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Jennifer Watkins, CFA, is a portfolio manager at Q-Metrics. She has derived a 2-factor arbitrage pricing theory (APT) model of expected returns she intends to use in her portfolio management strategies. The two-factor APT equation, in which the two factors are confidence risk and industrial production, is:

E(RP) = RT-bill + 0.06βp,CONF + 0.09βp,PROD


Watkins determines the sensitivity to each of the two factors for three diversified portfolios as well as for her benchmark, the Wilshire 5000. The results of her analysis are shown in the table below.
PortfolioSensitivity to Conf. Risk Factor Sensitivity to Indust. Prod. Factor
J1.501.00
K0.801.20
L1.002.00
Wilshire 50001.001.50

βp,CONF: a market confidence factor
βp,PROD: industrial production factor

RT-bill: the Treasury bill rate of return, assumed equal to 4%.

Watkins compares her data and results to that of a colleague who uses the Capital Asset Pricing Model (CAPM) to analyze the same portfolios. She determines that her analysis is more appropriate for the given portfolios.
What is the expected return on Portfolio K according to the APT equation?
A)

19.6%.
B)

15.6%.
C)

22.0%.



The β's in the APT equation are the factor sensitivities. The expected return on portfolio K is E(RK) = 0.04 + 0.06(0.80) + 0.09(1.20) = 19.6%.


Which of the following would be a valid reason for concluding that the APT analysis of Watkins is more appropriate than the CAPM analysis of her colleague?
A)
Investors have quadratic utility functions.
B)
Investors can borrow and lend at the risk-free rate.
C)
The APT model is less restrictive than the CAPM.



The true market portfolio contains all securities. The CAPM is a more restrictive model and requires that such a portfolio be mean/variance efficient while the APT does not. The Wilshire 5000 is a very diversified portfolio, but it does not contain all securities.

Which of the following is least likely one of the three equations needed to solve for the Industrial Production factor portfolio combination of J, K and L?
A)

1.50wJ + 0.80wK + 1.00wL = 0.
B)

wJ + wK + wL = 1.
C)

1.50wJ + 1.20wK + 2.00wL = 0.



A factor portfolio has a sensitivity of one to one factor and a sensitivity of zero for all other factors (in this case, a pure bet on industrial production). We need to create a factor portfolio (a combination of portfolios J, K and L) that has a factor sensitivity of zero to the confidence risk factor and a sensitivity of one to the industrial production factor. The three simultaneous equations to solve are:
Equation 1: wJ + wK + wL = 1 (portfolio weights sum to 1)
Equation 2: 1.50wJ + 0.80wK + 1.00wL = 0 (confidence risk portfolio sensitivity equals 0)
Equation 3: 1.00wJ + 1.20wK + 2.00wL = 1 (production portfolio sensitivity equals 1)

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Carrie Marcel, CFA, has long used the Capital Asset Pricing Model (CAPM) as an investment tool. Marcel has recently begun to appreciate the advantages of arbitrage pricing theory (APT). She used reliable techniques and data to create the following two-factor APT equation:

E(RP) = 6.0% + 12.0%βp,ΔGDP – 3.0%βp,ΔINF

Where ΔGDP is the change in GDP and ΔINF is the change in inflation. She then determines the sensitivities to the factors of three diversified portfolios that are available for investment as well as a benchmark index:

Portfolio

Sensitivity to ΔGDP

Sensitivity to ΔINF

Q

2.00

0.75

R

1.25

0.50

S

1.50

0.25

Benchmark Index

1.80

1.00

Marcel is investigating several strategies. She decides to determine how to create a portfolio from Q, R, and S that only has an exposure to ΔGDP. She also wishes to create a portfolio out of Q, R, and S that can replicate the benchmark. Marcel also believes that a hedge fund, which is composed of long and short positions, could be created with a portfolio that is equally weighted in Q, R, S and the benchmark index. The hedge fund would produce a return in excess of the risk-free return but would not have any risk.

Which of the following statements least likely describes characteristics of the APT and the CAPM?
A)
The APT is more flexible than the CAPM because it allows for multiple factors.
B)
Both models assume firm-specific risk can be diversified away.
C)
Both models require the ability to invest in the market portfolio.



The CAPM can be thought of as a subset of the APT, multifactor model. Therefore, fewer assumptions are needed for the APT model than the CAPM. Although it could be included as a factor, the APT does not require an investment in the market portfolio. APT can be thought of as a k factor model, while the CAPM is based on the risk-free asset and the market portfolio.

