# How to Calculate the Variance in a Portfolio

by Bradley James Bryant ; Updated July 27, 2017In the financial world, risk is the nemesis of return; that is, investors are usually forced to find the balance between the two, but most would prefer a no-risk, high-return investment. As a result, there are numerous measurements for risk in the investment community. One of the most popular is variance, which is the spread of values around the average return. The square root of variance is standard deviation, which is viewed as a measure of volatility.

Obtain the average return for each asset in your portfolio. Let's say you have three stocks with an average return of 8.9, 4.6 and -1.2 percent.

Subtract the mean from each return number. The mean is the average or the sum divided by the number of assets, which in this case equals 12.3 percent / 3, or 4.1 percent. The three subtraction results are (8.9 - 4.1), (4.6 - 4.1) and (-1.2 - 4.1), or 4.8, 0.5 and -5.3 percent.

Square each return result. The three results are (4.8 ^ 2), (0.5 ^ 2) and (-5.3 ^ 2), or 23.04, 0.25 and 28.09 percent squared.

Sum the squares. This equals 23.04, 0.25 and 28.09 percent squared, or 51.38 percent squared.

Divide the sum by the number assets in the portfolio. The answer is 51.38 / 3 = 17.13 percent squared. This is the variance for the portfolio, which represents the average fluctuation in the portfolio. The square root of 17.13 percent squared, or 4.14, in percent units, is the standard deviation, a measure of volatility.

#### Tips

Variance is difficult to interpret directly, so standard deviation is used instead. In the example presented, the standard deviation is 4.14 percent and the mean is 4.1 percent. One standard deviation translates into a probability of 68 percent. Therefore, about 68 percent of the time, you would expect the portfolio return to be between (4.1 - 4.14 = 0.04) and (4.1 + 4.14 = 8.24) percent.

#### Warnings

Variance and standard deviation should be applied to "normal" data, that is, data that clusters equally around an average value. Skewed and outlying data can reduce the significance you attach to variance and standard deviation.

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