Wednesday, July 09, 2008

Benford's Law

Benford's law states that the frequescey of the first digit in a set of numbers obeys a power law, so that for base 10 the odds of getting a "1" in the first digit is about 30%, a 2 about 18%, and decreasing to about 5% for a 9. This has to do with numbers generally having logarithmic distributions (for normally distributed variables, like IQ, you don't see Benford's law).

Anyway, I was reading about how you can apply Benford's law to accounting fraud, because fools who make up numbers will put in equal distributions of numbers starting with 9 vs. those starting with 1. But then I thought, most fraud pertains to a classification issue, such as classifying an expense as an investment, or accelerating income--the numbers are real, just relabeled. Further, someone might take a big number and back into it, but usually by adjusting a handful of numbers. If you are targeting the number X, and you have Y, all you need is one number (X-Y). You can't use Benford's law, which applies to frequencies, to disprove a handful of fudged numbers.

I see there are lots of conferences and books on this, because it's a neat finding, but I can't imagine is has significant practical value.


Michael F. Martin said...

Why do accountants enter adjusting entries?

Because without them a snapshot in time (the balance sheet) or the area under the time-varying curves of revenue and expenses (the income statement) would be inaccurate -- some costs are "incurred" in the sense of contractual obligation either earlier or later than the period of the statement.

But why do we need adjusting entries anymore when we could get the companies to simply post time-series of their cashflows online? All of the information needed for this is in the journal entries.

Tell me why this hasn't been done already.

Eric Falkenstein said...

Hmm. I don't really know. The statement of cash flows comes out after the income statement and balance sheet, so I presume there's some issue with definitions of what counts as an investment or capital issuance that people think is very subjective and important. Thus, people don't want it automated.

Michael F. Martin said...

You're right. You still need to make adjustments, even if you're looking at the whole time-series rather than just snapshots.

But why not show the time series with two colors, one for the cash and one for the adjustments?

Anonymous said...

Conferences on this. Really. Finance is an interesting field.

Anonymous said...

How about this... Use Benford's law to analyze a series of dollar amounts that are purported to be mathematical extensions of weight x price. For example, if you were a scrap metal dealer and were making up the costs of goods sold on weigh tickets that you produced for your accountant to prepare tax returns and you did this thousands of times. Given that every number 1-9 has an equal chance at appearing, a first or first and second number falling markedly outside of the Benford frequency ratio would indicate that the numbers were not truly random, but had been contrived.