved. Each beta will represent only the impact of the corresponding variable on returns.

The student has some flexibility in remembering which variables were used in the study. A general understanding of macroeconomic variables will be helpful in answering the question. The question provides an opportunity to measure the student's understanding of the types of risk that are relevant and how they can be explicitly considered in the model.