Question

You hold a diversified $ 100,000 portfolio consisting of 20 stocks with 5000 invested in each . The portfolio's beta is 1.12. You plan to sell a stock with b=0.90 and use the proceeds to buy a new stock with b=1.75. what will the portfolio new beta be ?

PLEASE Help me i'm so stuck on this problem

Answer 1

A portfolio beta is the weighted sum of the individual betas.

For a given portfolio beta of 1.12, and since the 20 constituent stocks are worth $5000 each, they have equal weights.

By exchanging one stock with beta of 0.9 for one with beta=1.75 the new portfolio beta is
(20*1.12-0.9+1.75)/20
= 1.1625
=1.16