Question 1

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.
E)all of the above.

Accepted Answer

A well-diversified portfolio is one that is diversified over a large enough number of securities that the nonsystematic variance is essentially zero. Therefore, choice A is the correct answer. Choice B is not specific enough as it depends on the number of securities in each industry sector. Choice C is not relevant as beta is a measure of systematic risk, not diversification. Choice D implies equal weighting, which is not necessary for diversification, and is therefore not accurate. Choice E is incorrect as not all of the options listed are correct.

Question 2

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 above factors were included in their model.

Accepted Answer

Chen, Roll, and Ross included all the listed factors in their multifactor model, which is known as the Arbitrage Pricing Theory (APT).

Question 3

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

The nonsystematic standard deviation of an equally-weighted portfolio can be calculated using the formula: σ(eP) = σ(ei) / √n, where σ(ei) is the average value of the nonsystematic standard deviation of individual securities, and n is the number of securities in the portfolio. Given σ(ei) = 20% and n = 40, σ(eP) = 20% / √40 = 3.16%.

Question 4

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

The answer of Which of the following is (are)true regarding...

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 Security Market Line (SML) derived from the Arbitrage Pricing Theory (APT) can indeed use any well-diversified portfolio as a benchmark, not just the market portfolio. This flexibility is a key feature of the APT approach to asset pricing.

Question 6

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

The expected return on a well-diversified portfolio A can be calculated using the following formula:
E(RA) = RF + β1[E(R1) - RF] + β2[E(R2) - RF]
where RF is the risk-free rate, β1 and β2 are the betas on the first and second factors, and E(R1) and E(R2) are the expected returns on the two factor portfolios.
Plugging in the given values, we get:
E(RA) = 0.03 + 0.80[0.15 - 0.03] + 0.50[0.06 - 0.03] = 0.141 or 14.1%
Therefore, the best choice is B.

Question 7

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

Arbitrage involves taking advantage of price differences in different markets or forms to make a risk-free profit. Option I is correct because arbitrage often involves creating a portfolio that requires no net investment (zero investment) but yields a profit due to price discrepancies. Option III is also correct because arbitrage typically involves making simultaneous trades in different markets to exploit price differences without needing a net investment. Options II and IV are not accurate descriptions of arbitrage strategies. Option II is incorrect because the focus on a zero-beta portfolio is not a requirement for arbitrage. Option IV is incorrect because it describes a simple buy low, sell high strategy, but arbitrage specifically involves simultaneous transactions to lock in a risk-free profit, not just a general strategy of buying in one market to sell in another.

Question 8

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)A,B,and C are false.

Accepted Answer

All three statements are false. The SML derived from the APT does not have a downward slope, it does not show expected return in relation to portfolio standard deviation, and it does not have an intercept equal to the expected return on the market portfolio. The benchmark portfolio for the SML must be the market portfolio.

Question 9

In a factor model,the return on a stock in a particular period will be related to
A)factor risk.
B)non-factor risk.
C)standard deviation of returns.
D)both A and B are true.
E)none of the above are true.

Accepted Answer

In a factor model, the return on a stock is influenced by both factor risk (systematic risk related to common factors) and non-factor risk (idiosyncratic or specific risk unique to the stock).

Question 10

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

The answer of The factor F in the APT model...

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 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 12

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

The APT (Arbitrage Pricing Theory) requires a benchmark portfolio that is well-diversified and lies on the SML (Security Market Line). This portfolio represents a combination of all risk factors that affect the prices of securities. It should not necessarily be equal to the true market portfolio, contain all securities in proportion to their market values, or be unobservable.

Question 13

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

In the context of the Capital Asset Pricing Model (CAPM), the expected excess return on a well-diversified portfolio is proportional to its beta coefficient. The beta measures the portfolio's sensitivity to market movements, and according to CAPM, this is the only risk that should affect the expected return of a well-diversified portfolio, as idiosyncratic risks are diversified away.

Question 14

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

Accepted Answer

The formula to calculate the nonsystematic standard deviation of an equally-weighted portfolio in the APT model is:

σ(εp) = [(1/N) ∑(n=1 to N)] wi2σi2

where:
N = number of securities in the portfolio
wi = weight of security i in the portfolio (usually equal for an equally-weighted portfolio)
σi = standard deviation of security i
σ(εp) = nonsystematic standard deviation of the portfolio

Substituting the given values:

N = 50
wi = 1/50 = 0.02 (equally-weighted portfolio)
σi = (eSi Ui Bi) = 0.25 (given)
σ(εp) = [(1/50) ∑(n=1 to 50)] (0.02)2 (0.25)2 = 0.003535

Therefore, the nonsystematic standard deviation of the equally-weighted portfolio is 3.54%, which corresponds to answer choice D.

Question 15

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)B and C
E)All of the above factors were included in their model.

Accepted Answer

Chen, Roll, and Ross included the Change in expected inflation and Change in unanticipated inflation in their multifactor model, but did not include the Change in industrial waste as a factor. Therefore, the correct choice is D, as B (Change in expected inflation) and C (Change in unanticipated inflation) are both included in the model.

Question 16

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 nonsystematic standard deviation of an equally-weighted portfolio can be calculated using the formula: σ(eP) = σ(ei) / √n, where σ(ei) is the average nonsystematic standard deviation of individual securities and n is the number of securities in the portfolio. Given σ(ei) = 20% and n = 20, σ(eP) = 20% / √20 = 4.47%.

Question 17

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 are correct.
B)I and IV are correct.
C)II and III are correct.
D)II and IV are correct.
E)Only I is correct.

Accepted Answer

In a single-factor security market with no-arbitrage, the expected return-beta relationship holds for all well-diversified portfolios (II) and for all but a small number of individual securities (III).

Question 18

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.
E)none of the above.

Accepted Answer

The Arbitrage Pricing Theory states that the expected return of a well-diversified portfolio can be explained by a linear combination of different macroeconomic factors (systematic risk) and the idiosyncratic factors (nonsystematic risk) specific to individual assets. As the size of the portfolio increases, the impact of idiosyncratic risk decreases and approaches zero, making the portfolio more diversified and less exposed to asset-specific risks. Therefore, the best choice is C, which states that the nonsystematic risk approaches zero as the portfolio becomes larger.

Question 19

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 refers to the act of taking advantage of price differences in different markets or securities to earn risk-free profits. This involves buying and selling the same asset in different markets or taking opposite positions in related assets to profit from price discrepancies. It does not necessarily involve buying low and selling high or short selling high and buying low as these activities involve taking risks and may not result in risk-free profits. Arbitrage also does not involve negotiating for favorable brokerage fees or hedging a portfolio through the use of options.

Question 20

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

The answer of Consider a well-diversified portfolio,A,in a two-factor economy.The...

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

A well-diversified portfolio is defined as

Which of the following factors did Chen,Roll and Ross not 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(e_i) equal to 20% and 40 securities?

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

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

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

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(e_i) equal to 18% and 250 securities?

The APT requires a benchmark portfolio

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 •(e_i) equal to 25% and 50 securities?

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(e_i) equal to 20% and 20 securities?

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

The term "arbitrage" refers to