Reading 66: Portfolio Concepts-LOS l 习题精选 2011, including, expected, relation, return

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Session 18: Portfolio Management: Capital Market Theory and the Portfolio Management Process
Reading 66: Portfolio Concepts

LOS l: Discuss the arbitrage pricing theory (APT), including its underlying assumptions and its relation to the multifactor models, calculate the expected return on an asset given an asset's factor sensitivities and the factor risk premiums, and determine whether an arbitrage opportunity exists, including how to exploit the opportunity.

 

 

Which of the following statements about multifactor models is CORRECT?

A) The multifactor model is a time-series regression that explains variation in one asset.

B) The multifactor model is a cross-sectional equilibrium pricing model that explains variation across assets.

C) The intercept term in a macroeconomic factor model is the risk-free rate.

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The multifactor model is a time-series regression that explains variation in one asset. APT is a cross-sectional equilibrium pricing model that explains variation across assets. The intercept term in a macroeconomic factor model is the asset's expected return.

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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%.

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The expected return on the Freedom Fund is 6% + (10.0%)(1.0) + (7.0%)(2.0) + (6.0%)(0.0) = 30.0%.

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

A) a relatively easy model to implement and test.

B) a useful model in calculating expected returns.

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

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The APT is less restrictive than the CAPM; it does not require the assumptions that investors have quadratic utility functions, security returns are normally distributed, or the existence of a mean variance efficient market portfolio. The CAPM is a subset of the APT where it is assumed that only the relationship to the market portfolio is useful in explaining returns. The APT is more flexible because it can have k factors. However, these factors are not defined in theory.

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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%.

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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 is NOT an assumption necessary to derive the arbitrage pricing theory (APT)?

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

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

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

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Derivation of the APT requires three assumptions:

1. Asset returns are described by a factor model.
2. A large number of assets are available, which means investors can create diversified portfolios in which firm-specific risk is eliminated.
3. 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.

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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.

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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) 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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The APT makes no assumption about a market portfolio.

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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) 5.0%.

B) 2.4%.

C) 3.0%.

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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%

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

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

B) sensitivity of the market portfolio to factor j.

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

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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).

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

A) is an equilibrium pricing model.

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

C) assumes that arbitrage opportunities are available to investors.

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