Question 1

The APT requires a benchmark portfolio
A)that is equal to the true market portfolio.
B)that contains all securities in proportion to their market values.
C)that need not be well-diversified.
D)that is well-diversified and lies on the SML.
E)that is unobservable.

Accepted Answer

Any well-diversified portfolio lying on the SML can serve as the benchmark portfolio for the APT.The true (and unobservable) market portfolio is only a requirement for the CAPM.

Question 2

In a factor model, the return on a stock in a particular period will be related to
A)factor risk.
B)nonfactor risk.
C)standard deviation of returns.
D)factor risk and nonfactor risk.
E)None of the options is true.

Accepted Answer

Factor models explain firm returns based on both factor risk and nonfactor risk.

Question 3

Which of the following factors did Chen, Roll, and Ross include in their multifactor model
A)Change in industrial waste
B)Change in expected inflation
C)Change in unanticipated inflation
D)Change in expected inflation and unanticipated inflation
E)All of the factors were included in their model.

Accepted Answer

Chen, Roll, and Ross included the change in expected inflation and the change in unanticipated inflation as well as the excess return of long-term corporate bonds over long-term government bonds in their model.

Question 4

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 18% and 250 securities A)1.14% B)625% C)0.5% D)3.54% E)3.16%

Accepted Answer

The nonsystematic standard deviation of an equally-weighted portfolio can be calculated using the formula: $\sigma_{p} = \frac{\sigma(e)}{\sqrt{n}}$, where $\sigma(e)$ is the average value of the nonsystematic risk (in this case, 18% or 0.18) and $n$ is the number of securities in the portfolio (250). Plugging in the values, we get $\sigma_{p} = \frac{0.18}{\sqrt{250}} \approx 0.0114$ or 1.14%.

Question 5

Which of the following is true about the security market line (SML) derived from the APT
A)The SML has a downward slope.
B)The SML for the APT shows expected return in relation to portfolio standard deviation.
C)The SML for the APT has an intercept equal to the expected return on the market portfolio.
D)The benchmark portfolio for the SML may be any well-diversified portfolio.
E)The SML is not relevant for the APT.

Accepted Answer

The benchmark portfolio does not need to be the (unobservable) market portfolio under the APT, but can be any well-diversified portfolio.The intercept still equals the risk-free rate.

Question 6

The factor F in the APT model represents
A)firm-specific risk.
B)the sensitivity of the firm to that factor.
C)a factor that affects all security returns.
D)the deviation from its expected value of a factor that affects all security returns.
E)a random amount of return attributable to firm events.

Accepted Answer

F measures the unanticipated portion of a factor that is common to all security returns.

Question 7

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 25% and 50 securities A)12.5% B)625% C)0.5% D)3.54% E)14.59%

Accepted Answer

Nonsystematic standard deviation (σ(e)) is given as 25%
Number of securities (n) = 50

Using the formula: 
σ(P) = [∑nσ(e)i^2]^0.5 / n
where σ(e)i is the standard deviation of the ith security.

As all the securities are equally weighted, σ(e)i = σ(e) = 25%
Therefore, σ(P) = [∑n(σ(e))^2]^0.5 / n
σ(P) = [n(σ(e))^2]^0.5 / n
σ(P) = (nσ(e))^0.5 / n
σ(P) = (50 * (0.25)^2)^0.5 / 50
σ(P) = 0.0354 or 3.54%

Therefore, the answer is D) 3.54%.

Question 8

In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its nonsystematic risk approaches
A)one.
B)infinity.
C)zero.
D)negative one.

Accepted Answer

As the number of securities, n, increases, the nonsystematic risk of a well-diversified portfolio approaches zero.

Question 9

A well-diversified portfolio is defined as
A)one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero.
B)one that contains securities from at least three different industry sectors.
C)a portfolio whose factor beta equals 1.0.
D)a portfolio that is equally weighted.

Accepted Answer

A well-diversified portfolio is one that contains a large number of securities, each having a small (but not necessarily equal) weight, so that nonsystematic variance is negligible.

Question 10

If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must be
A)inversely proportional to the risk-free rate.
B)inversely proportional to its standard deviation.
C)proportional to its weight in the market portfolio.
D)proportional to its standard deviation.
E)proportional to its beta coefficient.

Accepted Answer

For each well-diversified portfolio (P and Q, for example), it must be true that [E(r_p) - r_f]/β_p = [E(r_Q) - r_f]/β_Q.

Question 11

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 20 securities A)12.5% B)625% C)4.47% D)3.54% E)14.59%

Accepted Answer

The formula for non-systematic standard deviation is: σ(e) = sqrt((1/n) * ∑(w2i * σ2(ei)) where n is the number of securities, wi is the weight of ith security, and σ(ei) is the standard deviation of the ith security's returns. Given that the portfolio has 20 securities of equal weight, wi = 1/20 for each security. σ(e_i) is given to be 20% or 0.20. Plugging in the values, we get: σ(e) = sqrt((1/20) * 20 * σ2(ei)) σ(e) = sqrt(σ2(ei)) σ(e) = σ(ei) Therefore, the non-systematic standard deviation of an equally weighted portfolio is equal to the standard deviation of each individual security. Since no information is given about the standard deviation of individual securities or their weights, we cannot calculate the non-systematic standard deviation. However, we do know that it cannot be greater than 20% or 0.20 since the portfolio's average value is given to be 20%. Therefore, the best choice is C, 4.47%, which is the highest option that is less than or equal to 20%.

