Index Models

Question 1

The index model is estimated by applying regression analysis to excess rates of return. The slope of the regression curve is the ____ of an asset, whereas the intercept is the asset’s ____ during the sample period

a) beta, sigma
b) sigma, alpha
c) alpha, beta
d) beta, alpha

Answer 1

d) beta, alpha

Question 2

How is the total variance computed (breakdown formula)?

a) Total risk = Systematic risk - Firm specific risk
b) Total risk = Systematic risk + Firm specific risk
c) Total risk = Systematic risk + nonsystematic risk
d) b) Total risk = Systematic risk - nonsystematic risk

Answer 2

b) Total risk = Systematic risk + Firm specific risk

c) Total risk = Systematic risk + nonsystematic risk

Question 3

What is true about firm-specific and systematic risk?

a) They make up the unanticipated component of the stock return.
b) They are assumed correlated
c) The firm-specific risk is independent of shocks to the common factor that affect the entire economy.
d) Some securities will be more sensitive than other to macroeconomic shocks, this refinement is captured in the sensitivity coefficient beta.

Answer 3

a) They make up the unanticipated component of the stock return.
c) The firm-specific risk is independent of shocks to the common factor that affect the entire economy.
d) Some securities will be more sensitive than other to macroeconomic shocks, this refinement is captured in the sensitivity coefficient beta.

b is not true, the two are assumed UNCORRELATED.

Question 4

True or false.

Cyclical firms have greater sensitivity to the market (higher betas) and therefore greater systematic risk.

Answer 4

True

Question 5

What does the slope of the security characteristic line reflect?

a) The sensitivity of the security’s return to firm-specific conditions
b) The sensitivity of the security’s return to the market conditions
c) Market timing
d) Stockpicking

Answer 5

b) The sensitivity of the security’s return to the market conditions

A steeper line implies that the security’s rate of returns is more responsive to the market return

Question 6

The Index Model.

The intercept of the equation (α) is the security’s expected excess return when the market excess return is ________. The beta of the market index is ______. Cyclical or aggressive stocks have _______-than-average sensitivity to the broad economy and therefore have betas greater than 1. Conversely, the betas of defensive stocks are less than _________.

a) Positive, Negative, Higher, 1
b) Negative, 0, Lower, 1
c) 1, Positive, Lower, 1
d) 0, 1, Higher, 1

Answer 6

d) 0, 1, Higher, 1

The intercept of the equation (α) is the security’s expected excess return when the market excess return is zero. The beta of the market index is 1. Cyclical or aggressive stocks have higher-than-average sensitivity to the broad economy and therefore have betas greater than 1. Conversely, the betas of defensive stocks are less than 1

Question 7

Why is the Index model useful compared to the Markowitz model? What is the ‘cost’ of the model?

Answer 7

The number of estimates required is a small fraction of what otherwise would be needed.
The index model abstraction is crucial for specialization of effort in security analysis.
The index model suggests a simple way to compute covariances. They are due to the common influence of the single macroeconomic factor, represented by the market index return.

The ‘cost’ of the model lies in the restrictions it places on the structure of asset return uncertainty. The classification of uncertainty into macro- and micro risk oversimplifies uncertainty and misses some important sources of dependence in stock returns. Additionally a disadvantage arises from the model’s assumption that returns residuals are uncorrelated. This assumption will be incorrect if the index omits a significant risk factor.

Question 8

As the number of stocks included in a portfolio ________, the part of the portfolio risk attributable to nonmarket factors becomes even ________.

a) Decreases, smaller
b) Increases, larger
c) Increases, smaller
c) Decreases, larger

Answer 8

c) Increases, smaller

As the number of stocks included in a portfolio increases, the part of the portfolio risk attributable to nonmarket factors becomes even smaller.

This part of the risk is diversified away, and therefore will be of little concern to investors. In contrast, market risk remains, regardless of the number of firms in the portfolio.

Question 9

Why does the firm-specific components tend to cancel out as more and more stocks are added to the portfolio?

a) Law of large numbers
b) This doesn’t happen
c) Law of small numbers
d) Law of averages

Answer 9

d) Law of averages

Because the firm-specific components are independent, and all have zero expected value, the law of averages can be applied to conclude that as more and more stocks are added to the portfolio, the firm-specific components tend to cancel out, resulting in ever-smaller nonmarket risk.

This also leads to the portfolio variance to decrease.

Question 10

What does the R-square explain?

a) The variation in excess returns of the market index
b) The variation in actual returns of the market index
c) The variation in historical returns of the market index
d) The variation in excess returns of the securities expected return

Answer 10

a) The variation in excess returns of the market index

Explains ‘R^2’% of the variation in the security’s series.

