In accordance with the Arbitrage Pricing

| June 12, 2016

Question
In accordance with the Arbitrage Pricing Theory, assume that stock returns can be
explained by the following four factor model:
E(R) = RF + ß1F1 + ß2F2 + ß3F3 + ß4F4
Below please find betas for each of four stocks as follows; assume there is no firm specific
risk.
Stock

ß1

ß2

ß

ß

3

4

A

1.25

.70

.08

.65

B

.65

1.40

-.45

.85

C

.75

-.20

1.30

-.15

D

-.35

.80

1.20

1.45

The risk premiums for the factors are 6.2%, 5.7%, 3.9% and 7.0% respectively. If you
create a portfolio comprised of 25% of Stock A, 15% of Stock B, and 30% each of Stocks
C and D, what is the equation for your model? Assuming a risk-free rate of 6%, what is the
expected return on your portfolio?
Assume that the factors in this model include the following: Real growth in GDP (F 1),
unexpected inflation (F2), change in interest rates (F3), and change in expected inflation
(F4). What do the signs and magnitude of the corresponding betas tell you about the
stocks in this portfolio?
Factor models are one method of assessing risk and return, the Capital Asset Pricing
Model (CAPM) is another. How does this method that you have used above differ from the
CAPM? Under what conditions would you obtain the same expected return using either
method?

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