Question 1

Advantage(s)of the APT is(are)

Accepted Answer

The Arbitrage Pricing Theory (APT) does not require a specific benchmark market portfolio, which is an advantage over models like the CAPM that do.

Question 2

If you wanted to take advantage of a risk-free arbitrage opportunity,you should take a short position in _________ and a long position in an equally weighted portfolio of _______.

Accepted Answer

In a risk-free arbitrage opportunity, you take a short position in the overvalued asset (C) and a long position in an equally weighted portfolio of the undervalued assets (A and B) to exploit the price discrepancy.

Question 3

Consider the one-factor APT.Assume that two portfolios,A and B,are well diversified.The betas of portfolios A and B are 1.0 and 1.5,respectively.The expected returns on portfolios A and B are 19% and 24%,respectively.Assuming no arbitrage opportunities exist,the risk-free rate of return must be ____________.

Accepted Answer

According to the one-factor APT formula, the expected return on a portfolio can be estimated as:

E(R) = Rf + β × RP

Where Rf is the risk-free rate of return, β is the portfolio's beta, and RP is the risk premium, which is the excess return of the market over the risk-free rate.

Assuming that there are no arbitrage opportunities, the expected return on portfolio A can be estimated as:

19% = Rf + 1.0 × RP

Similarly, the expected return on portfolio B can be estimated as:

24% = Rf + 1.5 × RP

We can solve these two equations simultaneously to find the values of Rf and RP. Subtracting the first equation from the second, we get:

5% = 0.5 × RP

Therefore, RP = 10%.

Substituting this value of RP into either of the two equations above, we can solve for Rf:

19% = Rf + 1.0 × 10%
Rf = 9.0%

Therefore, the risk-free rate of return must be 9.0%. Answer: B

Question 4

The following factors might affect stock returns:

Accepted Answer

All of the above factors can affect stock returns. The business cycle can impact sales and profits of companies, which in turn affects stock prices. Interest rate fluctuations affect borrowing costs and investment decisions of companies, which can impact stock prices. Inflation rates affect consumer purchasing power and can impact company profits and stock prices.

Question 5

A zero-investment portfolio with a positive expected return arises when _________.

Accepted Answer

A zero-investment portfolio with a positive expected return can only arise when there is a risk-free arbitrage opportunity. This means that an investor can earn a risk-free profit without investing any money, which violates the efficient market hypothesis. Therefore, choice D is the correct answer. Choices A, B, and C are not sufficient conditions for a zero-investment portfolio with a positive expected return.

Question 6

A professional who searches for mispriced securities in specific areas such as merger-target stocks,rather than one who seeks strict (risk-free)arbitrage opportunities is engaged in

Accepted Answer

The professional who searches for mispriced securities in specific areas such as merger-target stocks is engaged in risk arbitrage. Risk arbitrageurs seek to profit from the price discrepancies that occur during a merger or acquisition, where the target company's stock price may not fully reflect the value of the deal. This type of arbitrage involves taking on some degree of risk, as the deal may not ultimately go through or may be renegotiated, leading to potential losses. Pure arbitrage, option arbitrage, and equilibrium arbitrage do not involve searching for mispriced securities in specific areas such as merger-target stocks, making them incorrect choices.

Question 7

Consider a one-factor economy.Portfolio A has a beta of 1.0 on the factor and portfolio B has a beta of 2.0 on the factor.The expected returns on portfolios A and B are 11% and 17%,respectively.Assume that the risk-free rate is 6% and that arbitrage opportunities exist.Suppose you invested $100,000 in the risk-free asset,$100,000 in portfolio B,and sold short $200,000 of portfolio A.Your expected profit from this strategy would be ______________.

Accepted Answer

The expected profit from the strategy is $1,000. The strategy involves borrowing $200,000 at the risk-free rate (6%) to invest in portfolio B and the risk-free asset, while shorting portfolio A. The expected return from the strategy is calculated as follows: $100,000 * 6% + $100,000 * 17% - $200,000 * 11% = $1,000.

Question 8

In terms of the risk/return relationship in the APT

Accepted Answer

Only factor risk commands a risk premium in market equilibrium, and only systematic risk is related to expected returns.

Question 9

If you invested in an equally weighted portfolio of stocks B and C,your portfolio return would be _____________ if economic growth was weak.

Accepted Answer

The answer of If you invested in an equally weighted...

Question 10

An investor will take as large a position as possible when an equilibrium price relationship is violated.This is an example of _________.

Accepted Answer

This scenario describes risk-free arbitrage, where an investor takes advantage of a market inefficiency to make a profit without taking on any risk. The violation of the equilibrium price relationship presents an opportunity for the investor to take a large position and make a profit without any possibility of loss. Choice A is not applicable, as dominance arguments pertain to game theory. Choice B pertains to portfolio optimization, and Choice D refers to the pricing of securities based on market risk and expected returns, which is not relevant in this scenario.

Question 11

Consider the multifactor APT. There are two independent economic factors, FS1U1B11S1U1B0and FS1U1B12S1U1B0. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: $$\begin{array} { | l | l | l | l | } \hline \underline { \text { Portfolio } } & \underline { B \text { on } } \mathbf { E } \underline { 1 } & \underline { \beta \text { on } } \mathrm { F } _ { 2 } & \underline { \text { Expected Return } } \ \hline \mathrm { A } & 1.0 & 2.0 & 19 \% \ \hline \mathrm { B } & 2.0 & 0.0 & 12 \% \ \hline \end{array}$$ -Assuming no arbitrage opportunities exist,the risk premium on the factor F₁portfolio should be __________.

