# Variance and Standard Deviation

Variance and standard deviation are both metrics that have to do with nearly every aspect of data analysis. If you're looking at the projected performance of a stock, for instance, standard deviation and variance will both play into how you asses the data. But what are they, and how can they help to make you a smarter investor? We'll look into variance and standard deviation and show you exactly how to read the numbers.

### Variance

Of the two, variance is a bit easier to calculate than standard deviation, but in the financial world standard deviation is more useful. Variance is the amount that a set of data varies from the mean of that data.
For instance, in order to calculate the amount of variance in a set of numbers like 2, 3, 8, 4, 5, and 9 we first need to add them together and divide by the amount of numbers in the set in order to get the mean. In this case, the mean is 5.16. In order to get the variance, we look at the difference between 5.16 and those numbers.

Variance is useful for a lot of things, but it's mostly used to make apples to apples comparisons within a set of data. A practical use for variance would be to find out whether the expected returns of a particular stock portfolio are in line with the real returns. In a perfect world, we'd plot the variance for each stock and then sell off underperforming assets, while doubling down on the ones that are overperforming. Of course, trading in the markets doesn't work this way, but variance can let us know whether your returns are greater or less than the returns of a group of other stocks.

### Standard Deviation

Standard deviation is harder to wrap your head around mathematically than variance, but it's the more useful of the two when we're looking at our portfolios. Standard deviation is simply the square root of the variance. It's useful because it tells us how much, on average, whether each stock in your portfolio is overperforming or underperforming as compared to every other stock. It's a way to quickly check whether an asset is doing exceptionally well or exceptionally poorly, based on how far away from the standard deviation its return is.

One use for standard deviation is figuring out the historical volatility of any asset. By looking at how the asset has performed over the years, finding the standard deviation for growth, and then comparing recent returns to that standard deviation we can tell whether an asset is growing or shrinking, and just how fast. We can also use it in a straightforward comparison with the volatility of other stocks, in order to find more or less volatility depending on the needs of an investor's current portfolio.

### Variance and Standard Deviation in Practice

Variance and standard deviation are advanced mathematical concepts that apply to the analysis of assets, and they take a little getting used to. Fortunately, it's easy enough to compare standard deviation and variance when they're laid out in front of you. And at the end of the day, that's what these concepts are really about. Finding a simple way to compare two assets in order to determine volatility and expected performance.
By Aaron Phillips
Aaron Phillips is a financial researcher and journalist based out of Michigan. He regularly writes the IG Daily and IG Weekly columns.

Copyrighted 2018. Content published with author's permission.

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