Deck 12: Arbitrage Pricing Theory

Question 1

Pure factor portfolios have _____ sensitivity to the factor

A) zero
B) unit
C) pure
D) increasing

Answer 1

B

Question 2

A similarity between APT and CAPM is that both

A) assume security sensitivities are explained by beta.
B) assumes investors want the largest return for a given level of risk.
C) make the same assumption about riskfree lending rates.
D) use the covariance between a security and the market.

Answer 2

B

Question 3

When an arbitrage pricing model is in equilibrium, there will be a ______ relationship between expected returns and factor sensitivities.

A) zero
B) increasing
C) linear
D) decreasing

Answer 3

C

Question 4

_______ risk is the portion of a security's total risk that is not related to moves in various common factors.

A) non-market
B) factor
C) nominal
D) idiosyncratic

Question 5

The APT approach assumes stock returns are related to the factors of

A) market returns only.
B) market returns and GDP.
C) GDP and CPI.
D) no specific variable.

Question 6

Strictly speaking, an arbitrage portfolio should have _____ nonfactor risk.

A) high
B) low
C) constant
D) zero

Question 7

In developing an arbitrage portfolio, the factor sensitivity of the portfolio will

A) remain the same as before.
B) decrease slightly.
C) decrease the expected portfolio return.
D) increase significantly.

Question 8

An arbitrage price model recommends buying more of Stock X anThe resulting effect should be

A) all prices should rise.
B) the returns on Y and Z should decline.
C) the return on X should decline.
D) the price of Y and Z should rise.

Question 9

Most research results have identified common factors that use

A) aggregate economic activity
B) gold prices
C) foreign exchange rates of the major economies
D) commodity prices

Question 10

In a two-factor model, each security will have _____ sensitivity coefficients.

A) two
B) one
C) none
D) many

Question 11

The essential logic of the arbitrage pricing theory is

A) investors will normally not observe arbitrage opportunities
B) investors will take advantage of arbitrage opportunities thus eliminating them
C) arbitrage opportunities are eliminated before most investors observe them
D) investors will observe and take advantage of arbitrage opportunities

Question 12

The arbitrage pricing theory was developed by ______ in the early 1970's.

A) Sharpe
B) Roll
C) Ross
D) Miller

Question 13

____ is the process of earning risk less profits by taking advantage of differential pricing for the same physical asset or security.

A) Anomalies
B) Aggregation
C) Abstraction
D) Arbitrage

Question 14

In a multiple-factor situation, the asset pricing line

A) becomes curved with a decreasing, positive slope.
B) contradicts the CAPM.
C) is still linear.
D) becomes flat.

Question 15

The APT asset pricing line is 6% + 2%(bp). If the portfolio has unit sensitivity to this factor, the expected return for the portfolio is

A) 6%.
B) 8%.
C) 12%.
D) 10%.

Question 16

An investor seeks to explore the possibility of forming an arbitrage portfolio in order to increase

A) the expected return without increasing risk
B) the expected return with increasing risk
C) the expected return
D) the expected risk

Question 17

Provided a proxy for the market portfolio could be found, then the CAPM and the APT would ________.

A) contradict each other in their assumptions
B) prove inconsistent
C) prove somewhat consistent
D) demonstrate perfect consistency

Question 18

The arbitrage price portfolio is assumed to have

A) only unique risk.
B) an expected return of 0.
C) only market risk.
D) no risk.

Question 19

APT assumes that an arbitrage portfolio's nonfactor risk is

A) -1.
B) +.5.
C) 0.
D) -.5.

Question 20

The assumptions found in the APT appear __________ the assumptions of the CAPM.

A) similar to
B) different than
C) relatively consistent with
D) slightly different than

Question 21

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

Question 22

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%

Question 23

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

Question 24

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.

Question 25

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

Question 26

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.

Question 27

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

Question 28

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

Question 29

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%

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 34

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.

Question 35

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.

Question 36

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.

Question 37

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

Question 38

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

Question 39

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

Question 40

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