Question 1

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 2

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 expected return on portfolio A is 6% + 1.2 * 4% + 0.8 * 3% = 13.2%.

Question 3

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 involves taking advantage of price differences in different markets or forms to make a risk-free profit. It does not inherently involve negotiation for fees, specific investment strategies like buying low and selling high or short selling, nor does it specifically relate to hedging strategies.

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 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 5

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 answer of Suppose you are working with two factor...

Question 6

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's multifactor model includes both changes in expected inflation and changes in unanticipated inflation among its factors, reflecting how different types of inflation expectations can impact asset prices.

Question 7

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 8

Which of the following factors were used by Fama and French in their multifactor model?
A) Return on the market index
B) Excess return of small stocks over large stocks
C) Excess return of high book-to-market stocks over low book-to-market stocks
D) All of the factors were included in their model.
E) None of the factors were included in their model.

Accepted Answer

Fama and French's multifactor model includes three key factors: the return on the market index, the excess return of small stocks over large stocks, and the excess return of high book-to-market stocks over low book-to-market stocks. These factors are used to explain stock returns.

Question 9

To take advantage of an arbitrage opportunity, an investor wouldI) 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 10

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

The nonsystematic standard deviation of an equally-weighted portfolio is calculated by dividing the average value of σ(e_i) by the square root of the number of securities. Given an average value of 25% and 50 securities, the calculation is 25% / sqrt(50) = 25% / 7.071 = 3.54%.

Question 11

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 12

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

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

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

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 19%. The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately
A) 1.58.
B) 1.13.
C) 1.25.
D) 0.76.

Accepted Answer

The beta of a well-diversified portfolio in the one-factor APT model is calculated as the ratio of the standard deviation of the portfolio to the standard deviation of the factor portfolio. Thus, beta = 19% / 12% = 1.58.

Question 15

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

All of the factors listed are indeed included in the Chen, Roll, and Ross multifactor model. This model is known for incorporating various economic and financial variables to explain stock returns, including industrial production changes, inflation expectations, and bond returns.

Question 16

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 are true.

Accepted Answer

In a factor model, the return on a stock is typically related to both factor risk (systematic risk that affects many or all securities) and nonfactor risk (unsystematic risk that is specific to a single asset or a small group of assets). Factor models aim to explain stock returns with these risks.

Question 17

Which of the following is false about the security market line (SML) derived from the APT?
A) The SML has an upward slope.
B) The SML for the APT shows expected return in relation to factor intensity.
C) The SML for the APT has an intercept that does not equal 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 Security Market Line (SML) derived from the Arbitrage Pricing Theory (APT) indeed has an upward slope, indicating that higher expected returns come with higher levels of risk (factor intensity), not portfolio standard deviation as E suggests. The intercept of the SML in the APT context does not necessarily equal the expected return on the market portfolio, and the benchmark portfolio can indeed be any well-diversified portfolio, not just the market portfolio. Therefore, E is false because it inaccurately describes the characteristics of the SML in the context of APT.

Question 18

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 19

Consider the single-factor APT. Stocks A and B have expected returns of 12% and 14%, respectively. The risk-free rate of return is 5%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of
A) 0.67.
B) 0.93.
C) 1.30.
D) 1.69.

Accepted Answer

The Arbitrage Pricing Theory (APT) posits that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors, plus an asset-specific factor. In the case of a single-factor model, the expected return can be simplified to: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Given the information, we can solve for Stock A's beta by setting up the equations for both stocks and solving for the unknown beta of Stock A. For Stock B, we have: 14% = 5% + 1.2 * (Market Return - 5%). We can use this information to find the market premium, and then apply it to find Stock A's beta, which results in a beta of 0.93 when arbitrage opportunities are ruled out, indicating that Stock A is less sensitive to market changes than Stock B.

Question 20

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%.

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

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?

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(ei) equal to 20% and 20 securities?

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

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

Which of the following factors were used by Fama and French 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 25% and 50 securities?

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

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 19%. The standard deviation on the factor portfolio is 12%. The beta of the well-diversified portfolio is approximately

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

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

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

The factor F in the APT model represents

Consider the single-factor APT. Stocks A and B have expected returns of 12% and 14%, respectively. The risk-free rate of return is 5%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of

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?

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 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 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 40 securities?