Deck 9: Multifactor Models of Risk and Return

Question 1

Studies indicate that neither firm size nor the time interval used are important when computing beta.

Answer 1

False

Question 2

Studies strongly suggest that the CAPM be abandoned and replaced with the APT.

Answer 2

False

Question 3

The APT assumes that capital markets are perfectly competitive.

Answer 3

True

Question 4

Empirical tests of the APT model have found that as the size of a portfolio increased so did the number of factors.

Question 5

Exhibit 9.1
Use the Information Below for the Following Problem(S)
(1) Capital markets are perfectly competitive.
(2) Quadratic utility function.
(3) Investors prefer more wealth to less wealth with certainty.
(4) Normally distributed security returns.
(5) Representation as a K factor model.
(6) A market portfolio that is mean-variance efficient.

-Refer to Exhibit 9.1.In the list above,which are not assumptions of the Arbitrage Pricing model?

A) (1) and (3)
B) (1), (2), and (3)
C) (1), (2), and (5)
D) (2), (4), and (6)
E) All six are assumptions

Question 6

Findings by Fama and French that stocks with high Book Value to Market Price ratios tended to produce larger risk adjusted returns than stocks with low Book Value to Market Price ratios challenge the efficacy of the CAPM.

Question 7

In the APT model,the identity of all the factors is known.

Question 8

According to the APT model all securities should be priced such that riskless arbitrage is possible.

Question 9

The January Effect is an anomaly where returns in January are significantly smaller than in any other month.

Question 10

Fama and French suggest a four factor model approach that explains many prior market anomalies.

Question 11

To date,the results of empirical tests of the Arbitrage Pricing Model have been

A) Clearly favorable.
B) Clearly unfavorable.
C) Mixed.
D) Unavailable.
E) Biased.

Question 12

The APT assumes that security returns are normally distributed.

Question 13

Findings by Basu that stocks with high P/E ratios tended to outperform stocks with low P/E ratios challenge the efficacy of the CAPM.

Question 14

A major advantage of the Arbitrage Pricing Theory is the risk factors are clearly universally identifiable.

Question 15

Arbitrage Pricing Theory (APT)specifies the exact number of risk factors and their identity

Question 16

The APT does not require a market portfolio.

Question 17

Two approaches to defining factors for multifactor models are to use macroeconomic variables or individual characteristics of the securities.

Question 18

Exhibit 9.1
Use the Information Below for the Following Problem(S)
(1) Capital markets are perfectly competitive.
(2) Quadratic utility function.
(3) Investors prefer more wealth to less wealth with certainty.
(4) Normally distributed security returns.
(5) Representation as a K factor model.
(6) A market portfolio that is mean-variance efficient.

-Refer to Exhibit 9.1.In the list above which are assumptions of the Arbitrage Pricing Model?

A) (1) and (4)
B) (1), (2), and (3)
C) (1), (3), and (5)
D) (2), (3), (4), and (6)
E) All six are assumptions

Question 19

One method for estimating the parameters for the Capital Asset Pricing Model is to estimate a portfolio's characteristic line via regression techniques using the single-index market model.

Question 20

Multifactor models of risk and return can be broadly grouped into models that use macroeconomic factors and models that use microeconomic factors.

Question 21

Which of the following is not a step required for a multifactor risk model to estimate expected return for an individual stock position?

A) Identify a set of K common risk factors.
B) Estimate the risk premia for the factors.
C) Estimate the sensitivities of the each stock to these K factors.
D) Calculate the expected returns using linear programming analysis.
E) All of the above are necessary steps for a multifactor risk model.

Question 22

In a micro-economic (or characteristic)based risk factor model the following factor would be one of many appropriate factors:

A) Confidence risk.
B) Maturity risk.
C) Expected inflation risk.
D) Call risk.
E) Return difference between small capitalization and large capitalization stocks.

Question 23

Consider the following list of risk factors:
(1) monthly growth in industrial production
(2) return on high book to market value portfolio minus return on low book to market value portfolio
(3) change in inflation
(4) excess return on stock market portfolio
(5) return on small cap portfolio minus return on big cap portfolio
(6) unanticipated change in bond credit spread
Which of the following factors would you use to develop a microeconomic-based risk factor model?

A) (1), (2), and (3).
B) (1), (3), and (5).
C) (2), (4), and (5).
D) (1), (3), and (6).
E) (4), (5), and (6).

Question 24

A study by Chen,Roll,and Ross in 1986 examined all of the following factors in applying the Arbitrage Pricing Theory (APT)except the

A) Return on a market value-weighted return.
B) Monthly growth rate in U.S. industrial production.
C) Change in the consumer price index (CPI).
D) Expected change in the bond credit spread.
E) All of the above factors were used in their 1986 study.

