Question

Consider the single factor APT. Portfolio A has a beta of 1.1 and an expected return of 23%. Portfolio B has a beta of .6 and an expected return of 19%. The risk-free rate of return is 6%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _________.

A;B

B;A

B;B

A;A

Answer 1

The correct option is option 1 .

The APT model helps in making profit by arbitrage and exploiting the pricing differences between the securities and purchasing the undervalued securities and selling the overvalued security.

Now, as the APT MODEL OF A IS:

E(R ) = RF + BETA * F

SO, 23 = 6 + 1.1 F

F = 15.45

Now, F is the factor sensitivity, which is the difference between the actual return and the expected return due to the unanticipated changes in the factors , the higher/lower the value of  the F, signifies that the security is undervalued/overvalued.

Now , taking security B :

E(R) = RF + BETA * F

19 = 6 + 0.6F

F = 21.67

So, since the value of the factor sensitivities of security B , is higher than A , it signifies that B is undervalued and A is overvalued. Hence, we should buy B and sell  A.

So, in order to take the advantage of arbitrage, and making profits without making an additional investment we should take advantage of the factor surprises, and but the security with the higher factor surprises(F) and sell the one with the lower factor surprise(F).