Question

Consider the single factor APT. Portfolio A has a beta of 1.3 and an expected return of 21%. Portfolio B has a beta of .7 and an expected return of 17%. The risk-free rate of return is 8%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio ________ and a long position in portfolio ________.

Answer 1

Answer:

Portfolio A and Portfolio B

Explanation:

In this question, we apply the Capital Asset Pricing Model (CAPM) formula which is shown below

Expected rate of return = Risk-free rate of return + Beta × (Market rate of return - Risk-free rate of return)

The Market rate of return - Risk-free rate of return) = Market risk premium

Let us assume the market risk premium be X

For Portfolio A:

21% = 8% + 1.3 × X

13% = 1.3  × X

So, the X = 10%

For Portfolio B:

17% = 8% + 0.7 × X

9% = 0.7  × X

So, the X = 12.86%

Based on the market risk premium calculations, we can conclude that Portfolio A should be in short position while Portfolio B should be in long position as portfolio B has higher market risk premium than B