How to Calculate Historical Variance & Return on a Stock

by Mark Kennan, Demand Media
    Stock volatility can be quantified with variance.

    Stock volatility can be quantified with variance.

    When picking investments, knowing the volatility of a stock can help you decide if it's right for your particular strategy. For example, if you're very risk-averse, stocks with low volatility might fit better in your portfolio. If you don't mind taking on extra risk in hopes of extra rewards, a higher volatility might be acceptable. The variance measures the differences between the annual returns of the stock: the higher the variance, the more volatile the stock. In order to calculate the variance, you first have to figure out the annual returns for each year, and then the overall average.

    Step 1

    Subtract the price at the start of the year from the price at the end of the year to find the raw increase in stock price. For example, if the stock started at $26 and ended the year at $29, the stock increased by $3.

    Step 2

    Divide the increase or decrease by the price at the start of the year. In this example, divide the $3 increase by the $26 starting price to find that the stock increased by 0.1154, or about 11.54 percent.

    Step 3

    Repeat steps 1 and 2 to calculate the return on the stock for each year. For example, if you wanted to know the variance over the past three years, you would calculate the returns for each of those years.

    Step 4

    Calculate the average return on the stock by adding the annual return and dividing the result by the number of years. In this example, if the stock increased by 11.54 percent in the first year, increased by 5.46 percent in the second year, and lost 2 percent in the third year, add 11.54 plus 5.46 minus 2 to get 15 percent. Then, divide 15 percent by 3 to get an average return of 5 percent, or 0.05.

    Step 5

    Calculate the difference between the average return and each annual return. In this example, the difference between 0.1154 and 0.05 is 0.0654 percent; the difference between 0.0546 and 0.05 is 0.0046, and the difference between minus 0.02 and 0.05 percent is 0.07.

    Step 6

    Square each of the differences. In this example, square 0.0546 to get 0.00298116, square 0.0046 to get 0.00002116 and square 0.07 to get 0.0049.

    Step 7

    Add each of the results. In this example, add 0.00298116 plus 0.00002116 plus 0.0049 to get 0.00790232.

    Step 8

    Divide the sum by the number of years minus 1. In this example, divide 0.00790232 by 2 to find the variance is 0.00395116, or about 0.395 percent.

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