What is the APT expected return on a factor portfolio exposed only to ΔGDP?
A)
18.0%.
B)
12.0%.
C)
15.0%.



A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors. The expected return on a “factor 1” portfolio is E(RR) = 6.0% + 12.0% (1.00) − 3.0%(0.00) = 18.0%.

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Given a three-factor arbitrage pricing theory (APT) model, what is the expected return on the Premium Dividend Yield Fund?
  • The factor risk premiums to factors 1, 2 and 3 are 8%, 12% and 5%, respectively.
  • The fund has sensitivities to the factors 1, 2, and 3 of 2.0, 1.0 and 1.0, respectively.
  • The risk-free rate is 3.0%.
A)

33.0%.
B)

50.0%.
C)

36.0%.



The expected return on the Premium Dividend Yield Fund is 3% + (8.0%)(2.0) + (12.0%)(1.0) + (5.0%)(1.0) = 36.0%.

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Which of the following assumptions is NOT necessary to derive the APT?
A)

The factor portfolios are efficient.
B)

Investors can create diversified portfolios with no firm-specific risk.
C)

A factor model describes asset returns.



The APT is an equilibrium model that assumes that investors can create diversified portfolios and that a factor model describes asset returns. It does NOT require that factor portfolios (nor, as in the capital asset pricing model [CAPM], the market portfolio) be efficient. In effect, the APT assumes investors simply like more money to less, while the CAPM assumes they care about expected return and standard deviation and invest in efficient portfolios. The APT makes no reference to mean-variance analysis or assumptions about efficient portfolios. This weaker set of assumptions is an advantage of the APT over the CAPM.

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Which of the following is NOT an underlying assumption of the arbitrage pricing theory (APT)?
A)
Asset returns are described by a K factor model.
B)
There are a sufficient number of assets for investors to create diversified portfolios in which firm-specific risk is eliminated.
C)
A market portfolio exists that contains all risky assets and is mean-variance efficient.



The APT makes no assumption about a market portfolio.

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The factor risk premium on factor j in the arbitrage pricing theory (APT) can be interpreted as the:
A)

sensitivity of the market portfolio to factor j.
B)

expected return investors require on a factor portfolio for factor j.
C)

expected risk premium investors require on a factor portfolio for factor j.



We can interpret the APT factor risk premiums similar to the way we interpret the market risk premium in the CAPM. Each factor price is the expected risk premium (extra expected return minus the risk-free rate) investors require for a portfolio with a sensitivity of one (βp,j =1) to that factor and a sensitivity of zero to all the other factors (a factor portfolio).

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The Arbitrage Pricing Theory (APT) has all of the following characteristics EXCEPT it:
A)
assumes that arbitrage opportunities are available to investors.
B)
is an equilibrium pricing model.
C)
assumes that asset returns are described by a factor model.



The APT assumes that no arbitrage opportunities are available to investors

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Which of the following is an equilibrium-pricing model?
A)

Macroeconomic factor model.
B)

Fundamental factor model.
C)

The arbitrage pricing theory (APT).



The APT is an equilibrium-pricing model; multi-factor models are “ad-hoc,” meaning the factors in these models are not derived directly from an equilibrium theory. Rather they are identified empirically by looking for macroeconomic variables that best fit the data.

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the arbitrage pricing theory (APT) holds, it determines:
A)

factor sensitivities in a multi-factor model.
B)

the factor prices in a multi-factor model.
C)

the intercept term in a multi-factor model.



One way to think about the relationship between the APT and multi-factor models is to recognize that the intercept term in a multi-factor model is the asset’s expected return; the APT is an expected return model that tells us what that intercept should be.

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One of the assumptions of the arbitrage pricing theory (APT) is that there are no arbitrage opportunities available. An arbitrage opportunity is:
A)

an investment that has an expected positive net cash flow but requires no initial investment.
B)

a factor portfolio with a positive expected risk premium.
C)

a portfolio with factor exposures that sum to one.


One of the three assumptions of the APT is that there are no arbitrage opportunities available to investors among these well-diversified portfolios. An arbitrage opportunity is an investment that has an expected positive net cash flow but requires no initial investment.
All factor portfolios will have positive risk premiums equal to the factor price for that factor. An arbitrage opportunity does not necessarily require a return equal to the risk-free rate, and the factor exposures for an arbitrage portfolio are all equal to zero.

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