CAPM CCAMP APT

Question 1

The model for the arbitrage pricing theory contains the factor F: what does this factor represent?

Answer 1

The factor F represents the deviation of the common factor from its expected value. Also known as the deviation from its expected value of a factor that affects all security returns.

Question 2

Does the CAPM and/or the APT provide guidance concerning determining the risk premium
on factor portfolios?

a. Both the CAPM and the multifactor APT
b. Neither the CAPM nor the multifactor APT
c. Only the CAPM
d. Only the multifactor APT

Answer 2

Only the CAPM

Question 3

!The Capital Asset Pricing Model is one of the most well-known asset pricing models. Please:

• Explain the logic behind relating required returns to beta instead of the standard deviation;
• Report the conclusions regarding the regression slope drawn by scholars who tested the CAPM;
• Relate the existence of low-volatility investing to this answer

Answer 3

1. Beta vs. Standard Deviation in CAPM:
   
   • CAPM uses beta because it assumes all investors hold the market portfolio, diversifying away the firm-specific risk. Beta measures an asset’s sensitivity to market movements, making it the relevant risk measure.
2. CAPM Regression Slope Conclusions:
   
   • Studies find the CAPM regression slope is too small. This means the expected market risk premium is smaller than observed, indicating that beta alone may not fully capture risk.
3. Low-Volatility Investing and CAPM:
   
   • Low-volatility investing challenges the idea that higher beta leads to higher returns. Low-beta stocks often provide higher returns than CAPM predicts. This supports the notion that beta may not capture all relevant risk factors.

Question 4

Explain the logic behind relating required returns to beta instead of the standard deviation;

Answer 4

Under the CAPM, the market portfolio is the optimal portfolio. Investors only incur market risk, which is measured by beta. Firm-specific risks, represented by the standard deviation, are diversified away.

Question 5

Which characteristic of the arbitrage pricing theory (APT) potentially provides the largest benefits over the CAPM?

a. Superior measurement of the risk-free rate of return over historical time periods.

b. The variability of coefficients of sensitivity to the APT factors for a given asset over time.

c. The identification of anticipated changes in production, inflation, and term structure as key factors in explaining the risk-return relationship.

d. The use of several factors instead of a single market index to explain the risk-return relationship.

Answer 5

The use of several factors instead of a single market index to explain the risk-return relationship.

Question 6

The efficient frontier is..

Answer 6

…the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.

Portfolios that lie below the efficient frontier are sub-op­timal, because they do not provide enough return for the level of risk.

Question 7

Elaborate on CAPM extensions and how they can help explain the conclusions from the first and second pass regression:

Answer 7

The CAPM extensions address different assumptions of the CAPM that maybe unrealistic.

For example, the Black CAPM (Zero-Beta Model) addresses the assumption that investors can borrow and lend at a common risk-free rate.

The Intertemporal CAPM (ICAPM) addresses the assumption that investors have a single period planning horizon and account for extra market sources of risk

Question 8

The benchmark of the arbitrage pricing theory is required to…

Answer 8

… any well-diversified portfolio lying on the SML can serve as the benchmark portfolio for the APT.

Question 9

The true (and unobservable) market portfolio is only a requirement for the CAPM.

Answer 9

True

Question 10

How would you incorporate liquidity into the CCAPM (Consumption Capital Asset Pricing Model)

Answer 10

In the same way, it would be incorporated into the conventional CAPM.

In CAPM, the expected return E(r), in addition to the market risk premium, also depends on the expected cost of illiquidity and three liquidity-related betas which measure the sensitivity of:

1. the security’s illiquidity to market illiquidity
2. the security’s return to market illiquidity
3. the security’s illiquidity to the market return.

A similar approach can be used for the CCAPM, except that the liquidity betas would be measured relative to consumption growth.

Question 11

The risk premium is…

Answer 11

…the difference between the return on a risky investment and the return on a
risk-free investment (government bonds).

Question 12

If the forecast rate of return is less than the required rate of return (CAPM), then the security is….

Answer 12

overvalued

Question 13

Two investors are comparing performance. One averaged a 20% rate of return and the other 18% rate of return. However, the beta of the first is 1.6 and the second 1.

Can you tell which investor was a better sector of individual stock (aside from the issue of general movements in the market?)

Answer 13

Νο.

We need the rf and rm in order to calculate the abnormal returns of each.

Question 14

According to CAMP the expected return of a portfolio with a beta of 1.0 and alpha of 0 is:

1. between the rm and rf
2. the risk-free rf
3. b(rm - rf)
4. the expected return on the market rm

Answer 14

the expected return on the market rm

Question 15

Two portfolios have the following characteristics:

A: beta 1.0, the specific risk for each security

A: beta 1.0, low specific risk for each security

Briefly explain whether investors should expect a high return from holding portfolio A versus portfolio B under asset pricing theory (CAPM). Assume that both portfolios are well diversified.

Answer 15

Under the CAPM, the only risk that investors are compensated for bearing is the risk that cannot be diversified away (systematic risk, beta).

