1、Chap ter 10 Arbitrage P ric ing Theory and Multifactor Models of Risk andRetur nMult iple Choice Questi ons1.A)B)C)D)E)a relati onship betwee n exp ected return and risk. APT sti pulatesCAPM sti pulatesBoth CAPM and APT sti pulateNeither CAPM nor APT sti pu lateNo pricing model has foundAn swer: C D

2、ifficulty: EasyRati on ale: Both models attem pt to exp la in asset pricing based on risk/retu rn relati on shi ps.2.Which pricing model pro vides no guida nee concerning the determ in ati on of the risk p remium on factor p ortfolios?A)B)C)D)E)The CAPMThe multifactor APTBoth the CAPM and the multif

3、actor APTNeither the CAPM nor the multifactor APTNone of the above is a true stateme nt.An swer: B Difficulty: ModerateRati on ale: The multifactor APT p rovides no guida nee as to the determ in ati on of the risk premium on the various factors. The CAPM assumes that the excess market return over th

4、e risk-free rate is the market p remium in the si ngle factor CAPM.3.An arbitrage opportunity exists if an in vestor can con struct a po rtfolio that will yield a sure p rofit.A)B)C)D)E)po sitive n egative zero all of the above none of the aboveinv estme ntAn swer: C Difficulty: EasyRati on ale: If

5、the inv estor can con struct a po rtfolio without the use of the in vestors own funds and the p ortfolio yields a p ositive p rofit, arbitrage opportun ities exist.4.5.6.LintnerModigliani and Miller RossSharpenone of the aboveThe APT was developed in 1976 byA)B)C)D)E)Answer: C Difficulty: EasyRation

6、ale: Ross developed this model in 1976.factor market index A and BA, B, and CA portfolio is a well-diversified portfolio constructed to have a beta of 1 onone of the factors and a beta of 0 on any other factor.A)B)C)D)E)Answer: A Difficulty: EasyRationale: A factor model portfolio has a beta of 1 on

7、e factor, with zero betas on other factors.arbitrage capital asset pricing factoring fundamental analysis none of the aboveThe exploitation of security mispricing in such a way that risk-free economic profits may be earned is called .A)B)C)D)E)Answer: A Difficulty: EasyRationale: Arbitrage is earnin

8、g of positive profits with a zero (risk-free) investment.2477.8.9.a com mon macroec ono mic factor firm-s pecific factors pricing errorn either A nor B both A and BAPT, CAPMAPT, 0PM CAPM,APT CAPM,OPM none of the aboveA, AA, BB, AB, BA, the riskless assetIn devel oping the APT, Ross assumed that un c

9、erta inty in asset retur ns was a result ofA)B)C)D)E)An swer: E Difficulty: ModerateRati on ale: Total risk (un certa in ty) is assumed to be comp osed of both macroec ono mic and firm-s pecific factors.Thepro vides an un equivocal stateme nt on the exp ected return-betarelati on shi p for all asset

10、s, whereas theimp lies that this relati on shi pholds for all but p erha ps a small nu mber of securities.A)B)C)D)E)An swer: C Difficulty: ModerateRati on ale: The CAPM is an asset -pricing model based on the risk/return relati onship of all assets. The APT imp lies that this relati onship holds for

11、 all well-diversified po rtfolios, and for all but p erha ps a few in dividual securities.Con sider a si ngle factor APT. Portfolio A has a beta of 1.0 and an exp ected return of 16%. Po rtfolio B has a beta of 0.8 and an exp ected retur n of 12%. The risk-free rate of return is 6%. If you wan ted t

12、o take adva ntage of an arbitrage opportuni ty, you should take a short p ositi on in p ortfolio and a long p ositi on in p ortfolio.A)B)C)D)E)An swer: C Difficulty: ModerateRatio nale: A: 16% = 1.0F + 6%; F = 10%; B: 12% = 0.8F + 6%: F = 7.5%; thus, short B and take a long p ositi on in A.10.11.12.

13、A, AA, BB, AB, B none of the aboveCon sider the sin gle factor APT. P ortfolio A has a beta of 0.2 and an exp ected retur n of 13%. P ortfolio B has a beta of 0.4 and an exp ected retur n of 15%. The risk-free rate of retu rn is 10%. If you wan ted to take adva ntage of an arbitrage opportun ity, yo

14、u should take a short p ositi on in p ortfolioand a long p ositi on in po rtfolio.A)B)C)D)E)An swer: C Difficulty: ModerateRati on ale: A: 13% = 10% + 0.2F; F = 15%; B: 15% = 10% + 0.4F; F = 12.5%; therefore, short B and take a long po siti on in A.3.6%6.0%7.3%10.1%none of the aboveCon sider the on

15、e-factor APT. The varia nee of returns on the factor po rtfolio is 6%. The beta of a well-diversified p ortfolio on the factor is 1.1. The varia nee of retur ns on the well-diversified po rtfolio is app roximately.A)B)C)D)E)An swer: C Difficulty: Moderate Ratio nale: Wp = (1.1)2(6%) = 7.26%.0.801.13

