Question 1

Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios?
A) The CAPM
B) The multifactor APT
C) Both the CAPM and the multifactor APT
D) Neither the CAPM nor the multifactor APT
E) None of the options are correct.

Accepted Answer

The multifactor Arbitrage Pricing Theory (APT) does not specify the risk premium for factor portfolios; it only suggests that returns are linearly related to various factors.

Question 2

Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor, and portfolio B has a beta of 2.0 on the factor. The expected returns on portfolios A and B are 11% and 17%, respectively. Assume that the risk-free rate is 6%, and that arbitrage opportunities exist. Suppose you invested $100,000 in the risk-free asset, $100,000 in portfolio B, and sold short $200,000 of portfolio A. Your expected profit from this strategy would be
A) −$1,000.
B) $0.
C) $1,000.
D) $2,000.

Accepted Answer

The expected return on portfolio A (with a beta of 1.0) can be calculated using the Capital Asset Pricing Model (CAPM) formula: $E(R_A) = R_f + \beta_A(E(R_M) - R_f)$, where $R_f$ is the risk-free rate, $\beta_A$ is the beta of portfolio A, and $E(R_M)$ is the expected market return. Given that portfolio A's expected return is 11%, and the risk-free rate is 6%, we can infer the market risk premium $E(R_M) - R_f$ is 5% (since $11% = 6% + 1.0 \times 5%$).For portfolio B, with a beta of 2.0, its expected return using CAPM would be $E(R_B) = R_f + \beta_B(E(R_M) - R_f) = 6% + 2.0 \times 5% = 16%$. However, the expected return given is 17%, indicating an arbitrage opportunity because the expected return is higher than what CAPM predicts.The strategy involves investing $100,000 in the risk-free asset, $100,000 in portfolio B, and short selling $200,000 of portfolio A. The expected profit from this strategy can be calculated as follows:- The return from the risk-free asset is $6\% \times \$100,000 = \$6,000$.- The return from portfolio B is $17\% \times \$100,000 = \$17,000$.- The loss from short selling portfolio A is $11\% \times \$200,000 = \$22,000$.The total expected profit is $\$6,000 + \$17,000 - \$22,000 = \$1,000$.

Question 3

Consider the one-factor APT. The variance of returns on the factor portfolio is 5%. The beta of a well-diversified portfolio on the factor is 1.2. The variance of returns on the well-diversified portfolio is approximately
A) 3.6%.
B) 7.2%.
C) 8.3%.
D) 19.1%.

Accepted Answer

In the one-factor Arbitrage Pricing Theory (APT) model, the variance of returns on a well-diversified portfolio ($\sigma^2_p$) can be approximated by the product of the square of the portfolio's beta ($\beta_p^2$) on the factor and the variance of returns on the factor portfolio ($\sigma^2_f$). Thus, $\sigma^2_p = \beta_p^2 \times \sigma^2_f$. Given $\beta_p = 1.2$ and $\sigma^2_f = 5%$, we calculate $\sigma^2_p = 1.2^2 \times 5\% = 1.44 \times 5\% = 7.2\%$.

Question 4

Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long position in portfolio _________.
A) A; A
B) A; B
C) B; A
D) B; B

Accepted Answer

According to the Arbitrage Pricing Theory (APT), the expected return on a portfolio should be linearly related to its beta with respect to the market. The formula to calculate the expected return is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). If we rearrange the formula to solve for the market return, we can compare the expected returns of both portfolios to see if they align with the APT. For Portfolio A: 13% = 10% + 0.2 * (Market Return - 10%)For Portfolio B: 15% = 10% + 0.4 * (Market Return - 10%)Solving these equations, we find that the expected market return implied by Portfolio A is higher than that implied by Portfolio B. This discrepancy suggests an arbitrage opportunity. To exploit this, one should short the portfolio that is overpriced (higher beta but lower than expected return) and go long on the portfolio that is underpriced (lower beta but higher than expected return). In this case, Portfolio B is overpriced relative to its expected return based on its beta, and Portfolio A is underpriced. Therefore, you should take a short position in Portfolio B and a long position in Portfolio A to exploit the arbitrage opportunity.

Question 5

In a multifactor APT model, the coefficients on the macro factors are often called
A) systematic risk.
B) factor sensitivities.
C) idiosyncratic risk.
D) factor betas.
E) factor sensitivities and factor betas.

Accepted Answer

The coefficients on the macro factors in a multifactor Arbitrage Pricing Theory (APT) model are referred to as factor sensitivities and factor betas. These terms are used interchangeably to describe how sensitive a security's returns are to changes in macroeconomic factors.

