Variance and Standard Deviation

By Douglas S. Ehrman

Variance measures how spread out a group of values are — in other words, how much they vary. Mathematically, variance is the average squared “deviation” (or difference) of each number in the group from the group’s mean value,
divided by the number of elements in the group. For example, for the numbers 8, 9, and 10, the mean is 9 and the variance is:

{(8-9)2 + (9-9)2 + (10-9)2}/3 = (1 + 0 + 1)/3 = .667

Now look at the variance of a more widely distributed set of numbers:

2, 9, and 16: {(2-9)2 + (9-9)2 + (16-9)2}/3 = (49 + 0 + 49)/3 = 32.67

The more varied the prices, the higher their variance — the more widely distributed they will be. The more varied a market’s price changes from day to day (or week to week, etc.), the more volatile that market is.

A common application of variance in trading is standard
deviation, which is the square root of variance. The standard deviation of 8, 9, and 10 is: .667 = .82; the standard deviation of 2, 9, and 16 is: 32.67 = 5.72.