Question

Consider the single factor APT. Portfolio A has a beta of 1.7 and an expected return of 19%. Portfolio B has a beta of .6 and an expected return of 15%. The risk-free rate of return is 11%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _________. Multiple Choice A;A A;B B;B B;A

Answer 1

Answer: A;B

Step-by-step explanation:

Consider the single factor APT. Portfolio A has a beta of 1.7 and an expected return of 19%. Portfolio B has a beta of .6 and an expected return of 15%. The risk-free rate of return is 11%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio A and a long position in portfolio B.

You should take a short position in the Portfolio with a lower risk premium and a long position on the Portfolio with a higher risk premium.

Using the single factor APT, the formula for risk premium can be derived from;

E(r) = Rf + beta (Risk premium on factor)

Portfolio A

19% = 11% + 1.7 * Risk premium

1.7 * risk premium = 8%

Risk Premium = 4.7%

Portfolio B

15% = 11% + 0.6 * RP

0.6 * RP = 4%

RP = 6.67%

Portfolio A Risk premium is lower so it should be shorted.

Portfolio B Risk premium is higher so it should taken a long position in.