Because systematic risk (measured by beta) is equal to 1.0 for both portfolios, an investor would expect the same rate of return from both portfolios A and B.

Moreover, since both portfolios are well diversified, it doesn’t matter if the specific risk of the individual securities is high or low. The firm-specific risk has been diversified away for both portfolios.

Question 16

Under the CAPM, the only risk that investors are compensated for the bearing is the.

Answer 16

… the risk that cannot be diversified away (systematic risk).

Question 17

If a portfolio is well diversified which risk is irrelevant (diversified away):

1. (firm) specific risk
2. systemic risk (beta)

Answer 17

1. (firm) specific risk SD or σ

Question 18

When a stock is held as a single stock portfolio, the standard deviation is … risk measure and beta …

Answer 18

SD relevant
beta irrelevant

Question 19

The APT itself does not guide the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Why for example is industrial production a reasonable factor to test for a risk premium?

Answer 19

APT factors must correlate with major sources of uncertainty. One should investigate factors which correlate with uncertainty in consumption and investment opportunities, such as GDP, the inflation rate, and interest rates.

Industrial production may be a good indicator of changes in the business cycle thus may correlate highly with uncertainties regarding investment and consumption opportunities.

Question 20

Claim: The APT factors must correlate with major sources of uncertainty, i.e., sources of uncertainty that are of concern to many investors.

Answer 20

True,

Researchers should investigate factors that correlate with uncertainty in consumption and investment opportunities.
GDP, the inflation rate, and interest rates are among the factors that can be expected to determine risk premiums.

Question 21

A portfolio with a beta of 0 is…

Answer 21

… the risk-free

Question 22

A portfolio with a beta of 1.0 and alpha of 0 is the…

Answer 22

… market portfolio

Question 23

Suppose that two actors have been identified for the US economy: the growth rate of industrial production IP and the inflation rate IR. IP is expected to be 5% and IR 4.2%. A stock with a beta of 1.6 on IP and 1.1 IR currently is expected to provide a rate of return of 13%. If industrial production grows by 7% while the inflation rate turns out to be 5.5% what is your revised estimate of the expected rate of return on the stock?

Answer 23

E(r) ‘ = E(r) +- (biΔIP + b2ΔIR)

The revised estimate of the expected rate of return on the stock would be the old estimate plus (since it is an increase with positive b) the sum of the products of the unexpected change in each factor times the respective sensitivity coefficient:

Revised estimate = 13% + [(1.6 × 2%) + (1.1 × 1.3%)] = 17.63%

Note that the IP estimate is computed as: 1.6 × (7% - 5%), and the IR estimate is computed as:
1.1 × (5.5% - 4.2 %).

Question 24

Report the conclusions regarding the regression slope drawn by scholars who tested theCAPM. Relate the existence of low-volatility investing to this answer.

Answer 24

It turns out the the (rm-rf) is lower than in reality, in other words, the slope of the regression line is too small.

Therefore low-beta shares get higher returns than expected, and high-betashares lower returns than justified by their beta.

Question 25

Assume that both portfolios A and B are well diversified, that E(rA) = 22% and E(rB) = 17%. If the economy has only one factor and bA =1.5 whereas bB = 1.1 what must be the risk-free rate?

Answer 25

Since the market has one factor, let It be risk premium = rp

22%=rf +(1.5× RP)
17%=rf +(1.1× RP)

Solving these equations, we obtain
rf = 3.25% and RP = 12.5%

Question 26

As a finance intern at Pork Products, Jennifer Wainwright’s assignment is to come up with fresh insights concerning the firm’s cost of capital. She decided that this would be a good opportunity to try out the new material on the APT that she learned last semester. She decides that three promising factors would be:

(a) the return on a broad-based index such as the S&P 500

(b) the level of interest rates, as represented by the yield to maturity on 10-year Treasury bonds

(c) the price of hogs, which is particularly important to her firm.

She plans to find the beta of Pork Products against each of these factors by using multiple regression and to estimate the risk premium associated with each exposure factor.

Comment on Jennifer’s choice of factors. Which are most promising concerning the likely impact on her firm’s cost of capital? Can you suggest improvements to her specifications?

Answer 26

The first two factors (sp 500, interest rates) seem promising since it’s likely to impact the firm’s cost of capital. Both are macro factors that would affect hedging demands across broad sectors of investors.

The third factor, while important this firm, is a poor choice for a multifactor SML because the price of hogs is of minor importance to most investors and is therefore highly unlikely to be a priced risk factor.

Better choices would focus on variables that investors in aggregate might find more important to their welfare like inflation uncertainty, short-term interest-rate risk, energy price risk, or exchange rate risk.

The important point here is that, in specifying a multifactor SML, we do not confuse risk factors that are important to a particular investor with factors that are important to investors in general; only the laisr are likely to command a risk premium in the capital markets.

Question 27

Small firms generally have relatively high loadings (high betas) on the SMB (small minus big) factor.

a. Explain why this is not surprising.

b. Now suppose two unrelated small firms merge. Each will be operated as an independent unit
of the merged company. Would you expect the stock market behaviour of the merged firm to
differ from that of a portfolio of the two previously independent firms? How does the merger affect market capitalization? What is the prediction of the FF model for the risk premium of the combined firm? Do we see a flow in the FF model?

