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.

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 )+0.051

b= 1.126316

So not when we replace one and get other stock

Portfolio beta =0.951.126316 + 0.05*1.75=1.1575

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