Risk analysis in the brazilian stock market: copula-APARCH modeling for value-at-risk

Risk management of stock portfolios is a fundamental problem for the financial analysis since it indicates the potential losses of an investment at any given time. The objective of this study is to use bivariate static conditional copulas to quantify the dependence structure and to estimate the risk measure Value-at-Risk (VaR). There were selected stocks that have been performing outstandingly on the Brazilian Stock Exchange to compose pairs trading portfolios (B3, Gerdau, Magazine Luiza, and Petrobras). Due to the flexibility that this methodology offers in the construction of multivariate distributions and risk aggregation in finance, we used the copula-APARCH approach with the Normal, T-student, and Joe-Clayton copula functions. In most scenarios, the results showed a pattern of dependence at the extremes. Moreover, the copula form seems not to be relevant for VaR estimation, since in most portfolios the appropriate copulas lead to significant VaR estimates. It has found that the best models fitted provided conservative risk measures, estimates at 5% and 1%, in a scenario more aggressive.