Question 6

Consider the multifactor model APT with two factors. Portfolio A has a beta of 1.20 on factor 1 and a beta of 1.50 on factor 2. The risk premiums on the factor-1 and factor-2 portfolios are 1% and 7%, respectively. The risk-free rate of return is 4%. The expected return on portfolio A is __________ if no arbitrage opportunities exist.
A) 13.5%
B) 15.0%
C) 15.7%
D) 23.0%

Accepted Answer

The expected return on portfolio A according to the Arbitrage Pricing Theory (APT) is calculated as follows: Expected Return = Risk-free rate + (Beta1 * Risk Premium1) + (Beta2 * Risk Premium2) = 4% + (1.20 * 1%) + (1.50 * 7%) = 4% + 1.2% + 10.5% = 15.7%.

Question 7

The ____________ provides an unequivocal statement on the expected return-beta relationship for all assets, whereas the _____________ implies that this relationship holds for all but perhaps a small number of securities.
A) APT; CAPM
B) APT; OPM
C) CAPM; APT
D) CAPM; OPM

Accepted Answer

The Capital Asset Pricing Model (CAPM) provides a clear expected return-beta relationship for all assets, assuming a linear relationship between the expected return of an asset and its beta. The Arbitrage Pricing Theory (APT), on the other hand, suggests this relationship holds for most but potentially not all securities, as it allows for multiple factors to influence returns, not just market risk.

Question 8

In developing the APT, Ross assumed that uncertainty in asset returns was a result of
A) a common macroeconomic factor.
B) firm-specific factors.
C) pricing error.
D) a common macroeconomic factor and firm-specific factors.

Accepted Answer

Ross's Arbitrage Pricing Theory (APT) posits that asset returns can be predicted using the relationship between those returns and various macroeconomic factors as well as firm-specific factors. This theory suggests that both types of factors—common macroeconomic and firm-specific—affect the uncertainty in asset returns.

Question 9

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 14%. The standard deviation on the factor portfolio is 10%. The beta of the well-diversified portfolio is approximately
A) 0.80.
B) 1.40.
C) 1.65.
D) 1.82.

Accepted Answer

The beta of a portfolio in the context of the Arbitrage Pricing Theory (APT) is calculated as the ratio of the portfolio's standard deviation to the standard deviation of the factor, multiplied by the correlation coefficient between the portfolio and the factor. For a well-diversified portfolio, the correlation with the factor is assumed to be 1. Therefore, the beta is calculated as the standard deviation of the portfolio (14%) divided by the standard deviation of the factor (10%), which equals 1.40.

Question 10

The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called
A) arbitrage.
B) capital-asset pricing.
C) factoring.
D) fundamental analysis.
E) None of the options are correct.

Accepted Answer

Arbitrage involves taking advantage of price differences in different markets or forms of a security to make a risk-free profit, which aligns with the exploitation of security mispricing for economic gain.

Question 11

An arbitrage opportunity exists if an investor can construct a __________ investment portfolio that will yield a sure profit.
A) positive
B) negative
C) zero
D) All of the options.
E) None of the options are correct.

Accepted Answer

An arbitrage opportunity exists if an investor can construct a zero investment portfolio (meaning no net outlay of funds) that will yield a sure profit. This involves taking advantage of price differences in different markets or forms without risk.

Question 12

In a multifactor APT model, the coefficients on the macro factors are often called
A) systematic risk.
B) firm-specific risk.
C) idiosyncratic risk.
D) factor loadings.

Accepted Answer

In a multifactor Arbitrage Pricing Theory (APT) model, the coefficients on the macro factors are referred to as factor loadings. These loadings measure the sensitivity of the asset's returns to changes in the macroeconomic factors.

Question 13

A _________ portfolio is a well-diversified portfolio constructed to have a beta of 1 on one of the factors and a beta of 0 on any other factor.
A) factor
B) market
C) index
D) factor and market
E) factor, market, and index

Accepted Answer

A factor portfolio is specifically designed to have a beta of 1 with respect to one factor, meaning it is fully sensitive to changes in that factor, and a beta of 0 with respect to all other factors, indicating no sensitivity to movements in those factors. This allows investors to isolate and gain exposure to specific risk factors.

Question 14

Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.75 on factor 1, and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exist?
A) 8.14%
B) 3%
C) 4%
D) 7.75%

Accepted Answer

The correct answer is A because the risk premium on factor 2 is 8.14%. This can be calculated using the following formula:Risk premium on factor 2 = (Expected return on stock A - Risk-free rate) / Beta on factor 2= (17.6% - 5%) / .86= 8.14%

Question 15

The APT was developed in 1976 by
A) Lintner.
B) Modigliani and Miller.
C) Ross.
D) Sharpe.

