Reading 66: Portfolio Concepts Los l(part1)~Q1-13 including, expected, relation, factors

youzizhang

 

LOS l, (Part 1): Discuss the arbitrage pricing theory (APT), including its underlying assumptions and its relation to the multifactor models.

Q1. Given a three-factor arbitrage pricing theory APT model, what is the expected return on the Freedom Fund?

• The factor risk premiums to factors 1, 2, and 3 are 10%, 7% and 6%, respectively.
• The Freedom Fund has sensitivities to the factors 1, 2, and 3 of 1.0, 2.0 and 0.0, respectively.
• The risk-free rate is 6.0%.

A)   33.0%.

B)   24.0%.

C)   30.0%.

 

Q2. Which of the following best completes the following statement? The capital asset pricing model (CAPM) is:

A)   a subset of the arbitrage pricing theory (APT) model.

B)   a relatively easy model to implement and test.

C)   a useful model in calculating expected returns.

 

Q3. 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(R_P) = R_T-bill + 0.06β_p,CONF + 0.09β_p,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.

Portfolio	Sensitivity to Conf. Risk Factor	Sensitivity to Indust. Prod. Factor
J	1.50	1.00
K	0.80	1.20
L	1.00	2.00
Wilshire 5000	1.00	1.50

β_p,CONF: a market confidence factor

β_p,PROD: industrial production factor

R_T-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)   15.6%.

B)   22.0%.

C)   19.6%.

 

Q4. 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)   The APT model is less restrictive than the CAPM.

C)   Investors can borrow and lend at the risk-free rate.

 

Q5. 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)   1.50w_J + 0.80w_K + 1.00w_L = 0.

B)   w_J + w_K + w_L = 1.

C)   1.50w_J + 1.20w_K + 2.00w_L = 0.

 

Q6. 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(R_P) = 6.0% + 12.0%β_p,ΔGDP – 3.0%β_p,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.

 

Q7. What is the APT expected return on a factor portfolio exposed only to ΔGDP?

A)   18.0%.

B)   12.0%.

C)   15.0%.

 

Q8. Marcie Deiner is an investment manager with G&G Investment Corporation. She works with a variety of clients who differ in terms of experience, risk aversion and wealth. Deiner recently attended a seminar on multifactor analysis. Among other things, the seminar taught how the assumptions concerning the Arbitrage Pricing Theory (APT) model are different from those of the Capital Asset Pricing Model (CAPM). One of the examples used in the seminar is below.

E(R_i) = R_f + f₁ B_i,1 + f₂ B_i,2 + f₃ B_i,3. where: f₁ =3.0%, f₂ = ?40.0%, and f₃ =50.0%.

Beta estimates for Growth and Value funds for a three factor model
	Factor 1	Factor 2	Factor 3
Betas for Growth	0.5	0.7	1.2
Betas for Value	0.2	1.8	0.6

For the model used as an example in the seminar, if the T-bill rate is 3.5%, what are the expected returns for the Growth and Value Funds?

         E(R_Growth)                                  E(R_Value)

 

A)    37.0%                                ?37.9%

B)    3.1%                                  ?3.16%

C)    33.5%                                ?41.4%

 

Q9. Which of the following is least likely an assumption of the APT model?

A)   no arbitrage opportunities are available to investors because capital markets are perfectly competitive.

B)   asset returns are normally distributed.

C)   a large number of available assets for investment allow investors to eliminate non-systematic risk through diversification.

 

Q10. 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)   36.0%.

B)   33.0%.

C)   50.0%.

 

Q11. Which of the following is NOT an assumption necessary to derive the arbitrage pricing theory (APT)?

A)   A large number of assets are available to investors.

B)   Asset returns are described by a k-factor model.

C)   The priced factors risks can be hedged without taking short positions in any portfolios.

 

Q12. Which of the following assumptions is NOT necessary to derive the APT?

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

B)   A factor model describes asset returns.

C)   The factor portfolios are efficient.

 

Q13. 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)   A market portfolio exists that contains all risky assets and is mean-variance efficient.

C)   There are a sufficient number of assets for investors to create diversified portfolios in which firm-specific risk is eliminated.

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