Question

Suppose you hold a diversified portfolio consisting of a $7500 investment in each of 20 different common stocks. The portfolio's beta is 1.12. Now, suppose you sell one of the stocks with a beta of 1.0 for $7500 and use the proceeds to buy another stock whose beta is 1.75. Calculate your portfolio's new beta.

Answer 1

The beta of the portfolio is the weighted average of the individual asset betas where
the weights are the portfolio weights.

To get portfolio beta we will replace 1 stock of 20 or 5% of the portfolio.

The other stocks are 95% of the portfolio. 1.12 =0.95 ( b )+0.05*1

b= 1.126316

So not when we replace one and get other stock
Portfolio beta =0.95*1.126316 + 0.05*1.75=1.1575