In a Portfolio of 40M equity and beta of 1.5, if we wish to reduce the beta to 0.5 using futures which has a beta of 1, the formula will be;

[ (0.5-1.5)/1 ] x 40m/futures price

But when we want to reduce 40M to 30M and the beta to 0.5, the target beta becomes 0, and portfolio beta remains 1.5. Why so?

In essence, we’re changing 10M of the equity to cash, which has a beta of zero. The existing beta on that 10M is 1.5.

I see, but when the question explicitly states that 10M needs to be reduced and *beta needs to be lowered to 0.5*, why don’t we consider 0.5 as the target beta?

Like for instance in this question from CFAI mock, the target beta is 0 even though they have mentioned the target beta of 1.08. What phrase in this question gives the indication to use target beta as 0 instead of 1.08 please?

0.5 is the target beta for the 30M that remains equity, not for the 10M that will no longer be equity.

Ahh I see. So first we reduce the beta to 0 for 10M. And then reduce the beta to 0.5 for the remaining of stocks?

Thank you so much! Your method of explaining concepts always works