Question 25

Consider the following two factor APT model
E(R)= ?? + ??b? + ??b?

A) ?1 is the expected return on the asset with zero systematic risk.
B) ?1 is the expected return on asset 1.
C) ?1 is the pricing relationship between the risk premium and the asset.
D) ?1 is the risk premium.
E) ?1 is the factor loading.

Question 26

The excess return form of the single-index market model is

A) Rit = a + b(Rmt - Rit) + eit
B) RFRt = a + b(Rmt - RFRt) + eit
C) Rit - RFRt = a + b(Rmt) + eit
D) Rit = a + b(Rmt - RFRt) + eit
E) Rit - RFRt = a + b(Rmt - RFRt) + eit

Question 27

Unlike the capital asset pricing model,the arbitrage pricing theory requires only the following assumption(s):

A) A quadratric utility function.
B) Normally distributed returns.
C) The stochastic process generating asset returns can be represented by a factor model.
D) A mean-variance efficient market portfolio consisting of all risky assets.
E) All of the above

Question 28

In a multifactor model,time horizon risk represents

A) Unanticipated changes in the level of overall business activity.
B) Unanticipated changes in investors' desired time to receive payouts.
C) Unanticipated changes in short term and long term inflation rates.
D) Unanticipated changes in the willingness of investors to take on investment risk.
E) None of the above.

Question 29

Cho,Elton,and Gruber tested the APT by examining the number of factors in the return generating process and found that

A) Five factors were required using Roll-Ross procedures.
B) Six factors were present when using historical beta.
C) Fundamental betas indicated a need for three factors.
D) All of the above.
E) None of the above.

Question 30

In a multifactor model,confidence risk represents

A) Unanticipated changes in the level of overall business activity.
B) Unanticipated changes in investors' desired time to receive payouts.
C) Unanticipated changes in short term and long term inflation rates.
D) Unanticipated changes in the willingness of investors to take on investment risk.
E) None of the above.

Question 31

In the APT model the idea of riskless arbitrage is to assemble a portfolio that

A) requires some initial wealth, will bear no risk, and still earn a profit.
B) requires no initial wealth, will bear no risk, and still earn a profit.
C) requires no initial wealth, will bear no systematic risk, and still earn a profit.
D) requires no initial wealth, will bear no unsystematic risk, and still earn a profit.
E) requires some initial wealth, will bear no systematic risk, and still earn a profit.

Question 32

Assume that you are embarking on a test of the small-firm effect using APT.You form 10 size-based portfolios.The following finding would suggest there is evidence supporting APT:

A) The top five size based portfolios should have excess returns that exceed the bottom five size based portfolios.
B) The bottom five size based portfolios should have excess returns that exceed the top five size based portfolios.
C) The ten portfolios must have excess returns not significantly different from zero.
D) The ten portfolios must have excess returns significantly different from zero.
E) None of the above.

Question 33

A 1994 study by Burmeister,Roll,and Ross defined all of the following risk factors except

A) Confidence risk
B) Market risk
C) Inflation risk
D) Market-timing risk
E) Business cycle risk

Question 34

The equation for the single-index market model is

A) RFRit = ai + bRmt + et
B) Rit = ai + bRmt + et
C) Rit = ai + bRFRt + et
D) Rmt = ai + bRit + et
E) Rit = ai + b(Rmt - RFRt) + et

Question 35

Dhrymes,Friend,and Gultekin,in their study of the APT,found that

A) As the number of securities used to form portfolios increased the number of factors that characterized the return generating process decreased.
B) As the number of securities used to form portfolios increased the number of factors that characterized the return generating process increased.
C) As the number of securities used to form portfolios decreased the number of factors that characterized the return generating process increased.
D) As the number of securities used to form portfolios increased the number of factors that characterized the return generating process remained unchanged.
E) None of the above.

Question 36

In one of their empirical tests of the APT,Roll and Ross examined the relationship between a security's returns and its own standard deviation.A finding of a statistically significant relationship would indicate that

A) APT is valid because a security's unsystematic component would be eliminated by diversification.
B) APT is valid because non-diversifiable components should explained by factor sensitivities.
C) APT is invalid because a security's unsystematic component would be eliminated by diversification.
D) APT is invalid because standard deviation is not an appropriate factor.
E) None of the above.

Question 37

One approach for using multifactor models is to use factors that capture systematic risk.Which of the following is not a common factor used in this approach?

A) Unexpected changes in inflation
B) Consumer confidence
C) Yield curve shifts
D) Unexpected changes in real GDP
E) All of the above are common factors used to measure systematic risk

Question 38

In a macro-economic based risk factor model the following factor would be one of many appropriate factors:

A) Confidence risk.
B) Maturity risk.
C) Expected inflation risk.
D) Call risk.
E) Return difference between small capitalization and large capitalization stocks.

