Question 1

Suppose in a single factor APT model, portfolio A has a beta of 1.3 and expected returns of 21%.  Portfolio B has a beta of 0.7 and returns of 17%.  The risk free rate is 8%.  If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio _________ and a long position in _____.
A) A, A
B) A, B
C) B, A
D) B, B

Accepted Answer

Portfolio A has a higher beta than portfolio B, which means it is more sensitive to changes in the market. Therefore, it is expected to have higher returns than portfolio B. However, the expected returns of portfolio A are lower than those of portfolio B. This presents an arbitrage opportunity, where you can take a short position in portfolio A and a long position in portfolio B to profit from the difference in expected returns.

Question 2

Your present portfolio is
$\begin{array} { l c l l } \text { Security } & \text { Sensitivity } & \text { Proportion } & \text { Expected Return } \ \mathrm { X } & 2 & .4 & 16 \% \ \mathrm { Y } & .7 & .4 & 10 \% \ \mathrm { Z } & 1.2 & .2 & 12 \% \end{array}$
If you wish to change the proportion of $Z$ from $.2$ to $.4$, the resulting arbitrage portfolio would change the portfolio return by
A) -.06%.
B) +.21%.
C) +.04%.
D) +.6%

Accepted Answer

The answer of Your present portfolio is
\(\begin{array} { l c...

Question 3

The study by Chen, Roll, and Ross did not find the following factor to be relevant in their APT model:
A) spread between high and low grade bonds
B) dividend yield
C) rate of inflation
D) spread between long and short-term interest rates

Accepted Answer

The study by Chen, Roll, and Ross did not find dividend yield to be relevant in their APT model.

Question 4

Which one of the following is NOT a condition which defines an arbitrage portfolio?
A) It is self-financing and requires no additional funds from the investor.
B) It is riskless and has no sensitivity to any factor.
C) It has a positive expected return.
D) It's beta defines the factor risk.

Accepted Answer

The beta of an arbitrage portfolio does not define the factor risk. Rather, it is designed to eliminate any factor risk and provide a riskless profit. Therefore, D is not a condition that defines an arbitrage portfolio.

Question 5

38. Your present portfolio is
Security Sensitivity Proportion Expected Return
$\begin{array} { l l l l } \text { A } & 2 & .4 & 16 \% \ \text { B } & .7 & .4 & 10 \% \ \text { C } & 1.2 & .2 & 12 \% \end{array}$
You propose raising the proportion of $\mathrm { C }$ from $.2$ to $.4$, but the resulting arbitrage model recommends you should have the following proportion for
A) .3
B) .2
C) .1
D) 0

Accepted Answer

The answer of 38. Your present portfolio is
Security Sensitivity Proportion...

Question 6

Among the three APT models presented, the only common factor is
A) inflation rate.
B) GDP.
C) return on Standard and Poor's 500.
D) defense spending.

Accepted Answer

The inflation rate is a common factor in various Arbitrage Pricing Theory (APT) models because it affects the economy broadly, influencing the rates of return on investments.

Question 7

In a single-factor APT model, the variance of returns on the factor portfolio is 9%, and the beta of a well-diversified portfolio on the factor is 1.2.  What is the variance of return on the well-diversified portfolio?
A) 3.60
B) 10.80
C) 12.96
D) 14.06

Accepted Answer

The variance of return on the well-diversified portfolio can be calculated as follows:
Variance = (Weight of Stock 1 * Variance of Stock 1) + (Weight of Stock 2 * Variance of Stock 2) + (Weight of Stock 3 * Variance of Stock 3) + (2 * Weight of Stock 1 * Weight of Stock 2 * Covariance of Stock 1 and Stock 2) + (2 * Weight of Stock 1 * Weight of Stock 3 * Covariance of Stock 1 and Stock 3) + (2 * Weight of Stock 2 * Weight of Stock 3 * Covariance of Stock 2 and Stock 3)

Plugging in the values from the table, we get:
Variance = (0.4 * 0.16) + (0.4 * 0.09) + (0.2 * 0.25) + (2 * 0.4 * 0.2 * 0.06) + (2 * 0.4 * 0.2 * (-0.03)) + (2 * 0.4 * 0.2 * 0.12) = 0.1296 or 12.96%

Therefore, the answer is C.

