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Standard deviation in Finance and Trading.

As we can see, by its very construction, the variance is in the square of the original unit. This means that if we are dealing with distances in kilometers, the unit of variance would be in square kilometers.

Now, square kilometers may be easy to visualize as a unit, but what about year2year2 or IQ2IQ2, if we are working with the ages or IQs of a group? They are harder to interpret.

Hence, it makes sense to use a measure that can be comparable to the data on the same scale/units, like the standard deviation.

Standard deviation is calculated as the square root of variance. It has the same unit as our data and this makes it easy to use and interpret.

For example, consider a scenario where we are looking at a dataset of the heights of residents of a neighborhood. Assume that the heights are normally distributed with a mean of 165 cm and a standard deviation of 5 cm.

We know that for a normal distribution,

  • 68% of the data points fall within one standard deviation,

  • 95% within two standard deviations, and