Statistical methods for decision support systems in finance: how Benford’s law predicts financial risk

Abstract

This paper merges the statistical analysis of data regularities and decision support systems for investors. Specifically, it discusses the Benford’s law as a decision support device for financial investments. In particular, we illustrate the role of such a property of financial data as risk predictor for financial markets. First of all, we show empirical evidence of accordance between data on market index daily returns and Benford’s law. Then, we highlight that on short time period (1 year) the deviations from Benford’s law are related to low risk and positive trend periods; the p value of the $$\chi ^2$$ χ 2 test against the Benford’s distribution displays some predicting power for the market average return and risk level.