Q14. Assume you are attempting to estimate the equilibrium expected return for a portfolio using a two-factor arbitrage pricing theory (APT) model. One factor is changes in the 30-year T-bond rate and the other factor is the percentage growth in gross national product (GNP). Assume that you have estimated the risk premium for the interest rate factor to be 0.02, and the risk premium on the GNP factor to be 0.03. The sensitivity of the portfolio to the interest rate factor is –1.2 and the portfolios sensitivity to the GNP factor is 0.80. Given a risk free rate equal to 0.03, what is the expected return for the asset?

A)   3.0%.

B)   5.0%.

C)   2.4%.

Q15. 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 risk premium investors require on a factor portfolio for factor j.

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

Q16. The Arbitrage Pricing Theory (APT) has all of the following characteristics EXCEPT it:

A)   is an equilibrium pricing model.

B)   assumes that arbitrage opportunities are available to investors.

C)   assumes that asset returns are described by a factor model.

Q17. Which of the following is an equilibrium-pricing model?

A)   Macroeconomic factor model.

B)   Fundamental factor model.

C)   The arbitrage pricing theory (APT).

Q18. If 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.

Q19. 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.

Q20. 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)   has fewer assumptions than CAPM.

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

Q21. Which of the following is not an assumption of the arbitrage pricing theory (APT)?

A)   Security returns are normally distributed.

B)   Returns on assets can be described by a multi-factor process.

C)   The market contains enough stocks so that unsystematic risk can be diversified away.

Q22. Which of the following is an assumption of the arbitrage pricing theory (APT)?

A)   No arbitrage opportunities exist.

B)   Returns are normally distributed.

C)   Investors have quadratic utility functions.

Q23. Which of the following is an assumption of the arbitrage pricing theory (APT)?

A)   Security returns are normally distributed.

B)   Assets are priced such that no arbitrage opportunities exist.

C)   Investors have quadratic utility functions.

Q24. Which of the following does NOT describe the arbitrage pricing theory (APT)?

A)   It is an equilibrium-pricing model like the CAPM.

B)   There are assumed to be at least five factors that explain asset returns.

C)   It requires a weaker set of assumptions than the CAPM to derive.

Q25. An arbitrage pricing theory (APT) model has the following characteristics:

• The risk free rate is 3.8%.
• Factor risk premiums are:

A.      (7%)

B.      (4%)

C.      (2%)

D.      (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%.

Q14. Assume you are attempting to estimate the equilibrium expected return for a portfolio using a two-factor arbitrage pricing theory (APT) model. One factor is changes in the 30-year T-bond rate and the other factor is the percentage growth in gross national product (GNP). Assume that you have estimated the risk premium for the interest rate factor to be 0.02, and the risk premium on the GNP factor to be 0.03. The sensitivity of the portfolio to the interest rate factor is –1.2 and the portfolios sensitivity to the GNP factor is 0.80. Given a risk free rate equal to 0.03, what is the expected return for the asset? fficeffice" />

A)   3.0%.

B)   5.0%.

C)   2.4%.

Correct answer is A)

The general form of the two-factor APT model is:  E(R_Port) = R_F = λ_interestβ_interest + λ_GNPβ_GNP, where the λ’s are the factor risk premiums and the β’s are the portfolio’s factor sensitivities.  Substituting the appropriate values, we have:

R_Port = 0.03 + 0.02(?1.2) + 0.03(0.80) = 3.0%

Q15. 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 risk premium investors require on a factor portfolio for factor j.

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

Correct answer is B)

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 (β_p,j =1) to that factor and a sensitivity of zero to all the other factors (a factor portfolio).

Q16. The Arbitrage Pricing Theory (APT) has all of the following characteristics EXCEPT it:

A)   is an equilibrium pricing model.

B)   assumes that arbitrage opportunities are available to investors.

C)   assumes that asset returns are described by a factor model.

Correct answer is B)

The APT assumes that no arbitrage opportunities are available to investors.

Q17. Which of the following is an equilibrium-pricing model?

A)   Macroeconomic factor model.

B)   Fundamental factor model.

C)   The arbitrage pricing theory (APT).

Correct answer is C)

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.

Q18. If 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.

Correct answer is C)

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.

Q19. 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.

Correct answer is A)        

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.

Q20. 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)   has fewer assumptions than CAPM.

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

Correct answer is C)        

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

Q21. Which of the following is not an assumption of the arbitrage pricing theory (APT)?

A)   Security returns are normally distributed.

B)   Returns on assets can be described by a multi-factor process.

C)   The market contains enough stocks so that unsystematic risk can be diversified away.

Correct answer is A)        

APT does not require that security returns be normally distributed.

Q22. Which of the following is an assumption of the arbitrage pricing theory (APT)?

A)   No arbitrage opportunities exist.

B)   Returns are normally distributed.

C)   Investors have quadratic utility functions.

Correct answer is A)        

APT assumes that:

§   Asset returns are described by a multiple factor process.

§   There are enough stocks that unsystematic risk can be diversified away.

§   No arbitrage opportunities exist.

Q23. Which of the following is an assumption of the arbitrage pricing theory (APT)?

A)   Security returns are normally distributed.

B)   Assets are priced such that no arbitrage opportunities exist.

C)   Investors have quadratic utility functions.

Correct answer is B)

APT implies that investors will undertake infinitely large positions (long and short) to exploit any perceived mispricing, causing asset prices to adjust immediately to their equilibrium values.

Q24. Which of the following does NOT describe the arbitrage pricing theory (APT)?

A)   It is an equilibrium-pricing model like the CAPM.

B)   There are assumed to be at least five factors that explain asset returns.

C)   It requires a weaker set of assumptions than the CAPM to derive.

Correct answer is B)

APT is a k-factor model, in which the number of factors, k, is assumed to be a lot smaller than the number of assets; no specific number of factors is assumed. Depending on the data used to fit the model, there may be as few as two or as many as seven factors.

Q25. An arbitrage pricing theory (APT) model has the following characteristics:

• The risk free rate is 3.8%.
• Factor risk premiums are:

A.      (7%)

B.      (4%)

C.      (2%)

D.      (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%.

Correct answer is B)

ffice:smarttags" />E(R) = 3.8 + (0.5 × 7) + (1.2 × 4) + (2.1 × 2) + (0.2 × 10) = 18.3.