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 . A. B;A
B. A;B
C. B;B
D. A; A

The portfolio weight in A is

The portfolio weight in B is

The portfolio weight in risk-free is

See expl below

Explanation:

For Portfolio A:

Given an expected return rate of 21% and a beta of 1.3.

Risk free rate of return = 8%

Let's use the CAPM equation:

21 = 8 + 1.3X

Let's take X as Risk Premium

For Portfolio B:

Given an expected return rate of 17% and a beta of 0.7

Risk free rate of return = 8%

Let's use the CAPM equation:

17 = 8 + 0.7X

Let's take X as Risk Premium

The risk premium of portfolio A is less than the risk premium of portfolio B, we should take a short position in portfolio A and a long position in portfolio B.

Option B is correct.

Let's find the portfolio weight.

Given:

Expected return of portfolio A =  21%

Expected return of portfolio B = 17%

We have a risk free rate of 8%

Let's assume we sell 2 shares of portfolio A and buy 3 shares of portfolio B,  i.e

(3 * 17%) - (2 * 21%) = 9%

The 9% is higher than the risk free rate(8%).

Therefore,

Portfolio weight in A = = 40% (short)

Portfolio weight in B = = 60% (long)

Portfolio weight in risk free = 0

This means in a complete portfolio of 5 shares, if we go 40% of portfolio A short and 60% of portfolio B long, we will have a return rate of 9% which is greater than the risk free rate of 8%

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