Consider a single factor APT.Portfolio A has a beta of 1.0 and an expected return of 16%.Portfolio B has a beta of 0.8 and an expected return of 12%.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)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 function of its factor betas and the risk premium associated with the factor. In this case, the single factor is not specified, but we can use the information provided to calculate the expected return on each portfolio based on their respective betas. The equation for the expected return of a portfolio is:
E(r) = Rf + beta x Risk Premium
Portfolio A:
E(r) = 6% + (1.0 x Risk Premium)
16% = 6% + (1.0 x Risk Premium)
Risk Premium = 10%
Portfolio B:
E(r) = 6% + (0.8 x Risk Premium)
12% = 6% + (0.8 x Risk Premium)
Risk Premium = 7.5%
Since Portfolio A has a higher expected return than Portfolio B but a lower beta, it is overpriced according to the APT. To take advantage of this arbitrage opportunity, you should short Portfolio A and long Portfolio B. If the APT is correct, and the risk-free rate is known with certainty, the profit from this trade is guaranteed.

Consider a Single Factor APT