Accepted Answer

The risk premium on the factor F₁ portfolio is 3%. This is because the expected return on portfolio A is 19%, and the risk-free rate is 6%. Therefore, the risk premium on portfolio A is 13%. The beta of portfolio A on factor F₁ is 1.0. Therefore, the risk premium on factor F₁ is 13% / 1.0 = 3%.

Question 12

An important difference between CAPM and APT is

Accepted Answer

CAPM depends on risk-return dominance, while APT depends on a no-arbitrage condition. CAPM assumes many small changes are required to bring the market back to equilibrium, while APT assumes a few large changes are required to bring the market back to equilibrium.

Question 13

Consider the multifactor APT. There are two independent economic factors, FS1U1B11S1U1B0and FS1U1B12S1U1B0. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: $$\begin{array} { | l | l | l | l | } \hline \underline { \text { Portfolio } } & \underline { B \text { on } } \mathbf { E } \underline { 1 } & \underline { \beta \text { on } } \mathrm { F } _ { 2 } & \underline { \text { Expected Return } } \ \hline \mathrm { A } & 1.0 & 2.0 & 19 \% \ \hline \mathrm { B } & 2.0 & 0.0 & 12 \% \ \hline \end{array}$$ -Assuming no arbitrage opportunities exist,the risk premium on the factor F₂ portfolio should be ___________.

Accepted Answer

Using the APT model, we can calculate the expected return on each portfolio as follows: For portfolio A: E(Ra) = Rf + β1f1 + β2f2 E(Ra) = 0.06 + (1.0)(-2%) + (2.0)(?) E(Ra) = 0.06 + 0.04f2 19% = 0.06 + 0.04f2 f2 = 325% For portfolio B: E(Rb) = Rf + β1f1 + β2f2 E(Rb) = 0.06 + (2.0)(-2%) + (0.0)(?) E(Rb) = 0.02 12% = 0.06 + 0.0 + 0.0 Thus, the risk premium on the factor F₂ portfolio can be calculated as: RP2 = (E(Ra) - E(Rb)) / β2 RP2 = (19% - 12%) / 2.0 RP2 = 3.5% Therefore, the closest option is C (5%).

Question 14

The APT differs from the CAPM because the APT _________.

Accepted Answer

The APT recognizes multiple systematic risk factors, whereas the CAPM focuses solely on market risk. Additionally, the APT recognizes multiple unsystematic risk factors, making option C partially correct but not the best choice. Option B is incorrect, as diversification is still important under the APT framework. Option A is incorrect because it mischaracterizes the differences between the APT and the CAPM.

Question 15

Portfolio A has expected return of 10% and standard deviation of 19%.Portfolio B has expected return of 12% and standard deviation of 17%.Rational investors will

Accepted Answer

Rational investors prefer higher returns for lower risk. Portfolio B offers a higher expected return with a lower standard deviation compared to Portfolio A, making it more attractive. Selling A short and buying B aligns with this preference.

Question 16

If you invested in an equally weighted portfolio of stocks A and B,your portfolio return would be ___________ if economic growth were moderate.

Accepted Answer

The answer of If you invested in an equally weighted...

Question 17

Consider the multifactor APT.The risk premiums on the factor 1 and factor 2 portfolios are 5% and 3%,respectively.The risk-free rate of return is 10%.Stock A has an expected return of 19% and a beta on factor 1 of 0.8.Stock A has a beta on factor 2 of ________.

Accepted Answer

The answer of Consider the multifactor APT.The risk premiums on...

Question 18

Consider the single factor APT.Portfolios A and B have expected returns of 14% and 18%,respectively.The risk-free rate of return is 7%.Portfolio A has a beta of 0.7.If arbitrage opportunities are ruled out,portfolio B must have a beta of __________.

Accepted Answer

According to the single factor APT, the expected return of a portfolio is determined by the risk-free rate plus the product of the portfolio's beta and the risk premium. For Portfolio A: 14% = 7% + 0.7 * (Risk Premium). Solving gives a Risk Premium of 10%. For Portfolio B: 18% = 7% + Beta * 10%. Solving for Beta gives Beta = 1.10.

Question 19

The feature of the APT that offers the greatest potential advantage over the CAPM is the ______________.

Accepted Answer

The APT's use of several factors instead of a single market index to explain the risk-return relationship offers the greatest potential advantage over the CAPM, as it allows for a more comprehensive and nuanced understanding of the sources of risk and return in an asset's performance. This approach is particularly valuable in complex or rapidly changing markets where a single market index may not capture all relevant factors.

Question 20

If you invested in an equally weighted portfolio of stocks A and C,your portfolio return would be ____________ if economic growth was strong.

Accepted Answer

If economic growth is strong, the return for stock A is 15% and for stock C is 30%. An equally weighted portfolio means each stock contributes equally, so the portfolio return is (15% + 30%) / 2 = 22.5%.

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

Advantage(s) of the APT is(are)

If you wanted to take advantage of a risk-free arbitrage opportunity,you should take a short position in ___ and a long position in an equally weighted portfolio of _.