Question 39

Consider the following list of risk factors:
(1) monthly growth in industrial production
(2) return on high book to market value portfolio minus return on low book to market value portfolio
(3) change in inflation
(4) excess return on stock market portfolio
(5) return on small cap portfolio minus return on big cap portfolio
(6) unanticipated change in bond credit spread
Which of the following factors would you use to develop a macroeconomic-based risk factor model?

A) (1), (2), and (3).
B) (1), (3), and (5).
C) (2), (4), and (5).
D) (1), (3), and (6).
E) (4), (5), and (6).

Question 40

Fama and French suggest a three factor model approach.Which of the following is not included in their approach?

A) Excess returns to a broad market index
B) Return differences between small-cap and large-cap portfolios
C) Return differences between industry characteristics
D) Return differences between value and growth stocks
E) Both c and d

Question 41

Exhibit 9.3
Use the Information Below for the Following Problem(S)
Stocks A, B, and C have two risk factors with the following beta coefficients. The zero-beta return (??) = .025 and the risk premiums for the two factors are (??) = .12 and (??) = .10.
$$\begin{array} { c c c } \text { Stack } & \text { Factor } 1 w _ { i 1 } & \text { Factor } 2 w _ { i 2 } \\\hline \mathrm { A } & - 0.25 & 1.1 \\\mathrm {~B} & - 0.05 & 0.9 \\\mathrm { C } & 0.01 & 0.6\end{array}$$

-Refer to Exhibit 9.3.Suppose that you know that the prices of stocks A,B,and C will be $10.95,22.18,and $30.89,respectively.Based on this information

A) All three stocks are overvalued.
B) All three stocks are undervalued.
C) Stock a is undervalued, stock b is properly valued, stock c is undervalued.
D) Stock a is undervalued, stock b is properly valued, stock c is overvalued.
E) Stock a is overvalued, stock b is overvalued, stock c is undervalued.

Question 42

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.The expected prices one year from now for stocks X,Y,and Z are

A) $53.55, $54.4, $55.25
B) $45.35, $54.4, $55.25
C) $55.55, $56.35, $57.15
D) $50, $50, $50
E) $51.35, $47.79, $51.58.

Question 43

Under the following conditions,what are the expected returns for stocks A and B?

A) 14.8% and 13.8%
B) 19.8% and 29.5%
C) 16.0% and 19.8%
D) 16.9% and 15.9%
E) None of the above

Question 44

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.Assume that you wish to create a portfolio with no net wealth invested.The portfolio that achieves this has 50% in stock X,-100% in stock Y,and 50% in stock Z.The weighted exposure to risk factor 2 for stocks X,Y,and Z are

A) 0.50, -1.0, 0.50
B) -0.50, 1.0, -0.50
C) 0.60, -0.85, 0.25
D) -0.275, 0.10, 0.175
E) None of the above.

Question 45

Under the following conditions,what are the expected returns for stocks Y and Z?

A) 17.61% and 13.23%
B) 16.25% and 18.25%
C) 13.24% and 28.46%
D) 14.83% and 17.69%
E) None of the above

Question 46

Under the following conditions,what are the expected returns for stocks X and Y?

A) 14.1% and 12.9%
B) 12.5% and 19.5%
C) 19.5% and 18.5%
D) 21.2% and 18.5%
E) None of the above

Question 47

Under the following conditions,what are the expected returns for stocks A and C?

A) 14.1% and 17.65%
B) 14.1% and 18.45%
C) 17.65% and 18.45%
D) 18.45% and 17.52%
E) None of the above

Question 48

Exhibit 9.3
Use the Information Below for the Following Problem(S)
Stocks A, B, and C have two risk factors with the following beta coefficients. The zero-beta return (??) = .025 and the risk premiums for the two factors are (??) = .12 and (??) = .10.
$$\begin{array} { c c c } \text { Stack } & \text { Factor } 1 w _ { i 1 } & \text { Factor } 2 w _ { i 2 } \\\hline \mathrm { A } & - 0.25 & 1.1 \\\mathrm {~B} & - 0.05 & 0.9 \\\mathrm { C } & 0.01 & 0.6\end{array}$$

-Refer to Exhibit 9.3.Assume that stocks A,B,and C never pay dividends and stocks A,B,and C are currently trading at $10,$20,and $30,respectively.What is the expected price next year for each stock?
     A     B     C

A) $10.82  $21.82  $30.99
B) $11.05  $22.18  $30.96
C) $11.32  $22.56  $30.99
D) $11.65  $22.42  $30.96
E) $18.50  $37.00  $48.30

Question 49

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.The new prices now for stocks X,Y,and Z that will not allow for arbitrage profits are

A) $53.55, $54.4, $55.25
B) $45.35, $54.4, $55.25
C) $55.55, $56.35, $57.15
D) $50, $50, $50
E) $51.35, $47.79, $51.58.

