Fluctuations of company yearly profits versus scaled revenue: Extreme events and fat tail distributions

Eduardo Roman and Riccardo A. Siliprandi

UniversitÓ degli Studi di Milano-Bicocca, Dipartimento di Fisica "G. Occhialini", Milano, Italy

Authors: H.E. Roman, R.A. Siliprandi, C. Riccardi C. Dose and M. Porto

Annual revenues and earnings data are analized for the 500 largest-revenue US companies during the period 1954-2007. Mean year profits are found to be proportional to mean year revenues, exception made for few anomalous years (1991/92/93 and 2001/02), from which a linear relation between company expected mean profit and revenue is postulated. Mean annual revenues are used to scale both company profits and revenues. Annual profit fluctuations are obtained as difference between actual annual profit and its expected mean value, scaled by a power of the revenue in order to get a stationary behavior as a function of revenue. Profit fluctuations are found to be broadly distributed having approximate power-law tails with a Levy-type exponent alpha=1.7. The temporal evolution of profit fluctuations for single companies are obtained from which the associated autocorrelations can be calculated. An attempt is made to identify extreme events by distinguishing profit fluctuations over the `typical' years from those within the above mentioned anomalous years