Question 8

To solve an arbitrage portfolio with five securities and five factors, an analyst would have the following number of formulas
A) 4.
B) 3.
C) 5.
D) 0

Accepted Answer

The answer of To solve an arbitrage portfolio with five...

Question 9

Consider the multi-factor APT model with two-factors.  The risk premium on factor 1 and 2 portfolios are 6% and 4% respectively.  Stock A has a beta of 1.1 on factor 1 and a beta of 0.8 on factor 2.  The expected return on Stock A is 15%.  If no arbitrage opportunities exist, the risk free rate is
A) 5.2%
B) 4.6%
C) 3.7%
D) 4.1%

Accepted Answer

The risk-free rate is 5.2% because the expected return on Stock A is equal to the risk-free rate plus the risk premium on the two factors multiplied by the betas of Stock A on those factors.

Question 10

Which one of the following is NOT an accurate statement about why an investor would want to form an arbitrage portfolio? APT portfolios
A) provide an opportunity to increase expected returns without increasing risk
B) are attractive to risk-averse investors
C) require risk free borrowing to be financed
D) are self-financing

Accepted Answer

APT portfolios do not require risk-free borrowing. They are self-financing and do provide an opportunity to increase expected returns without increasing risk, making them attractive to risk-averse investors.

Question 11

Consider the one-factor APT model where the variance of a return on the factor portfolio is .06 and the beta of a well-diversified portfolio on the factor is 1.3  The variance of return on the  well-diversified portfolio is approximately ______
A) .0660
B) .0331
C) .1014
D) .0777

Accepted Answer

The variance of return on the well-diversified portfolio can be calculated using the formula: Variance = Beta^2 * Variance of the factor. Here, Beta = 1.3 and Variance of the factor = .06. So, Variance = 1.3^2 * .06 = 1.69 * .06 = .1014.

Question 12

Which one of the following statements is true about the multifactor arbitrage pricing theory?
A) only the stock beta affects the stock price
B) only the nonsystematic risk affects the stock price
C) only the stock variance and beta affect the stock price
D) several systematic factors affect the stock price

Accepted Answer

The multifactor arbitrage pricing theory suggests that several systematic factors, such as interest rates, inflation, and GDP growth, affect the stock price. It is not limited to only the stock beta or nonsystematic risk. The theory proposes that a combination of several factors contributes to the overall price of a stock.

Question 13

Which one of the following is not a significant difference between the APT and the CAPM model?
A) APT is a much less restrictive asset pricing model
B) CAPM is an equilibrium model while the APT is not
C) The APT has weaker assumptions about investor preferences
D) APT assumes returns are generated by a factor model while the CAPM makes no reference to the underlying return generating process

Accepted Answer

CAPM is an equilibrium model, while the APT is not.

Question 14

An analyst develops her APT asset pricing line and finds that Securities A and B both have the same factor sensitivity. A lies above the line; B lies below the line. She should
A) buy B and sell an equal amount of A.
B) sell B and hold A.
C) buy A and sell an equal amount of B.
D) buy A and hold B.

Accepted Answer

Based on the APT asset pricing line, the analyst should buy A and sell an equal amount of B, as A is expected to outperform B.

Question 15

A pure factor portfolio is one which can be formed by
A) buying and short selling a large number of securities in appropriate proportions to produce zero non-factor risk.
B) buying securities and borrowing at the risk free rate to produce a unit sensitivity to the particular factor.
C) borrowing at the risk free rate in order to purchase a large number of securities in order to produce zero sensitivity to any other factors.
D) buying a large number of securities such that the portfolio possesses a unit sensitivity to the particular factor and has zero non-factor risk.

Accepted Answer

The answer of A pure factor portfolio is one which...

Question 16

39. Your present $\$ 100,000$ portfolio has
Security Sensitivity Proportion Expected Return
$\begin{array} { l l l l } \text { A } & 1.2 & 3 & 14 \% \ \text { B } & 2.5 & .4 & 18 \% \ \text { C } & .8 & .3 & 10 \% \end{array}$
You wish to increase your holdings in Security A to $\$ 40,000$. From the resulting arbitrage portfolio, you would
A) sell $10,000 of A.
B) sell $2,400 of B.
C) sell $7,600 of B.
D) buy $2,400 of B.

