Chap010 Text Bank(1) Solution

Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Chapter 10 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 Both models attempt to explain asset pricing based on risk/return relationships. Difficulty: Easy

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 APT, CAPM, and CCAPM models attempt to explain asset pricing based on risk/return relationships. Difficulty: Easy

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 The coefficients are called factor betas, factor sensitivities, or factor loadings. Difficulty: Easy

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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. Difficulty: Moderate

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 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. Difficulty: Easy

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

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 Arbitrage is earning of positive profits with a zero (risk-free) investment.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return Difficulty: Easy

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

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 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.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 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. Difficulty: Moderate

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 welldiversified portfolio is approximately __________. A. 3.6% B. 6.0% C. 7.3% D. 10.1% E. none of the above s2P = (1.1)2(6%) = 7.26%. Difficulty: Moderate

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 welldiversified portfolio is approximately __________. A. 0.80 B. 1.13 C. 1.25 D. 1.56 E. none of the above (18%)2 = (16%)2 b2; b = 1.125.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 A: 15% = 6% + bF; B: 18% = 6% + 1.0F; F = 12%; thus, beta of A = 9/12 = 0.75. Difficulty: Moderate

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 16.4% = 1.4(3%) + .8F + 6%; F = 7.75. Difficulty: Difficult

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 7% + 0.75(1%) + 1.25(7%) = 16.5%.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 $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. Difficulty: Moderate

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 A: 19% = rf + 1(F); B: 24% = rf + 1.5(F); 5% = .5(F); F = 10%; 24% = rf + 1.5(10); rf = 9%.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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

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

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

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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

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 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%. Difficulty: Difficult

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 welldiversified portfolios:

29. 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 2A: 38% = 12% + 2.0(RP1) + 4.0(RP2); B: 12% = 6% + 2.0(RP1) + 0.0(RP2); 26% = 6% + 4.0(RP2); So, RP2 = 5; A: 19% = 6% + RP1 + 2.0(5); RP1 = 3%. Difficulty: Difficult

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 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. Difficulty: Easy

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 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 riskfree arbitrage. The larger the positions, the greater the risk-free arbitrage profits. Difficulty: Moderate

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

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 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. Difficulty: Easy

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. 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. Difficulty: Easy

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

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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

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. 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. Difficulty: Difficult

40. A professional who searches for mispriced securities in specific areas such as mergertarget 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. Risk arbitrage involves searching for mispricings based on speculative information that may or may not materialize. Difficulty: Moderate

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.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

As the number of securities, n, increases, the nonsystematic risk of a well-diversified portfolio approaches zero.

Difficulty: Easy

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. 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.

Difficulty: Moderate

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. 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.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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 welldiversified 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.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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. Difficulty: Moderate

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. 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. Difficulty: Easy

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. A. I and IV B. I and III C. II and III D. I, III, and IV E. II, III, and IV 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. Difficulty: Difficult

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. F measures the unanticipated portion of a factor that is common to all security returns.

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return Difficulty: Moderate

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

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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. 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. Difficulty: Moderate

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. 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. Difficulty: Moderate

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

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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% E(RA) = 3 +0.8 * (15 - 3) + 0.5 * (6 - 3) = 14.1 Difficulty: Moderate

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

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. 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. Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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. Fama and French included all three of the factors listed.

Difficulty: Moderate

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

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. Black argues that past risk premiums on firm-characteristic variables, such as those described by Fama and French, are problematic because they may result from data snooping.

Difficulty: Moderate

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Chapter 10 - Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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. Multifactor models seek to improve the performance of the single-index model by 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 Difficulty: Easy

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

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