How to calculate systematic risk for a hedged portfolio?

Question

If I form a trading strategy of buying one portfolio with beta risk of 1.12 and selling another portfolio with beta risk of 1.16. What is the beta risk of this hedged portfolio? Average them?

Answer 1

The beta of a portfolio is the market weighted average of the betas of the assets.

Here, your portfolio beta is

(1.12*M1 - 1.16M2)/(M1-M2)

where M1 is the market value bought and M2 is the market value sold.

Note that the beta is not defined if M1 = M2. As the market values approach the same value, the beta would go off towards negative infinity.