Appendix

STANDARD DEVIATION

Standard deviation is a statistical measure of variability among a data set such as the daily percentage returns of an investment portfolio or equity index.

A low standard deviation indicates that the data points tend to be very close to the average of all the data points, while a high standard deviation indicates that the data points are spread out over a larger range from the average of all the data points.

As we’ve seen, standard deviation is often used to measure confidence in statistical results. We would be about 68 percent certain that any data point would be within 1 standard deviation of the average of all the data points. We’d be about 95 percent certain that the data point would be within 2 standard deviations of the average of all the data points.

The formula for standard deviation is:

Unnumbered Display Equation

Let’s calculate the standard deviation for some daily index returns by hand to better understand the concepts. In real life there’s no reason to do this as any spreadsheet can accomplish the calculation nearly instantaneously.

10 Days' Returns

  0.56%

–0.22%

  0.64%

  0.45%

–0.81%

  0.70%

–0.11%

  1.01%

  0.37%

–0.67%

Step 1: Calculate the average of all 10 data points.

Unnumbered Display Equation

Step 2: Calculate the deviation of each data point from the average and the square of that ...

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