16、1.251.56 none of the aboveCon sider the on e-factor APT. The sta ndard deviati on of returns on a well-diversified po rtfolio is 18%. The sta ndard deviati on on the factor po rtfolio is 16%. The beta of the well-diversified po rtfolio is app roximately.A)B)C)D)E)An swer: B Difficulty: ModerateRatio

17、 nale: (18%)2 = (16%)2 b2; b = 1.125.13.14.15.0.671.001.301.69none of the aboveConsider 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 bet

18、a of .A)B)C)D)E)Answer: E Difficulty: ModerateRationale: A: 15% = 6% + bF; B: 8% = 6% + 1.0F; F = 12%; thus, beta of A = 9/12 = 0.75.2%3%4%7.75%none of the aboveConsider 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 facto

19、r 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)B)C)D)E)Answer: D Difficulty: DifficultRationale: 16.4% = 1.4(3%) + .8x + 6%; x = 7.75.13.5%15.0%16.5%23.0%none of the aboveConsider th

20、e 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 opport

21、unities exist.A)B)C)D)E)Answer: C Difficulty: ModerateRationale: 7% + 0.75(1%) + 1.25(7%) = 16.5%.16.17.18.6.0%6.5%6.8%7.4%none of the aboveConsider 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

22、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)B)C)D)E)Answer: C Difficulty: ModerateRationale: 17% = x% + 1.2(5%) + 0.7(6%); x = 6.8%.Consider a one-factor economy. Portfolio A has a beta of

23、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

24、 sold short $200,000 of portfolio A. Your expected profit from this strategy would be .A)B)C)D)E)-$1,000$0$1,000$2,000none of the aboveAnswer: C Difficulty: ModerateRationale: $100,000(0.06) = $6,000 (risk-free position); $100,000(0.17) = $17,000 (portfolio B); -$200,000(0.11) = -$22,000 (short posi

25、tion, portfolio A); 1,000 profit.4.0%9.0%14.0%16.5%none of the aboveConsider 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. Assumin

26、g no arbitrage opportunities exist, the risk-free rate of return must be .A)B)C)D)E)Answer: B Difficulty: ModerateRationale: 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 port

27、folios are 5% and 3%, res pectively. The risk-free rate of return is 10%. Stock A has an exp ected retur n of 19% and a beta on factor 1 of 0.8. Stock A has a beta on factor 2 ofA)B)C)D)E)1.331.501.672.00none of the aboveAn swer: C Difficulty: ModerateRatio nale: 19% = 10% + 5%(0.8) + 3%(x); x = 1.6

28、7.0.451.001.101.22 none of the above20. Consider the single factor APT. Portfolios A and B have expected returns of 14% and 18%, res pectively. The risk-free rate of return is 7%. Portfolio A has a beta of 0.7. If arbitrage opportun ities are ruled out, p ortfolio B must have a beta of.A)B)C)D)E)An

29、swer: C Difficulty: ModerateRatio nale: A: 14% = 7% + 0.7F; F = 10; B: 18% = 7% + 10b; b = 1.10.Use the followi ng to an swer questi ons 21-24:There are three stocks, A, B, and C. You can either inv est in these stocks or short sell them. There are three p ossible states of n ature for econo mic gro

30、wth in the upcoming year; econo mic growth may be strong, moderate, or weak. The retu rns for the upcoming year on stocks A, B, and C for each of these states of n ature are give n below:A39%17%-5%B30%15%0%Ce%14%22%Weak GrowthStockState of N且tUTCModerate Growth21.22.23.3.0%14.5%15.5%16.0%none of the

31、 aboveIf you invested in an equally weighted portfolio of stocks A and B, your portfolio return would be if economic growth were moderate.A)B)C)D)E)Answer: D Difficulty: EasyRationale: E(Rp) = 0.5(17%) + 0.5(15%) = 16%.17.0%22.5%30.0%30.5%none of the aboveIf you invested in an equally weighted portf

32、olio of stocks A and C, your portfolio return would be if economic growth was strong.A)B)C)D)E)Answer: B Difficulty: EasyRationale: 0.5(39%) + 0.5(6%) = 22.5%.-2.5%0.5%3.0%11.0%none of the aboveIf you invested in an equally weighted portfolio of stocks B and C, your portfolio return would be if econ

33、omic growth was weak.A)B)C)D)E)Answer: D Difficulty: EasyRationale: 0.5(0%) + 0.5(22%) = 11%.24. If you wan ted to take adva ntage of a risk-free arbitrage opportuni ty, you should take a short p ositi on inand a long po siti on in an equally weighted po rtfolio ofA)B)C)D)E)A, B and CB, A and CC, A

34、and BA and B, Cnone of the above, none of the aboveAn swer: C Difficulty: DifficultRatio nale: E(Ra) = (39% + 17% - 5%)/3 = 17%; E(Rb) = (30% + 15% + 0%)/3 = 15%; E(Rc) = (22% + 14% + 6%)/3 = 14%; E(FP) = -0.5(14%) + 0.5(17% + 15%)/2; -7.0% + 8.0% = 1.0%.Use the follow ing to an swer questi ons 25-2

