Standard deviation is a statistical measure that represents the rate of divergence from the mean in a data set. The higher the standard deviation, the more the elements of the data set deviate from one another.
Standard Deviation Formula
It is calculated by first finding the variance, which is the sum of the difference between each data point and the mean. For example, a data set of 4, 6 and 8 will have a mean of 6 (4 + 6 + 8 = 18 and 18 / 3 = 6). The variance will then be (6 – 4) + (6 – 6) + (8 – 6), with each being squared to eliminate any negative numbers.
The final result (8) is divided by the number of data points – 1 (2), which gives the variance (4). The standard deviation is the square root of the variance (2), which eliminates the squaring.
It is important to also note that data sets often follow certain patterns of distribution that are common in nature, which offer additional insight into the qualities of that data set.
Standard Deviation in Finance
It is used in finance to understand the volatility of a relevant measure or indicator. For example, a stock may have the same average (mean) price over two different years, but it could also have significantly different standard deviations over those same years.
In this case, the year with the low standard deviation would have seen little volatility in the price of the stock, while the year with the high standard deviation would have seen huge swings in the price, even if the average price ended up the same in the end.
It is an essential addition to other measures and indicators that offers a fuller picture of a set of financial data.
Final Thoughts
Much of the investing world is focused on reducing variation and the risk that is associated with it. For, example, a mutual fund with lower yet steadier returns will often be preferred over one with higher average returns that are more variable.
However, day traders are often seeking out variation so that they can capture those quick price swings. That is why standard deviation is such an important measure and such an important concept for day traders to understand.