## 26 junho 2015

### Lei de Benford, demonstrações financeiras e desempenho

Deutsche Bank is recommending a pretty simple math trick that can give you at least an indication whether something is up, even if it doesn't tell you precisely what's wrong. It all rests around Benford's Law, also known as the law of natural numbers. Named after physicist Frank Benford, the law says that in a set of data gathered from real life, such as stock prices, birth rates, and electricity bills, the number "one" will appear most frequently as the first digit of numbers — for example 12, 145, or 1,012. Numbers starting with two to nine then occur much less frequently, getting less common the higher you get.

To give an example, if I took 20 stock prices at random, Benford's Law says about 30%, or six, would begin with the digit one — 110 pence, 134 pence, and 154 pence let's say. The frequency of numbers beginning with digits two, three, four, and so on would decline in probability until we reach nine, the first digit in less than 5% of numbers in real-life data sets.

Whatever is behind the law, Deutsche Bank thinks it can be used to spot companies to steer clear of. In a note sent out Thursday the bank says the law applies equally well to balance sheets and income statements as it does other data sets. Deutsche is by no means the first to suggest this.
If the figures deviate from the law — one is the first digit in 60% of numbers or all digits are equally frequent, say — this "may signal accounting irregularities."
Even if the numbers aren't dodgy, Deutsche Bank's analysis says companies that don't adhere to the law tend to underperform the market anyway, so it's still best to steer clear of them.

Outros estudos sobre o mesmo tema podem ser encontrados aqui