How to Find the New Beta of a Portfolio

The beta of a portfolio measures the portfolio’s correlation with the overall stock market and equals the sum of each stock’s weighted beta, which equals each stock’s beta times its proportion of the portfolio. Each time you add or remove stock from your stock portfolio, you affect the beta of the portfolio. A portfolio with a beta of 1 moves with the market. A beta greater than 1 means the portfolio moves more than the market. A beta lower than 1 means the portfolio moves less than the market. You can calculate your portfolio’s new beta after you change the selection of stocks in your portfolio.

Determine the total value of your portfolio, the number of stocks in the portfolio, the value of each stock and the beta of the portfolio before you made any changes to the portfolio. For example, assume you have a $4,000 portfolio equally invested in four stocks with each stock having a value of $1,000. Assume the portfolio’s beta is 0.89.

Determine the value of the stock that you sold from your portfolio and its beta, and determine the beta and the amount of the stock with which you replaced it. In this example, assume you sold $1,000 of a stock with a beta of 1.2 and replaced it with the same amount of a stock with a beta of 0.7.

Divide the value of the stock you sold from the portfolio’s value to determine the proportion of the portfolio you sold. Then subtract your result from 1 to calculate the proportion of the portfolio that remains. In this example, divide $1,000 by $4,000 to get 0.25, or 25 percent, which is the proportion of the portfolio you sold. Then subtract 0.25 from 1 to get 0.75, or 75 percent. This is the proportion that remains.

Multiply the proportion of the portfolio you sold by the beta of the stock. Then subtract your result from the portfolio’s beta to calculate the weighted beta of the portion that remains. In this example, multiply 25 percent, or 0.25, by 1.2 to get 0.3. Then subtract 0.3 from 0.89 to get 0.59, which represents the weighted beta of the remaining portion of the portfolio.

Multiply the proportion of the portfolio that represents the replacement stock by the stock’s beta to calculate the weighted beta of that stock. In this example, you are replacing the stock you sold with the same amount of a new stock, so the replacement stock’s proportion of the portfolio is 0.25. Multiply 0.25 by 0.7 to get a weighted beta of 0.18.

Add the weighted beta of the replacement stock to the weighted beta of the portion of the portfolio that you kept to calculate the new beta of the portfolio. In this example, add 0.18 to 0.59 to get a new beta of 0.77. This means the portfolio’s beta decreased from 0.89 to 0.77 by replacing the stock, which means the portfolio has lower risk.