Question 1

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...

Question 2

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

Accepted Answer

A zero-investment portfolio with a positive expected return is indicative of a risk-free arbitrage opportunity, where an investor can make a profit with no net investment and no risk. This situation arises when there is a mispricing of assets that the investor can exploit.

Question 3

The APT requires a benchmark portfolio

Accepted Answer

The Arbitrage Pricing Theory (APT) requires a benchmark portfolio that is well-diversified and lies on the Security Market Line (SML) to ensure that it accurately reflects systematic risk factors.

Question 4

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year (each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: $\begin{array}{cccc}
&\text { State of Nature }&\text {Moderate }&\text { Weak }\
\text { Stock } & \text { Strong Growth } & \text { Growth } & \text { Growth } \
\text { A } & 39\% & 17 \% & -5 \% \
\text { B } & 30 \% & 15 \% & 0\% \
\text { C } &6\% &14\% &22\%
\end{array}$

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

The return for an equally-weighted portfolio of stocks A and C if economic growth was strong would be the average of their returns in that state. For stock A, the return is 39%, and for stock C, it is 6%. The average of these two returns is $(39\% + 6\%)/2 = 22.5\%$.

Question 5

Which of the following factors might affect stock returns?

Accepted Answer

All of the options listed (the business cycle, interest rate fluctuations, and inflation rates) can affect stock returns. The business cycle influences corporate earnings, interest rate fluctuations can affect borrowing costs and consumer spending, and inflation rates can impact purchasing power and cost structures for companies.

Question 6

An important difference between CAPM and APT is

Accepted Answer

The answer of An important difference between CAPM and APT...

Question 7

In terms of the risk/return relationship in the APT,

Accepted Answer

The Arbitrage Pricing Theory (APT) posits that only factor risks, which are systematic, command a risk premium in market equilibrium. This is because systematic risks affect the entire market and cannot be diversified away, whereas nonsystematic risks, which are specific to individual securities, can be mitigated through diversification.

Question 8

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 is an example of a risk-free arbitrage, where an investor takes advantage of a price discrepancy without risk to make a profit. Arbitrage opportunities occur when an asset is priced differently in two markets, and investors can buy low in one market and sell high in another, capturing the price difference as profit. This does not involve dominance arguments, the mean-variance efficiency frontier, or the capital asset pricing model, which are related to other aspects of finance and investment theory.

Question 9

Consider the multifactor APT. There are two independent economic factors, F₁ and F₂. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: $\text { Portfolio }$ Assuming no arbitrage opportunities exist, the risk premium on the factor F₂ portfolio should be

Accepted Answer

The answer of Consider the multifactor APT. There are two...

Question 10

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

Risk arbitrage involves searching for mispriced securities in areas such as merger-target stocks, which carries more risk compared to pure (risk-free) arbitrage. This strategy is not about exploiting risk-free opportunities but rather about taking calculated risks on securities that are believed to be mispriced due to specific events or conditions, such as mergers and acquisitions.

Question 11

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

The expected return on a portfolio in the one-factor APT is given by the formula: Expected Return = Risk-Free Rate + Beta * (Market Risk Premium). Using the given data for portfolios A and B, we can set up two equations and solve for the risk-free rate. Solving these equations shows that the risk-free rate is 9.0%.

Question 12

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year (each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: $\begin{array}{cccc}
&\text { State of Nature }&\text {Moderate }&\text { Weak }\
\text { Stock } & \text { Strong Growth } & \text { Growth } & \text { Growth } \
\text { A } & 39\% & 17 \% & -5 \% \
\text { B } & 30 \% & 15 \% & 0\% \
\text { C } &6\% &14\% &22\%
\end{array}$

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 return for an equally-weighted portfolio of stocks A and B during moderate growth is calculated as the average of their returns: (17% + 15%) / 2 = 16.0%.

Question 13

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

Accepted Answer

The Arbitrage Pricing Theory (APT) posits that as a portfolio becomes more diversified, its nonsystematic (or idiosyncratic) risk, which is unique to individual assets, is reduced. In the limit of a perfectly diversified portfolio, nonsystematic risk approaches zero because the unique risks of individual assets cancel out.

Question 14

A well-diversified portfolio is defined as

Accepted Answer

A well-diversified portfolio is one that holds a large enough number of different securities such that the unsystematic (or specific) risk is nearly eliminated. This is because unsystematic risk, which is unique to individual securities, can be reduced through diversification, whereas systematic risk, which affects the market as a whole, cannot.

Question 15

There are three stocks: A, B, and C. You can either invest in these stocks or short sell them. There are three possible states of nature for economic growth in the upcoming year (each equally likely to occur); economic growth may be strong, moderate, or weak. The returns for the upcoming year on stocks A, B, and C for each of these states of nature are given below: $\begin{array}{cccc}
&\text { State of Nature }&\text {Moderate }&\text { Weak }\
\text { Stock } & \text { Strong Growth } & \text { Growth } & \text { Growth } \
\text { A } & 39\% & 17 \% & -5 \% \
\text { B } & 30 \% & 15 \% & 0\% \
\text { C } &6\% &14\% &22\%
\end{array}$

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 There are three stocks: A, B, and...

Question 16

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

The answer of Consider the single factor APT. Portfolios A...

Question 17

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

Accepted Answer

The Arbitrage Pricing Theory (APT) allows for multiple factors to explain the risk-return relationship, unlike the Capital Asset Pricing Model (CAPM) which relies on a single market index. This multi-factor approach is considered a significant advantage of APT over CAPM.

Question 18

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 19

Consider the multifactor APT. There are two independent economic factors, F₁ and F₂. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: $\text { Portfolio }$ Assuming no arbitrage opportunities exist, the risk premium on the factor F₁ portfolio should be

Accepted Answer

The risk premium on the factor F1 portfolio is determined by the difference in expected returns of the portfolios, adjusted for their sensitivities to the factors. Given no arbitrage, the risk premium on F1 is 3%.

Question 20

The APT differs from the CAPM because the APT

Accepted Answer

The Arbitrage Pricing Theory (APT) differs from the Capital Asset Pricing Model (CAPM) by recognizing multiple systematic risk factors, rather than focusing on a single market risk factor as the CAPM does.

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