Limiarização de retornos para quantificação de riscos em mercados financeiros

Abstract

In this work is proposed a methodology which quantifies a posteriori the financial risk. Therefore, it was used financial time series of the daily closing prices of 12 representative stock market indices, with daily granularity over 16 years period January 02, 1995 to December 30, 2010. From the series of returns, it was possible to verify the range of market volatility in the time window analyzed, defining a typical fluctuation interval. In these fluctuations both losses and gains exist, the real losses being defined as the return below a certain threshold and the real gains as the returns above this same threshold. Therefore, this threshold can be understood as the market’s cost. In this view, at such a threshold the real losses and the real gains are in equality, that is, the profit is zero and reflects the balance of the process. Thus, risk was defined as the difference between real losses and real gains for a given market cost value. In addition, given the cumulative distributions of real losses and real gains it was developed a functional form for the adjustments of such distributions. Thus, it was possible to calculate the expected risk for market cost intervals.