Question 11

True or false

The adjusted R-square (slightly smaller) corrects for an upward in R-square that arises because we use estimated values of two parameters: the slope and intercept (beta and alpha), rather than their true, but unobservable, values.

Answer 11

True

Question 12

The standard error of the regression is the standard deviation of the ______ .

a) Systematic risk
b) Firm specific risk
c) Excess returns
d) Risk premium

Answer 12

b) Firm specific risk

The standard error of the regression is the standard deviation of the residual, e_i. High standard errors imply greater impact on firm-specific events from one month to the next.

Question 13

What does a security’s negative alpha imply?

a) The security will assume a long position in the optimal risky portfolio
b) The security will assume a short position in the passive portfolio
c) The security will assume a short position in the optimal risky portfolio
d) The security will assume a short position in the active portfolio

Answer 13

c) The security will assume a short position in the optimal risky portfolio

As the number of securities with nonzero alpha values increases, the active portfolio will itself be better diversified and its weight in the overall risky portfolio will increase at the expense of the passive index portfolio.

Question 14

Which two components does the optimal risky portfolio consist of?

a) Active and neutral portfolio
b) Passive and neutral portfolio
c) Passive and market index portfolio
d) Active and passive/ market index portfolio

Answer 14

d) Active and passive/ market index portfolio

Question 15

What is the basic trade-off when departing from pure indexing in favor of an actively managed portfolio?

a) Between the probability of superior performance against the certainty of additional transaction fees.
b) Between the probability of superior performance against the certainty of additional management fees.
c) Between the probability of some return against the certainty of additional management fees.
d) Between the probability of some return against the certainty of additional transaction fees.

Answer 15

b) Between the probability of superior performance against the certainty of additional management fees.

Question 16

True or false.

We call alpha a ‘nonmarket’ return premium because it is the portion of the returns that is independent of market performance.

Answer 16

True

That is, the alpha of an asset is diversifiable: as more and more stocks are added to the portfolio, the firm-specific component tends to cancel out, resulting in ever-smaller nonmarket risk.

Question 17

How can you identify firm-specific risk from a regression line?

Answer 17

A stock’s firm-specific risk can be seen from deviations from the SCL. Deviations are measured by the vertical distance of each observation from the SCL.

Question 18

How can you identify systematic risk from a regression line?

Answer 18

Beta is the slope of the SCL, which is the measure of systematic risk.

Question 19

How can you identify alpha from a regression line?

Answer 19

Alpha is the intercept of the SCL with the expected return axis.

Question 20

Jagannathan and Wang study shows two important deficiencies in tests of the single-index model. Which are not part of these two?

a) A human capital factor may be important in explaining returns. The study proves that the model including the human capital factor performs better than the CAPM
b) The study finds that beta is actually cyclical and changes over time depending on the market activity and the state of the economy - therefore, the CAPM and the index model, where we assume constant beta - are suboptimal.
c) if human capital factor and dynamic beta are incorporated in explaining expected returns, anomalies such as the size and book-to-market effects are mitigated
d) Net worth is a significant explanatory variable: wealthier people hold a larger proportion of stocks.

Answer 20

WRONG: d) Net worth is a significant explanatory variable: wealthier people hold a larger proportion of stocks. This is found in a study by John Heaton and Debora Lucas.

The other options correctly sum up Jagannathan and Wang’s study.

Question 21

According to John Heaton and Debora Lucas (2000), which of the following are determinants for stock holding? I.e., determinants that affect the attractiveness of holding stocks. Select 1-4:

a) Net worth: wealthier people hold a larger proportion of stocks
b) Relative business: if you are a businessman owning a company, you are less likely to hold liquid stocks because you are not incentivized to increase the risk of your portfolio by adding single stocks
c) Age of respondent: the older you are, the more likely you are to hold stocks
d) Investment experience: if you are a very experienced trader, the chances of holding stocks relative to market index is higher

Answer 21

a) Net worth: wealthier people hold a larger proportion of stocks
b) Relative business: if you are a businessman owning a company, you are less likely to hold liquid stocks because you are not incentivized to increase the risk of your portfolio by adding single stocks
c) Age of respondent: the older you are, the more likely you are to hold stocks

Question 22

If the residual variance of an asset increases, what happens to the assets positions in the optimal portfolio?

a) Greater
b) Smaller
c) Constant
d) This cannot be determined

Answer 22

b) Smaller

Therefore, other things equal, the greater the residual variance of an asset, the smaller its position in the optimal risky portfolio. That is, increased firm-specific risk reduces the extent to which an active investor will be willing to depart from an indexed portfolio.