# Can You Take a Weighted Average of Equity Betas?

by Nola Moore

Investors talk a lot about portfolio diversification, or the art of using a variety of investments to offset risk. If one type of investment performs poorly, you have other things in the portfolio that may still perform well. Beta is one measurement of risk -- it measures an equity's volatility. A weighted average beta shows how each equity holding's beta factors into the big picture and is key to ensuring you have a well-diversified portfolio.

Beta is a measurement of volatility, or how much a stock price fluctuates relative to the rest of the market as represented by the S&P 500 stock index. Mathematically speaking, beta represents the slope of the line obtained through regression analysis of the stock's price over five to 10 years. If that seems overly complicated, just know that beta values greater than one are more volatile than average, and those less than one are less volatile than average. Investors consider high volatility more risky than low volatility because there is a larger chance of a rapid and significant price change.

### Weighted Betas

An equity portfolio holds several different stocks, and each holding has a market value. In most cases, those market values aren't equal across the board -- you aren't likely to hold \$10,000 each of Companies A, B and C. Instead, you might hold \$5,000 of Company A, \$17,000 of Company B and \$8,000 of Company C. If you only look at a stock's plain beta, without accounting for its total proportion of the portfolio, you may miss the true level of volatility risk. The risk of a high beta is significantly less if it is only 5 percent of the portfolio than if it is 80 percent. Investors analyze this by weighting the beta by accounting for market value.

### Calculating Weighted Beta and Portfolio Beta

Calculating weighted beta is fairly simple. Begin by dividing each stock's market value by the market value of the whole portfolio. This tells you what percentage of the portfolio is devoted to each stock. Multiply this percentage by the stock's beta to find a weighted beta. Notice that this effectively reduces the beta for all stocks, and that larger holdings have somewhat larger weighted betas than smaller ones. You can add betas together to get a total beta by sector or for the portfolio as a whole.

### Using Weighted Beta in Analysis

Individual weighted betas more accurately reflect the risk of any particular holding in your portfolio. Use this number to analyze the effects of increasing or decreasing a stock position, or of adding a new stock. Use the portfolio total beta to determine whether or not the whole portfolio matches your risk tolerance. Remember that betas can change every day, and they reflect past performance only. As such, beta should be only one measurement of risk -- be sure to review overall company performance and health, and to spread holdings among business sectors and sizes to fully diversify your portfolio.