# In accordance with the Arbitrage Pricing Theory

June 14, 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

ß3

ß4

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 (F1), 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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