Reading 64: Portfolio Concepts-LOS L习题精选 2010, statements, following, including

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

Which of the following statements about multifactor models is CORRECT?

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

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

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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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) 4.49%.

C) 11.38%.

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

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Michael Paul, a portfolio manager, is screening potential investments and suspects that an arbitrage opportunity may be available. The three portfolios that meet his screening criteria are detailed below:

Portfolio	Expected Return	Beta
A	12%	1.0
B	16%	1.3
C	8%	0.9

Which of the following portfolio combinations produces the highest return while maintaining a beta of 1.0?

Portfolio A

Portfolio B

Portfolio C

A) 25% 50% 25%

B) 100% 0% 0%

C) 50% 18% 32%

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Portfolio Weights			Expected Return	Beta
A	B	C
25%	50%	25%	13.00%	1.13
0%	36%	64%	11.52%	1.00
50%	18%	32%	11.44%	1.00
100%	0%	0%	12.00%	1.00

There is no arbitrage opportunity available. Investing 100% in Portfolio A yields the highest return for this risk level (i.e., beta = 1).

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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:

1. (7%)
2. (4%)
3. (2%)
4. (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) 18.3%.

B) 14.5%.

C) 20.1%.

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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 is an assumption of the arbitrage pricing theory (APT)?

A) Returns are normally distributed.

B) Investors have quadratic utility functions.

C) No arbitrage opportunities exist.

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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.

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

A) Security returns are normally distributed.

B) Investors have quadratic utility functions.

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

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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.

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

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

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

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

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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.

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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) has fewer assumptions than CAPM.

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

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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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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.

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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.