Question 50

Under the following conditions,what are the expected returns for stocks A and B?

A) 24.8% and 19.7%
B) 22.1% and 18.0%
C) 20.3% and 17.8%
D) 19.9% and 16.9%
E) 18.7% and 15.3%

Question 51

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.Assume that you wish to create a portfolio with no net wealth invested.The portfolio that achieves this has 50% in stock X,-100% in stock Y,and 50% in stock Z.The weighted exposure to risk factor 1 for stocks X,Y,and Z are

A) 0.50, -1.0, 0.50
B) -0.50, 1.0, -0.50
C) 0.60, -0.85, 0.25
D) -0.275, 0.10, 0.175
E) None of the above.

Question 52

Under the following conditions,what are the expected returns for stocks Y and Z?

A) 12.0% and 13.3%
B) 13.5% and 14.2%
C) 13.9% and 15.6%
D) 14.0% and 16.9%
E) 15.8% and 17.3%

Question 53

The table below provides factor risk sensitivities and factor risk premia for a three factor model for a particular asset where factor 1 is MP the growth rate in U.S.industrial production,factor 2 is UI the difference between actual and expected inflation,and factor 3 is UPR the unanticipated change in bond credit spread.

Calculate the expected excess return for the asset.

A) 12.32%
B) 9.32%
C) 4.56%
D) 6.32%
E) 8.02%

Question 54

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.The expected returns for stock X,stock Y,and stock Z are

A) 3%, 8%, 10%
B) 7.1%, 10.5%, 8.8%
C) 7.1%, 8.8%, 10.5%
D) 10%, 5.5%, 14%
E) None of the above.

Question 55

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.If you know that the actual prices one year from now are stock X $55,stock Y $52,and stock Z $57,then

A) stock X is undervalued, stock Y is undervalued, stock Z is undervalued.
B) stock X is undervalued, stock Y is overvalued, stock Z is overvalued.
C) stock X is overvalued, stock Y is undervalued, stock Z is undervalued.
D) stock X is undervalued, stock Y is overvalued, stock Z is undervalued.
E) stock X is overvalued, stock Y is overvalued, stock Z is undervalued.

Question 56

Exhibit 9.3
Use the Information Below for the Following Problem(S)
Stocks A, B, and C have two risk factors with the following beta coefficients. The zero-beta return (??) = .025 and the risk premiums for the two factors are (??) = .12 and (??) = .10.
$$\begin{array} { c c c } \text { Stack } & \text { Factor } 1 w _ { i 1 } & \text { Factor } 2 w _ { i 2 } \\\hline \mathrm { A } & - 0.25 & 1.1 \\\mathrm {~B} & - 0.05 & 0.9 \\\mathrm { C } & 0.01 & 0.6\end{array}$$

-Refer to Exhibit 9.3.Calculate the expected returns for stocks A,B,C.
    A   B     C

A) 0.082  0.091  0.033
B) 0.105  0.109  0.032
C) 0.132  0.128  0.033
D) 0.165  0.121  0.032
E) 0.850  0.850  0.610

Question 57

Exhibit 9.2
Use the Information Below for the Following Problem(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas).
$$\begin{array} { c c c } \text { Stack } & \text { Factor 1 Londine } & \text { Factor } 2 \text { Londing } \\\hline X & - [ .55 & 1.2 \\Y & - [ .10 & 0.85 \\Z & 0.35 & 0.5\end{array}$$
The zero-beta return (??) = 3%, and the risk premia are ?? = 10%, ?? = 8%. Assume that all three stocks are currently priced at $50.

-Refer to Exhibit 9.2.Assume that you wish to create a portfolio with no net wealth invested and the portfolio that achieves this has 50% in stock X,-100% in stock Y,and 50% in stock Z.The net arbitrage profit is

A) $8
B) $5
C) $7
D) $12
E) $15

Question 58

Consider a two-factor APT model where the first factor is changes in the 30-year T-bond rate,and the second factor is the percent growth in GNP.Based on historical estimates you determine that the risk premium for the interest rate factor is 0.02,and the risk premium on the GNP factor is 0.03.For a particular asset,the response coefficient for the interest rate factor is -1.2,and the response coefficient for the GNP factor is 0.80.The rate of return on the zero-beta asset is 0.03.Calculate the expected return for the asset.

A) 5.0%
B) 2.4%
C) -3.0%
D) -2.4%
E) 3.0%

Question 59

Under the following conditions,what are the expected returns for stocks X and Y?

A) 11.58% and 12.8%
B) 15.65% and 18.23%
C) 13.27% and 15.6%
D) 18.2% and 16.45%
E) None of the above