York University

ADMD 4501

CHAPTER 9

MULTIFACTOR MODELS OF RISK AND RETURN

TRUE/FALSE QUESTIONS

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

 

 2                             The APT does not require a market portfolio.

 

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

 

 4                             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.

 

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

 

 6                             The APT assumes that capital markets are perfectly competitive.

 

 7                             The APT assumes that security returns are normally distributed.

 

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

 

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

 

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

 

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

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

 

 

 

 

 

 

 

 

 

MULTIPLE CHOICE PROBLEMS

 

1. 1                      Under the following conditions, what are the expected returns for stock X and Y?

?⁰ = 0.04                                             b_x,1 = 1.2

k₁ = 0.035                                           b_x,2 = 0.75

k₂ = 0.045                                          b_y,1 = 0.65

b_y,2 = 1.45

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

 

 

 

 

 

2. 2                      Under the following conditions, what are the expected returns for stock Y and Z?

?⁰ = 0.05                                               b_y,1 = 0.75

k₁ = 0.06                                               b_y,2 = 1.35

k₂ = 0.05                                              b_z,1 = 1.5

b_z,2 = 0.85

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

 

(d) 3                      Under the following conditions, what are the expected returns for stock A and B?

?⁰ = 0.035                                            b_a,1 = 1.00

k₁ = 0.05                                               b_a,2 = 1.40

k₂ = 0.06                                              b_b,1 = 1.70

b_b,2 = 0.65

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

 

1. 4                      Under the following conditions, what are the expected returns for stock X and Y?

?⁰ = 0.05                                               b_x,1 = 0.90

k₁ = 0.03                                               b_x,2 = 1.60

k₂ = 0.04                                              b_y,1 = 1.50

b_y,2 = 0.85

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

 

2. 5                      Under the following conditions, what are the expected returns for stock A and C?

?⁰ = 0.07                                               b_a,1 = 0.95

k₁ = 0.04                                               b_a,2 = 1.10

k₂ = 0.03                                              b_c,1 = 1.10

b_c,2 = 2.35

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

(e) 6       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%

 

 

USE THE FOLLOWING INFORMATION FOR THE NEXT SEVEN PROBLEMS

 

Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas)

 

Stock	Factor 1 Loading	Factor 2 Loading
X	-0.55	1.2
Y	-0.10	0.85
Z	0.35	0.5

 

The zero-beta return (λ₀) = 3%, and the risk premia are λ₁ = 10%, λ₂ = 8%. Assume that all three stocks are currently priced at $50.

 

(c) 7                       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.

 

(a) 8                       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.

4. 9                      If you know that the actual prices one year from now are stock X $55, stock Y

$52, and stock Z $57, then

1. 1. stock X is undervalued, stock Y is undervalued, stock Z is undervalued.
   2. stock X is undervalued, stock Y is overvalued, stock Z is overvalued.
   3. stock X is overvalued, stock Y is undervalued, stock Z is undervalued.
   4. stock X is undervalued, stock Y is overvalued, stock Z is undervalued.
   5. stock X is overvalued, stock Y is overvalued, stock Z is undervalued.

 

(d) 10                    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.

 

(c) 11                     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.

 

1. 12                    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
   1. $8
   2. $5
   3. $7

d)            $12

e)            $15

 

(e) 13                    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.

 

 

(a) 14                    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.

 

Risk	Factor Sensitivity(β	Risk
Factor	)	Premium(λ)
MP	1.76	0.0259
UI	-0.8	-0.0432
UPR	0.87	0.0149

 

Calculate the expected excess return for the asset.

a) 12.32%

b) 9.32%

c) 4.56%

d) 6.32%

e) 8.02%