# How to Calculate Variance Using Beta

by Bryan Keythman

A stock’s variance measures the extent to which its actual returns differ from its expected returns. A stock with a higher variance has higher risk. A stock’s beta measures the extent to which a stock’s price moves with the market, which has a beta of 1. A beta greater than 1 means a stock moves more than the market. A beta of less than 1 means a stock moves less than the market. You can use a stock’s beta to calculate its expected return, which you can use to calculate its variance.

1. Visit any financial website that provides stock and investment information. Find a stock’s beta, listed in the stock’s quote section. Determine the three-month Treasury bill yield, listed in the website’s bonds section. For example, assume a stock’s beta is 1.2. Assume the three-month Treasury bill yields 4 percent.

2. Find the stock’s adjusted closing price on the first and last day of each of the past three years, listed in the historical prices section of the stock’s quote section.

3. Subtract each year’s beginning price from its ending price. Divide each result by its respective beginning price to calculate each year’s percentage return. In this example, if the stock’s beginning price last year was \$10 and its ending price was \$12, subtract \$10 from \$12 to get \$2. Divide \$2 by \$10 to get a return of 0.2, or 20 percent. Assume 8 percent and 11 percent returns in the other two years.

4. Estimate the market return, which is the percentage return you expect the overall stock market to generate over the next year. In this example, assume that you expect the market will generate a 12 percent return over the next year.

5. Subtract the three-month Treasury yield from the expected market return. Multiply your result by the stock’s beta. Then add your result to the three-month Treasury yield to calculate the stock’s expected return, or average return. In this example, subtract 4 percent, or 0.04, from 12 percent, or 0.12, to get 0.08. Multiply 0.08 by 1.2 to get 0.096. Add 0.04 and 0.096 to get an expected return of 0.14, or 14 percent.

6. Subtract the stock’s expected return from each year’s actual return. Square each result. In this example, subtract 0.14 from 0.2 to get 0.06. Subtract 0.14 from 0.08 to get -0.06. Subtract 0.14 from 0.11 to get -0.03. Square each result to get 0.0036, 0.0036 and 0.0009.

7. Add your results from Step 6 together. Then divide that result by (t - 1), in which t represents the number of years of returns you are using in the calculation. Continuing the example, t would be 3 because there are three years of returns in the calculation. Add 0.0036, 0.0036 and 0.0009 to get 0.0081. Divide 0.0081 by (3 - 1) to get a variance of 0.00405.

#### Tips

• Compare a stock’s beta with those of other stocks to compare their risk.
• Use returns from a greater number of years to get a more accurate result.