Deck 6: Factor Models and the Arbitrage Pricing Theory

Question 1

Explain the multifactor model equation.

Answer 1

The algebraic representation of a multifactor model-that is,a factor model with more than one common factor-is given by the following equation: r₁= $\alpha$ _i + $\beta$ _i1²F₁+ $\beta$ _i2²F₂+...+ $\beta$ _ik²F_K+ $\varepsilon$ ₁ The assumption behind the equation is that securities returns are generated by a relatively small number of common factors,for which different securities have different sensitivities,along with uncorrelated firm-specific components,which contribute negligible variance in well-diversified portfolios.The Fs in equation can be thought of as proxies for new information about macroeconomic variables,such as industrial production,inflation,interest rates,oil prices and share price volatility.Because Fs represent new information,they are generally scaled to have means of zero,which also has the convenient benefit of allowing the $\alpha$ s to be interpreted as the mean returns of securities.Investors and other market participants obtain information about these macroeconomic factors from a variety of sources,including economic announcements,such as the employment,inflation and interest rate announcements.

Question 2

Which of the following is a non-diversifiable risk?

A)Capital restructuring
B)Cost-cutting measures
C)Change in interest rate
D)Change in the credit rating of a firm

Answer 2

C

Question 3

Which of the following is true of firm characteristics to estimate factors?

A)It provides the most intuitive interpretation of the market factors.
B)It uses macroeconomic time-series that capture changes in productivity,interest rates and inflation to act as proxies for the factors generating security returns.
C)Portfolios are selected on the basis of past return anomalies.
D)It assumes that covariances are constant.

Answer 3

C

Question 4

Factor risk is not diversifiable in the context of a portfolio because:

A)the portfolios with approximately equal weight on all securities have residuals with standard deviations that are approximately directly proportional to the square root of the number of securities.
B)when more securities are added to the portfolio,the total risk of the portfolio will be the cumulative risk of the individual securities.
C)the portfolios with different weights on all securities have residuals with standard deviations that are approximately inversely proportional to the square root of the total market capitalization.
D)the returns due to each factor?s realized values are perfectly correlated across securities.

Question 5

Which of the following is an assumption of the arbitrage pricing theory?

A)There are always arbitrage opportunities when multiple markets exist.
B)All the securities in the portfolio are perfectly positively correlated.
C)Returns can be described by factor models.
D)The securities in the portfolio are perfectly negatively correlated.

Question 6

Based on the market model,explain the two components of total riskof a security or a portfolio.

Question 7

The _____ of a security is the portion of the security?s return variance that is explained by market movements.

A)systematic risk
B)business-specific risk
C)non-market risk
D)diversifiable risk

Question 8

Explain the construction of tracking portfolio for factor betas.

Question 9

Which of the following is true of the multi-factor model based on the following equation? var(r₁)= $\beta$ _i1²var(F₁)+ $\beta$ _i1²var(F₂)+ ...+ $\beta$ _ik²var(F_K)+ var( $\varepsilon$ ₁)

A)The sum of the first K term is the total risk of the security.
B)The last term represents the firm-specific risk.
C)The first term represents the firm-specific risk.
D)The last K term is the total risk of the security.

Question 10

If equity A's beta on the inflation factor is 1.2,equity B's is 2.6 and equity C's is 3,a portfolio that has weights of 0.5 on equity A,0.3 on equity B and 0.2 on equity C has a factor beta of _____ on this factor.

A)1
B)1.98
C)6.8
D)3

Question 11

Factor analysis:

A)uses macroeconomic time-series that capture changes in productivity,interest rates and inflation to act as proxies for the factors generating security returns.
B)is a statistical estimation technique based on the idea that the covariances between security returns provide information that can be used to determine the common factors that generate the returns.
C)establishes the correlation between the changes in one factor and the undiversifiable risk.
D)assumes that there is no correlation between the factors which affect the price of securities.

Question 12

The unsystematic risk is:

A)the portion of return variance that cannot be explained by market movements.
B)the portion of the security?s return variance that is explained by market movements.
C)the total variance of a security's returns.
D)the total risk that cannot be diversified away.

Question 13

Which of the following is true of pure factor portfolios?

A)They have no firm-specific risk.
B)They have no systematic risk.
C)They are sensitive to the market factor and other major economic factors.
D)They are portfolios with a sensitivity of 1 to all of the factors.

Question 14

Which of the following is true of the market model regression?

A)The regression intercept has a variance equal to the marginal variance.
B)The regression slope coefficient is a constant.
C)The market return and the regression residual are uncorrelated.
D)The regression residual is the component which measures the sensitivity of a security?s return to the market return.

Question 15

Explain the factor analysis to generate factor portfolios.

Question 16

Which of the following is an empirical implication of the APT?

A)Low market-to-book equities are more sensitive to swings in the business cycle and changes in credit conditions.
B)The only risk securities have is unsystematic risk.
C)The expected return of any portfolio with factor betas that are all equal to zero is the risk-free rate.
D)The expected returns of securities decrease linearly with increases in a given factor beta.

Question 17

Which of the following is true of the comparison between CAPM and APT models?

A)In contrast to the CAPM,the APT model allows for the possibility that investors hold the same exact portfolios.
B)In contrast to the APT model,the CAPM assumes that there are no arbitraging opportunities.
C)Compared to the APT model,the CAPM is a complex method to estimate the expected returns.
D)Both models assume that the markets are frictionless.

Question 18

A financial analyst is estimating factor beta for a portfolio.He uses a regression of the historical returns of the security against the historical factor realizations.Which of the following is the factor beta using this regression analysis?

A)The sum of regression intercept and residual
B)The regression intercept
C)The regression residual
D)The slope coefficient in the regression

Question 19

The statistic used in the regression equation,R-squared:

A)represents the portion of variance in market returns due to systematic changes.
B)measures the fraction of the market risk premium due to total risk.
C)measures influence of market returns on the beta of the security.
D)measures the fraction of the return variance due to systematic risk.