Question

We have two economic factors F₁ and F₂ in a two-factor APT model. We have the following data on three well-diversified portfolios.

Stock	Expected return	bi1	bi2
A	7%	2	-1
B	17%	1	2
C	12%	1	?

If the risk free rate is 2%, what is stock C's b_i2 so that there is no arbitrage opportunity in the market?

Group of answer choices

0.5

-1

2

1

Answer 1

Solution:

As per Arbitration pricing theory,

Expected return = R(f) + b1f1 + b2f2

For Stock A, 7 = 2 + 2 f1 - 1 f2 ,

So, 2 f1 - f2 = 5, so f2 = 2f1 - 5 ----------------- (a)

Now for Stock B , 17 = 2 + f1 + 2f2 ---------------- (b)

Using equation (a) and putting in (b) , we get

2( 2f1-5) +f1 = 15

5f1 = 25, and value of f1 = 5.

so value of f2 = 2(5) - 5 = 5

Hence , f1= 5 and f2 = 5

So we can calculate now for stock C, since for no arbitrage, the factors will be same

For stock C : 12 = 2 + b1f1 + b2f2

12 = 2 + 5 + 5b2

so, b2 = 1

Hence the bi2 for stock C = 1