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
E)none of the above

Question

Quizplus · Accepted Answer

According to the APT, the expected return on a portfolio can be calculated as follows: E(Ri) = Rf + bi * (E(Rm) - Rf), where Rf is the risk-free rate, bi is the beta of the security, and E(Rm) is the expected return on the market. Based on this, the expected return on Portfolio A is 10% + 0.2 * (E(Rm) - 10%) = 13%, which implies that the expected return on the market should be 16.5%. Similarly, the expected return on Portfolio B is 10% + 0.4 * (E(Rm) - 10%) = 15%, which implies that the expected return on the market should be 17.5%. However, the expected return of the market cannot be both 16.5% and 17.5% at the same time, creating an arbitrage opportunity. To take advantage of this, we should short sell Portfolio B (with the higher expected return) and use the proceeds to buy Portfolio A (with the lower expected return). This will result in a riskless profit equal to the difference in expected returns, which is 2%.

Consider the Single Factor APT