Analysis of shares frequency components on daily value-at-risk in emerging and developed markets

Abstract

Value-at-Risk was estimated using the technique of wavelet decomposition with the goal to analyze the frequency components’ impacts on variances of daily stock returns, and VaR forecasts. Daily returns of twenty-one shares of the Ibovespa and daily returns of twenty-two shares of the DJIA were used. The FIGARCH(1,d,1) model was applied to the reconstructed returns to model and establish the prediction of conditional variance, applying the rolling window technique. The Value-at-Risk was then estimated, and the results showed that the DJIA shares showed more efficient market behavior than those of Ibovespa. The differences in behavior induce to affirm that VaRs, used in the analysis of financial assets from different markets with different governance premises, should be estimated by series of returns reconstructed by aggregations of components of different frequencies. A set of back-testing was applied to confront the estimated VaRs, which demonstrated that the estimations of VaRs models are consistent.