Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. 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) A; A
B) A; B
C) B; A
D) B; B

Question

Quizplus · Accepted Answer

According to the APT, the expected return of a portfolio is a linear function of its beta and the risk premium associated with the underlying factor. In this case, the single factor is not specified, but we can infer that the market is the underlying factor since both Portfolio A and Portfolio B have positive betas. According to the APT equation:

Expected Return = Risk-free Rate + (Beta x Risk Premium)

We can solve for the risk premium for each portfolio:

For Portfolio A: 
13% = 10% + (0.2 x Risk Premium) 
Risk Premium = 15%

For Portfolio B: 
15% = 10% + (0.4 x Risk Premium) 
Risk Premium = 12.5%

We note that Portfolio B has a lower risk premium despite having a higher expected return, implying that it is overpriced. To take advantage of this arbitrage opportunity, we should short Portfolio B (sell it) and long Portfolio A (buy it). This is because we expect Portfolio B to deliver a lower return than what its beta suggests, while we expect Portfolio A to deliver a higher return than what its beta suggests.

Consider the Single Factor APT