Question 12

Suppose you are working with two factor portfolios, portfolio 1 and portfolio 2.The portfolios have expected returns of 15% and 6%, respectively.Based on this information, what would be the expected return on well-diversified portfolio A, if A has a beta of 0.80 on the first factor and 0.50 on the second factor The risk-free rate is 3%.
A)15.2%
B)14.1%
C)13.3%
D)10.7%
E)8.4%

Accepted Answer

E(R_A) = 3 + 0.8 × (15 - 3) + 0.5 × (6 - 3) = 14.1.

Question 13

To take advantage of an arbitrage opportunity, an investor would I) construct a zero investment portfolio that will yield a sure profit.
II) construct a zero beta investment portfolio that will yield a sure profit.
III) make simultaneous trades in two markets without any net investment.
IV) short sell the asset in the low-priced market and buy it in the high-priced market.
A)I and IV
B)I and III
C)II and III
D)I, III, and IV
E)II, III, and IV

Accepted Answer

Only I and III are correct.II is incorrect because the beta of the portfolio does not need to be zero.IV is incorrect because the opposite is true.

Question 14

Which of the following factors did Chen, Roll, and Ross not include in their multifactor model
A)Change in industrial production
B)Change in expected inflation
C)Change in unanticipated inflation
D)Excess return of long-term government bonds over T-bills
E)All of the factors are included in the Chen, Roll, and Ross multifactor model.

Accepted Answer

Chen, Roll, and Ross included the four listed factors as well as the excess return of long-term corporate bonds over long-term government bonds in their model.

Question 15

Imposing the no-arbitrage condition on a single-factor security market implies which of the following statements
I. The expected return-beta relationship is maintained for all but a small number of well-diversified portfolios.
II. The expected return-beta relationship is maintained for all well-diversified portfolios.
III. The expected return-beta relationship is maintained for all but a small number of individual securities.
IV. The expected return-beta relationship is maintained for all individual securities.
A)I and III
B)I and IV
C)II and III
D)II and IV
E)Only I is correct.

Accepted Answer

The expected return-beta relationship must hold for all well-diversified portfolios and for all but a few individual securities; otherwise arbitrage opportunities will be available.

Question 16

Which of the following is false about the security market line (SML) derived from the APT
A)The SML has a downward slope.
B)The SML for the APT shows expected return in relation to portfolio standard deviation.
C)The SML for the APT has an intercept equal to the expected return on the market portfolio.
D)The benchmark portfolio for the SML may be any well-diversified portfolio.
E)The SML has a downward slope, shows expected return in relation to portfolio standard deviation, and has an intercept equal to the expected return on the market portfolio.

Accepted Answer

The benchmark portfolio does not need to be the (unobservable) market portfolio under the APT, but can be any well-diversified portfolio.The intercept still equals the risk-free rate.

Question 17

Consider a well-diversified portfolio, A, in a two-factor economy.The risk-free rate is 6%, the risk premium on the first factor portfolio is 4% and the risk premium on the second factor portfolio is 3%.If portfolio A has a beta of 1.2 on the first factor and .8 on the second factor, what is its expected return
A)7.0%
B)8.0%
C)9.2%
D)13.0%
E)13.2%

Accepted Answer

.06 + 1.2 (.04) + .8 (.03) = .132.

Question 18

Which of the following is(are) true regarding the APT
I. The security market line does not apply to the APT.
II. More than one factor can be important in determining returns.
III. Almost all individual securities satisfy the APT relationship.
IV. It doesn't rely on the market portfolio that contains all assets.
A)II, III, and IV
B)II and IV
C)II and III
D)I, II, and IV
E)I, II, III, and IV

Accepted Answer

All except the first item are true.There is a security market line associated with the APT.

Question 19

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 40 securities A)12.5% B)625% C)0.5% D)3.54% E)3.16%

Accepted Answer

According to the APT model, the nonsystematic standard deviation of an equally weighted portfolio is given by the square root of the sum of the squared standard deviations of each security in the portfolio divided by the number of securities in the portfolio. Thus, nonsystematic standard deviation = sqrt[(1/40)*(σ(e_i)^2)] = sqrt[(1/40)*(0.2^2)] = 0.032 Therefore, the answer is E) 3.16%.

Question 20

The term "arbitrage" refers to
A)buying low and selling high.
B)short selling high and buying low.
C)earning risk-free economic profits.
D)negotiating for favorable brokerage fees.
E)hedging your portfolio through the use of options.

Accepted Answer

Arbitrage is exploiting security mispricings by the simultaneous purchase and sale to gain economic profits without taking any risk.A capital market in equilibrium rules out arbitrage opportunities.

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

The APT requires a benchmark portfolio

In a factor model, the return on a stock in a particular period will be related to

Which of the following factors did Chen, Roll, and Ross include in their multifactor model

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(ei) equal to 18% and 250 securities

Which of the following is true about the security market line (SML) derived from the APT

The factor F in the APT model represents

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(ei) equal to 25% and 50 securities

In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its nonsystematic risk approaches

A well-diversified portfolio is defined as

If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must be

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(ei) equal to 20% and 20 securities

Which of the following factors did Chen, Roll, and Ross not include in their multifactor model

Which of the following is false about the security market line (SML) derived from the APT

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(ei) equal to 20% and 40 securities

The term "arbitrage" refers to

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 18% and 250 securities

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 25% and 50 securities

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 20 securities

In the APT model, what is the nonsystematic standard deviation of an equally weighted portfolio that has an average value of σ(e_i) equal to 20% and 40 securities