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Standard deviations as measures of volatility (law department spending)

Let’s convert a common description for stock markets – volatility – to an application for law departments. A law department tracks the amount of all bills that come from outside counsel each quarter. The department then creates a chart with columns corresponding to the number of bills it receives during the quarter by equal value ranges (e.g., $1 to $1,000; $1001 to $2000 etc.) increasing to a column for the largest bill range on the right. With that data someone could calculate the standard of deviation for that humped graph. If the bills are normally distributed (which is a significant if), one standard deviation on either side of the average bill size covers 66 percent of the bills.

If the law department diligently did this quarter by quarter, the standard deviations each quarter will vary. They vary because the frequency of amounts billed in a quarter has unpredictability, some volatility. Sometimes there will be very large bills, sometimes a preponderance of relatively small bills. Likewise, the prices of shares on an exchange exhibit variability and standard deviation captures that volatility.

Over time, the law department may see in its patterns of volatility a way to better predict its spending in future quarters (See my posts of July 25, 2005; and Nov. 13, 2005 on power law distributions; and Jan. 14, 2007 on correlations and the squares of them to give the explanatory percentage.).

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