How to Calculate Beta From Volatility & Correlation

by Kathryn Christopher

    The beta of a particular stock can be found from the volatility of the broad stock market's returns, such as the S&P 500 index, the volatility of the particular stock’s returns and information on the correlation between the particular stock's returns and the market’s returns. Using these three pieces of information, the beta of the stock is calculated as the covariance of the stock's returns with the market's returns divided by the variance of the market. Volatility is defined as the standard deviation of returns.

    Step 1

    Gather your three input statistics. In the following example, assume the volatility of the broad stock market's returns is 10 percent, the volatility of the stock’s returns is 20 percent and the correlation between the stock's returns and the market’s returns is 0.6.

    Step 2

    Multiply the correlation coefficient by the volatility of the stock's returns and by volatility of the market's returns: (0.6)(.20)(.1) = 0.012. This is the numerator of the ratio used to calculate beta. The numerator is the covariance of the stock returns with the market returns.

    Step 3

    Square the volatility of the market returns: (0.1)(0.1) = 0.01. This is the denominator of the ratio used to calculate beta. The denominator is the variance of the market returns which is equal to its standard deviation squared.

    Step 4

    Divide the numerator by the denominator: 0.012/0.01 = 1.2. This is the beta of the stock.

    Tip

    • Volatility measures the stock’s total risk. Beta measures one component of total risk: the stock's systematic risk. If the beta you calculate is greater than 1, then the stock has more systematic risk than the broad stock market. If the beta you calculate is less than 1, the stock has less systematic risk than the stock market.
    • Beta tells you how much the stock return is expected to move on average for a 1 percent move in the broad market return. For example, if the stock’s beta is 2 and the market return increases by 1 percent, your stock is expected to increase by 2 percent. On the other hand, if the market return decreases by 1 percent, your stock is expected to decrease by 2 percent.

    Warning

    • There are some boundaries that your statistics must fall within. If they do not, your starting data is not correct. The correlation coefficient is bounded by minus 1 and positive 1. The volatility statistics must be positive. Your calculated variance must be positive. The covariance and beta are not bounded, but negative values are rare.

    References (1)

    • Essentials of Investments; Zvi Bodie et al.

    Photo Credits

    • Hemera Technologies/AbleStock.com/Getty Images

    About the Author

    Kathryn Christopher has been writing about investments for more than 20 years. Her work has appeared in the "Journal of Alternative Investments" and numerous other academic and industry publications. She works at Wiggin Financial Planning, teaches for UMASSOnline from South Florida, and holds a PhD in finance from the University of Massachusetts.

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