Checking financial markets via Benford's law: The S&P 5000 case

In general, in a given financial market, the probability distribution of the first significant digit of the prices/returns of the assets listed therein follows Benford’s law, but does not necessarily follow this distribution in case of anomalous events. In this paper we investigate the empirical probability distribution of the first significant digit of S&P 500’s stock quotations. The analysis proceeds along three steps. First, we consider the overall probability distribution during the investigation period, obtaining as result that it essentially follows Benford’s law, i.e., that the market has ordinarily worked. Second, we study the day-by-day \ud probability distributions. We observe that the majority of such distributions follow Benford’s law and that the non-Benford days are generally associated to events such as the Wall Street crash on February 27, 2007. Finally, we take into account the sequences of consecutive non-Benford days, and find that, generally, they are rather short