Answer 27

The Fama-French (FF) three-factor model holds that one of the factors driving returns is firm size. An index with returns highly correlated with firm size (i.e., firm capitalization) that captures this factor is SMB (small minus big), the return for a portfolio of small stocks in excess of the return for a portfolio of large stocks. The returns for a small firm will be positively correlated with SMB. Moreover, the smaller the firm, the greater its residual from the other two factors, the market portfolio and the HML portfolio, which is the return for a portfolio of high book-to-market stocks in excess of the return for a portfolio of low book-to-market stocks. Hence, the ratio of the variance of this residual to the variance of the return on SMB will be larger and, together with the higher correlation, results in a high beta on the SMB factor.
b. This question appears to point to a flaw in the FF model. The model predicts that firm size affects average returns so that, if two firms merge into a larger firm, then the FF model predicts lower average returns for the merged firm. However, there seems to be no reason for the merged firm to underperform the returns of the component companies, assuming that the component firms were unrelated and that they will now be operated independently. We might therefore expect that the performance of the merged firm would be the same
as the performance of a portfolio of the originally independent firms, but the FF model predicts that the increased firm size will result in lower average returns. Therefore, the question revolves around the behavior of returns for a portfolio of small firms, compared to the return for larger firms that result from merging those small firms into larger ones. Had past mergers of small firms into larger firms resulted, on average, in no change in the resultant larger firms’ stock return characteristics (compared to the portfolio of stocks of the merged firms), the size factor in the FF model would have failed.
Perhaps the reason the size factor seems to help explain stock returns is that, when small firms become large, the characteristics of their fortunes (and hence their stock returns) change in a significant way. Put differently, stocks of large firms that result from a merger of smaller firms appear empirically to behave differently from portfolios of the smaller component firms. Specifically, the FF model predicts that the large firm will have a smaller risk premium. Notice that this development is not necessarily a bad thing for the stockholders of the smaller firms that merge. The lower risk premium may be due, in part, to the increase in value of the larger firm relative to the merged firms.

Question 28

Jeffrey Bruner, CFA, uses the capital asset pricing model (CAPM) to help identify mispriced

securities. A consultant suggests Bruner use arbitrage pricing theory (APT) instead. In compare-
ing CAPM and APT, the consultant makes the following arguments:

a. Both the CAPM and APT require a mean-variance efficient market portfolio.
b. Neither the CAPM nor the APT assumes normally distributed security returns.
c. The CAPM assumes that one specific factor explains security returns but APT does not.
State whether each of the consultant’s arguments is correct or incorrect. Indicate, for each
incorrect argument, why the argument is incorrect.

Answer 28

a.This statement is incorrect. The CAPM requires a mean-variance efficient market portfolio, but APT does not.

b. This statement is incorrect. The CAPM assumes normally distributed security returns, but APT does not.

c. This statement is correct.

Question 29

According to the theory of arbitrage:

a. High-beta stocks are consistently overpriced.
b. Low-beta stocks are consistently overpriced.
c. Positive alpha investment opportunities will quickly disappear.
d. Rational investors will pursue arbitrage opportunities consistent with their risk tolerance.

Answer 29

Positive alpha investment opportunities will quickly disappear.

Question 30

The general arbitrage pricing theory (APT) differs from the single-factor capital asset pricing
model (CAPM) because the APT:

a. Places more emphasis on market risk.
b. Minimizes the importance of diversification.
c. Recognizes multiple unsystematic risk factors.
d. Recognizes multiple systematic risk factors.

Answer 30

Recognizes multiple systematic risk factors.

Question 31

An investor takes as large a position as possible when an equilibrium price relationship is violated. This is an example of:

a. A dominance argument.
b. The mean-variance efficient frontier.
c. Arbitrage activity.
d. The capital asset pricing model.

Answer 31

Arbitrage activity

Investors will take on as large a position as possible only if the mispricing opportunity is an arbitrage.

Otherwise, considerations of risk and diversification will limit the position they attempt to take in the mispriced security.

Question 32

In contrast to CAPM, arbitrage pricing theory:

a. Requires that markets be in equilibrium.
b. Uses risk premiums based on micro variables.
c. Specifies the number and identifies specific factors that determine expected returns.
d. Does not require restrictive assumptions concerning the market portfolio.

Answer 32

Does not require restrictive assumptions concerning the market portfolio.

Question 33

In the absence of arbitrage opportunities, expected excess returns of portfolios that are well-diversified must be…

Answer 33

proportional to its beta coefficient.

Question 34

Assume that the single index model holds, and that you held the (well-diversified) marketportfolio with a very large number of securities. If the standard deviation of your portfolio was 0.20 and σM was 0.10, the β of the portfolio would be approximately…

Answer 34

SD portfolio = Beta*SD market

Hence b = sd p / sd m = 0.2/0.1 = 2

Question 35

In the absence of arbitrage opportunities, expected excess returns of portfolios that are well-diversified must be…

Answer 35

0