Accepted Answer

The Arbitrage Pricing Theory (APT) was developed by Stephen Ross in 1976. It is a theory that provides the foundation for understanding the relationship between the return of an asset and its risk in comparison to the market.

Question 16

Consider a single factor APT. Portfolio A has a beta of 1.0 and an expected return of 16%. Portfolio B has a beta of 0.8 and an expected return of 12%. The risk-free rate of return is 6%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _______.
A) A; A
B) A; B
C) B; A
D) B; B
E) A; the riskless asset

Accepted Answer

Portfolio A offers a higher return than Portfolio B for the same level of risk (beta), indicating an arbitrage opportunity. Therefore, short Portfolio B and long Portfolio A.

Question 17

Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 6%, respectively. Stock A has a beta of 1.2 on factor-1, and a beta of 0.7 on factor-2. The expected return on stock A is 17%. If no arbitrage opportunities exist, the risk-free rate of return is
A) 6.0%.
B) 6.5%.
C) 6.8%.
D) 7.4%.

Accepted Answer

The expected return on stock A can be calculated using the APT formula: Expected Return = Risk-free rate + (Beta1 * Risk Premium1) + (Beta2 * Risk Premium2). Plugging in the values: 17% = Risk-free rate + (1.2 * 5%) + (0.7 * 6%). Solving for the risk-free rate gives 6.8%.

Question 18

Consider the single-factor APT. Stocks A and B have expected returns of 12% and 19%, respectively. The risk-free rate of return is 3%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of
A) 0.47.
B) 1.00.
C) 1.30.
D) 1.69.
E) 0.75.

Accepted Answer

The single-factor APT (Arbitrage Pricing Theory) formula is: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Given that there are no arbitrage opportunities, we can set up equations for both stocks A and B based on their expected returns, betas, and the risk-free rate. For Stock B, we have 19% = 3% + 1.2 * (Market Return - 3%). Solving for Market Return gives us 16.67%. Using this Market Return in the formula for Stock A, we can solve for Stock A's beta, which results in a beta of approximately 0.47.

Question 19

In a multifactor APT model, the coefficients on the macro factors are often called
A) systematic risk.
B) firm-specific risk.
C) idiosyncratic risk.
D) factor betas.

Accepted Answer

In a multifactor Arbitrage Pricing Theory (APT) model, the coefficients on the macro factors are referred to as factor betas. These betas measure the sensitivity of the asset's returns to changes in the underlying macroeconomic factors.

Question 20

Consider the multifactor APT with two factors. Stock A has an expected return of 14%, a beta of 1.2 on factor 1, and a beta of .8 on factor 2. The risk premium on the factor-1 portfolio is 3%. The risk-free rate of return is 4%. What is the risk-premium on factor 2 if no arbitrage opportunities exist?
A) 2%
B) 4%
C) 6%
D) 8%

Accepted Answer

The expected return on a stock according to the Arbitrage Pricing Theory (APT) can be calculated using the formula: $E(R_i) = R_f + \beta_{i1}RP_1 + \beta_{i2}RP_2 + ... + \beta_{in}RP_n$, where $E(R_i)$ is the expected return on asset i, $R_f$ is the risk-free rate, $\beta_{ij}$ is the sensitivity of the ith asset to factor j, and $RP_j$ is the risk premium for factor j. For Stock A, we have $E(R_A) = 14\%$, $R_f = 4\%$, $\beta_{A1} = 1.2$, $RP_1 = 3\%$, and $\beta_{A2} = 0.8$. Plugging these into the APT formula gives us $14\% = 4\% + 1.2(3\%) + 0.8(RP_2)$. Solving for $RP_2$ gives us $RP_2 = 8\%$.

Quiz 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return

Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios?

Consider the one-factor APT. The variance of returns on the factor portfolio is 5%. The beta of a well-diversified portfolio on the factor is 1.2. The variance of returns on the well-diversified portfolio is approximately

In a multifactor APT model, the coefficients on the macro factors are often called

The provides an unequivocal statement on the expected return-beta relationship for all assets, whereas the _ implies that this relationship holds for all but perhaps a small number of securities.

In developing the APT, Ross assumed that uncertainty in asset returns was a result of

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 14%. The standard deviation on the factor portfolio is 10%. The beta of the well-diversified portfolio is approximately

The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called

An arbitrage opportunity exists if an investor can construct a __________ investment portfolio that will yield a sure profit.

In a multifactor APT model, the coefficients on the macro factors are often called

A _________ portfolio is a well-diversified portfolio constructed to have a beta of 1 on one of the factors and a beta of 0 on any other factor.

The APT was developed in 1976 by

Consider the single-factor APT. Stocks A and B have expected returns of 12% and 19%, respectively. The risk-free rate of return is 3%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of

In a multifactor APT model, the coefficients on the macro factors are often called