VALUE AT RISK na gestão de risco dos índices setoriais da bolsa de valores brasileira

Abstract

This study proposes to find the Value at Risk (VaR) model with a satisfactory result in the validation test, based on a database composed of the daily nominal net returns of seven sectorial indexes of the Brazilian stock market. They are the Consumption Index (ICON), the Electric Energy Index (IEE), the Financial Index (IFNC), the Basic Materials Index (IMAT), the Real State Index (IMOB), the Industrial Sector Index (INDX) and the Public Utility Index (UTIL). Four types of VaR were estimated, covering the first and second statistical moments (mean and standard deviation) under conditions called unconditional (fixed over time) and conditional (variable over time). Another aspect considered in estimating these models concerns the probability distribution of the series of returns. Gaussian and non-Gaussian models were estimated, the latter represented by theoretical probability distributions that showed a good fit for the data. Thus, the four models are: Unconditional Gaussian VaR, Conditional Gaussian VaR, Unconditional Best Fitting VaR and Conditional Best Fitting VaR The effectiveness of the VaR values was measured by means of a violations test, which i. disapproved the Unconditional Gaussian VaR models at 99% confidence for all studied indexes, however approving them at 95% confidence; ii. Disapproved the Unconditional Best Fitting VaR models at 99% confidence for the IEE, IMAT, IMOB and UTIL indexes; however approving them for all indexes at 95% and iii. approved all indexes in the conditional models, both Gaussian and Best Fitting, in both confidence intervals.