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Gold Horizon, an investment firm, utilizes a three-factor APT model for its Unique & Rich (U&R) fund. The risk-free rate equals 4%. Using the table below, determine U&R’s expected return.

GNP
Factor

Inflation Factor

Investor Confidence
Factor

U&R factor beta

1.75

1.5

1.25

Factor risk premium

0.020

0.015

0.013

A)
7.38%.
B)
11.38%.
C)
4.49%.



E(RU&R) = 0.04 + 1.75(0.02) + 1.5(0.015) + 1.25(0.013)
E(RU&R) = 0.04 + 0.035 + 0.0225 + 0.01625
E(RU&R) = 11.375% ≈ 11.38%

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An arbitrage pricing theory (APT) model has the following characteristics:
  • The risk free rate is 3.8%.
  • Factor risk premiums are:
  • (7%)
  • (4%)
  • (2%)
  • (10%)

Assume Silver Linings Fund has the following sensitivities to the factors:
  • Sensitivity to A is 0.5.
  • Sensitivity to B is 1.2.
  • Sensitivity to C is 2.1.
  • Sensitivity to D is 0.2.

The expected return on the Silver Linings Fund is:
A)
14.5%.
B)
18.3%.
C)
20.1%.



E(R) = 3.8 + (0.5 × 7) + (1.2 × 4) + (2.1 × 2) + (0.2 × 10) = 18.3.

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Which of the following statements regarding the arbitrage pricing theory (APT) as compared to the capital asset pricing model (CAPM) is least accurate? APT:
A)
does not require that one of the risk factors is the market portfolio; unlike the CAPM.
B)

is often times thought of as a special case of the CAPM.
C)

has fewer assumptions than CAPM.



The CAPM is often times thought of as a special case of the APT since CAPM has only one factor, the market portfolio.

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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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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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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) 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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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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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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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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