How to Calculate Historical Variance & Return on a Stock

by Bryan Keythman

The historical return on a stock is the percentage the stock’s adjusted price changed over a certain period of time, such as one year. A stock’s historical variance measures the difference between the stock’s returns for different periods and its average return. A stock with a lower variance typically generates returns that are closer to its average. A stock with a higher variance can generate returns that are much higher or lower than expected, which increases uncertainty and increases the risk of losing money. You can calculate variance and returns using a stock’s historical price information.

Visit any financial website that provides stock information, such as Yahoo Finance, DailyFinance or MSN Money. Find the stock’s adjusted closing price at the beginning and end of each of the past five years in its historical prices section. The adjusted closing price adjusts for dividends and stock splits.

Subtract each year’s beginning price from its ending price. Divide each result by its respective beginning price to calculate the stock’s historical return each year. For example, if the stock’s adjusted closing price was $20 on the first day of last year and $25 on the last day of last year, subtract $20 from $25 to get $5. Divide $5 by $20 to get 0.25, which is a historical return of 25 percent last year. In this example, assume the historical returns for the other four years were 10 percent, 3 percent, 15 percent and 17 percent.

Add together the historical annual returns. Divide your result by the number of years of returns to calculate the historical average annual return. In this example, add 0.25, 0.1, 0.03, 0.15 and 0.17 to get 0.7. Divide 0.7 by 5 years of returns to get an average annual return of 0.14, or 14 percent.

Subtract the average annual return from each actual annual return to calculate the difference between each actual return and the average return. In this example, subtract 0.14 from 0.25 to get 0.11. Subtract the average return from each remaining annual return to get -0.04, -0.11, 0.01 and 0.03.

Calculate the square of each difference. In this example, square 0.11 to get 0.0121. Square each of the remaining results to get 0.0016, 0.0121, 0.0001 and 0.0009.

Add together each result. In this example, add 0.0121, 0.0016, 0.0121, 0.0001 and 0.0009 to get 0.0268.

Subtract 1 from the number of years of returns. In this example, subtract 1 from 5 to get 4.

Divide your Step 6 result by your Step 7 result to calculate the stock’s variance. Continuing with the example, divide 0.0268 by 4 to get 0.0067.

Tip

  • Compare the variance and returns of different stocks. The stock with the lowest variance and highest returns has lower historical risk and higher historical performance.