35、6:Con sider the multifactor APT. There are two independent econo mic factors, Fand F2. The risk-free rate of return is 6%. The followi ng in formatio n is available about two well-diversifiedpo rtfolios:PortfolioB on FlP on F，Ejected ReturnA1.02. a -15%B2.0c.a13%25.3%4%5%6%none of the aboveAssu ming

36、 no arbitrage opportun ities exist, the risk p remium on the factor F P ortfolio should be.A)B)C)D)E)An swer: A Difficulty: DifficultRatio nale: 2A: 38% = 12% + 2.0(R P1) + 4.0(R P2); B: 12% = 6% + 2.0(R P1) +0.0(R P2); 26% = 6% + 4.0(R P2); RP2 = 5; A: 19% = 6% + RP1 + 2.0(5); RP1 = 3%.26.27.28.3%4

37、%5%6%none of the aboveAssuming no arbitrage opportunities exist, the risk premium on the factor 2F portfolio should be .A)B)C)D)E)Answer: C Difficulty: DifficultRationale: See solution to previous problem.A zero-investment portfolio with a positive expected return arises whenA)B)C)D)E)an investor ha

38、s downside risk only the law of prices is not violated the opportunity set is not tangent to the capital allocation line a risk-free arbitrage opportunity exists none of the aboveAnswer: D Difficulty: EasyRationale: When an investor can create a zero-investment portfolio (by using none of the invest

39、ors own funds) with a possibility of a positive profit, a risk-free arbitrage opportunity exists.a dominance argumentthe mean-variance efficiency frontier a risk-free arbitragethe capital asset pricing model none of the aboveAn investor will take as large a position as possible when an equilibrium p

40、rice relationship is violated. This is an example of .A)B)C)D)E)Answer: C Difficulty: ModerateRationale: 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 arbit

41、rage. The larger the positions, the greater the risk-free arbitrage profits.29.30.places more emphasis on market risk minimizes the importance of diversification recognizes multiple unsystematic risk factors recognizes multiple systematic risk factors none of the aboveThe APT differs from the CAPM b

42、ecause the APTA)B)C)D)E)Answer: D Difficulty: ModerateRationale: The CAPM assumes that market returns represent systematic risk. The APT recognizes that other macroeconomic factors may be systematic risk factors.A)B)C)D)E)use of several factors instead of a single market index to explain the risk-re

43、turn relationship identification of anticipated changes in production, inflation and term structure as key factors in explaining the risk-return relationship superior measurement of the risk-free rate of return over historical time periods variability of coefficients of sensitivity to the APT factor

44、s for a given asset over time none of the aboveThe feature of the APT that offers the greatest potential advantage over the CAPM is the31.In terms of the risk/return relationship A)B)C)D)E)Answer: A Difficulty: EasyRationale: The advantage of the APT is the use of multiple factors, rather than a sin

45、gle market index, to explain the risk-return relationship. However, APT does not identify the specific factors.only factor risk commands a risk premium in market equilibrium. only systematic risk is related to expected returns.only nonsystematic risk is related to expected returns.A and B.A and C.An

46、swer: D Difficulty: EasyRationale: 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 business cycle

47、. interest rate fluctuations. inflation rates. all of the above. none of the above.The following factors might affect stock returns:A)B)C)D)E)Answer: D Difficulty: Easy33.Advantage(s) of the APT is(are) A)B)C)D)E)that the model provides specific guidance concerning the determination of the risk prem

48、iums on the factor portfolios.that the model does not require a specific benchmark market portfolio. that risk need not be considered.A and B. B and C.Rationale: A, B, and C all are likely to affect stock returns.Answer: B Difficulty: EasyRationale: The APT provides no guidance concerning the determ

49、ination 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.Borrow at the risk free rate and buy A. Sell A short and buy B.Sell B short and buy A.Borrow a

50、t the risk free rate and buy B. Lend at the risk free rate and buy B.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)B)C)D)E)Answer: B Difficulty: EasyRationale: Rational investors wi

51、ll arbitrage by selling A and buying B.35. An important difference between CAPM and APT is A)B)C)D)E)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 ar

52、e required to bring the market back to equilibrium.implications for prices derived from CAPM arguments are stronger than prices derived from APT arguments.all of the above are true. both A and B are true.Answer: E Difficulty: DifficultRationale: Under the risk-return dominance argument of CAPM, when

53、 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 equilibriu

54、m. Implications derived from APT are much stronger than those derived from CAPM, making C an incorrect statement.pure arbitrage. risk arbitrage. option arbitrage. equilibrium arbitrage. none of the above.36. A professional who searches for mispriced securities in specific areas such as merger-target

55、 stocks, rather than one who seeks strict (risk-free) arbitrage opportunities is engaged inA)B)C)D)E)Answer: B Difficulty: ModerateRationale: Risk arbitrage involves searching for mispricings based on speculative information that may or may not materialize.one. infinity.zero. negative one.none of th

56、e above.38.A well-diversified portfolio is defined as A)B)C)D)E)one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero.one that contains securities from at least three different industry sectors. a portfolio whose factor beta equals 1.0.a portfolio that is equally weighted.all of the above.37.In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its nonsyst