Question

Suppose you held a diversified portfolio consisting of 10 different common stocks, investing $500 in each stock. The portfolio’s beta is 1.9. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 0.8 for $500 and use the proceeds to buy another stock with a beta of 1.25. What would your portfolio’s new beta be?

Answer 1

The total proceeds from the portfolio will be:

$\text{Total Proceeds}=500\times 10=5000$

After the withdrawal of one stock from the portfolio the new beta will be:

$\beta=1.9-\dfrac{500}{5000}\times 0.8=1.82.$

As a result of purchasing another stock the resultant beta will be:

$\beta _\text{Portfolio}=1.82+\dfrac{500}{5000}\times 1.25=1.945$

It is evident that the portfolio beta will increase.