Question 1

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%.

Accepted Answer

s²_P = (1.45)²(11%) = 23.13%.

Question 2

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.

Accepted Answer

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

Question 3

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.

Accepted Answer

The answer of Name three variables that Chen, Roll, and...

Question 4

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%

Accepted Answer

3% + 0.8(3%) + 1.1(5%) + 1.25(2%) = 13.4%.

Question 5

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.

Accepted Answer

The answer of Discuss the similarities and the differences between...

Question 6

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

Accepted Answer

The answer of Discuss arbitrage opportunities in the context of...

Question 7

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 options.
E)None of the options is true.

Accepted Answer

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.

Question 8

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

Accepted Answer

As per the APT, the expected return of a portfolio can be represented as the sum of risk premium associated with different factors multiplied by their respective factor sensitivities (betas). In this case, we have only one factor.

Expected return on portfolio A = Risk-free rate + 2.0(Risk premium)
22% = 4% + 2.0(Risk premium)
Risk premium = 9%

Expected return on portfolio B = Risk-free rate + 1.5(Risk premium)
17% = 4% + 1.5(Risk premium)
Risk premium = 8.67%

The arbitrage opportunity exists when two portfolios have the same expected return but have different betas. Here, portfolio A has a higher expected return than portfolio B, but it also has a higher beta.

To take advantage of this situation, we should short portfolio with a higher beta (portfolio A) and long portfolio with a lower beta (portfolio B). The risk-free asset is not involved in this arbitrage opportunity.

Hence, the correct answer is option C - Short position in portfolio A and a long position in portfolio B.

Question 9

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.

Accepted Answer

16% = 4% + 6%(1.3) + 4%(x); x = 1.05.

Question 10

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.

Accepted Answer

(22%)² = (14%)²b²; b = 1.57.

Question 11

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)1.58.
B)1.13.
C)1.25.
D)0.76.

Accepted Answer

(19%)² = (12%)²b²; b = 1.58.

Question 12

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

Accepted Answer

The answer of Consider the single factor APT.Portfolio A has...

Question 13

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%.

Accepted Answer

s²_P = (1.25)²(9%) = 14.06%.

Question 14

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%

Accepted Answer

.05 + .6 (.04) + 1.8 (.06) = .182.

Question 15

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

Accepted Answer

The answer of Discuss the advantages of arbitrage pricing theory...

Question 16

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.

Accepted Answer

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.

Question 17

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

Accepted Answer

The answer of Discuss the advantages of the multifactor APT...

Question 18

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. 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(r_p) = 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.Feedback: The student can apply arbitrage principles.

Accepted Answer

The answer of Security A has a beta of 1.0...

Question 19

Which of the following factors were used by Fama and French in their multifactor 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 factors were included in their model.
E)None of the factors were included in their model.

Accepted Answer

Fama and French included all three of the factors listed.

Question 20

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.

Accepted Answer

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

Quiz 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return

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

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

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.

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.

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

Multifactor models seek to improve the performance of the single-index model by

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

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

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

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

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

Black argues that past risk premiums on firm-characteristic variables, such as those described by Fama and French, are problematic because

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

Which of the following factors were used by Fama and French in their multifactor model

Multifactor models, such as the one constructed by Chen, Roll, and Ross, can better describe assets' returns by