Answer:
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
[tex] X = \frac{21-8}{1.3} = 10 [/tex]
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
[tex] X = \frac{17-8}{0.7} = 12.86 [/tex]
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 = [tex] \frac{2}{2+3} = \frac{2}{5} = 0.40 [/tex] = 40% (short)
Portfolio weight in B = [tex] \frac{3}{2+3} = \frac{3}{5} = 0.60 [/tex] = 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%
