Susan's investment portfolio currently contains three stocks that have a total value equal to $100,000. The beta of this portfol
io is 1.5. Susan is considering investing an additional $50,000 in a stock that has a beta equal to 3. After she adds this stock, what will be the portfolio's new beta?
A stock portfolio's overall beta is found by multiplying each stock's beta times the percentage of the overall portfolio it makes up and adding these terms together. Since the current portfolio's beta is known, we can treat all the stocks in the portfolio as a single stock for calculating its weight in the new portfolio. Thus, our new portfolio will have a value of $150,000, $100,000, or 2/3, of which has a beta of 1.5 and $50,000, or 1/3, of which has a beta of 3. Then the beta of the new portfolio will be 1.5*(2/3) + 3*(1/3) = 2.