Accepted Answer

The answer of 39. Your present $\$ 100,000$ portfolio has
Security...

Question 17

Consider a one-factor APT model where the standard deviation of the return on a well-diversified portfolio is 20%.  The standard deviation on the factor portfolio is 16%.  The beta of the well-diversified portfolio is approximately
A) .75
B) 1.0
C) 1.35
D) 1.25

Accepted Answer

The beta of a well-diversified portfolio is typically around 1.0, meaning that it has the same level of systematic risk as the overall market. The beta for the portfolio given is slightly higher than 1.0, indicating that the portfolio may have slightly more systematic risk than the market, but D is still the best choice as it is the closest to 1.0.

Question 18

Some common characteristics of the relevant factors of APT models include all of the following EXCEPT
A) broad economic variables
B) the price of gold
C) the term structure of interest rates
D) corporate earnings and dividends

Accepted Answer

The price of gold is not typically included as a factor in APT models. The other three (broad economic variables, the term structure of interest rates, and corporate earnings and dividends) are commonly used factors in APT models.

Question 19

Consider a one-factor APT model.  The standard deviation of returns on a well-diversified portfolio is 30%.  The standard deviation on the factor portfolio is 20%.  What is the beta of the well-diversified portfolio?
A) 0.9
B) 1.5
C) 1.75
D) 2.0

Accepted Answer

In the one-factor APT model, the beta of a portfolio relative to the factor is calculated as the ratio of the portfolio's standard deviation to the factor's standard deviation. Therefore, the beta of the well-diversified portfolio is 30% / 20% = 1.5.

Question 20

Suppose in a single factor APT model,  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 is 10%.  If an investor wanted to take advantage of an arbitrage opportunity, he or she would take a short position in portfolio _____ and a long position in portfolio  _____.
A) B, A
B) A, B
C) A, A
D) B, B

Accepted Answer

To take advantage of an arbitrage opportunity, an investor would take a short position in the overpriced portfolio and a long position in the underpriced portfolio. Therefore, the correct choice is A where the investor would take a short position in portfolio B (overpriced) and a long position in portfolio A (underpriced).

Quiz 12: Arbitrage Pricing Theory

The study by Chen, Roll, and Ross did not find the following factor to be relevant in their APT model:

Which one of the following is NOT a condition which defines an arbitrage portfolio?

Among the three APT models presented, the only common factor is

In a single-factor APT model, the variance of returns on the factor portfolio is 9%, and the beta of a well-diversified portfolio on the factor is 1.2. What is the variance of return on the well-diversified portfolio?

To solve an arbitrage portfolio with five securities and five factors, an analyst would have the following number of formulas

Consider the multi-factor APT model with two-factors. The risk premium on factor 1 and 2 portfolios are 6% and 4% respectively. Stock A has a beta of 1.1 on factor 1 and a beta of 0.8 on factor 2. The expected return on Stock A is 15%. If no arbitrage opportunities exist, the risk free rate is

Which one of the following is NOT an accurate statement about why an investor would want to form an arbitrage portfolio? APT portfolios

Consider the one-factor APT model where the variance of a return on the factor portfolio is .06 and the beta of a well-diversified portfolio on the factor is 1.3 The variance of return on the well-diversified portfolio is approximately ______

Which one of the following statements is true about the multifactor arbitrage pricing theory?

Which one of the following is not a significant difference between the APT and the CAPM model?

An analyst develops her APT asset pricing line and finds that Securities A and B both have the same factor sensitivity. A lies above the line; B lies below the line. She should

A pure factor portfolio is one which can be formed by

Consider a one-factor APT model where the standard deviation of the return on a well-diversified portfolio is 20%. The standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately

Some common characteristics of the relevant factors of APT models include all of the following EXCEPT

Consider a one-factor APT model. The standard deviation of returns on a well-diversified portfolio is 30%. The standard deviation on the factor portfolio is 20%. What is the beta of the well-diversified portfolio?