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.

股票投资组合的风险管理是财务分析的一个基本问题，因为它表明了任何给定时间投资的潜在损失。本研究的目的是使用双变量静态条件联结来量化依赖结构并估计风险度量的风险价值 (VaR)。选择在巴西证券交易所表现出色的股票组成配对交易组合（B3、Gerdau、Magazine Luiza 和 Petrobras）。由于该方法在构建金融中的多元分布和风险聚合方面提供了灵活性，我们使用了带有正态分布的 copula-APARCH 方法，T-student 和 Joe-Clayton copula 函数。在大多数情况下，结果显示出极端的依赖模式。此外，copula 形式似乎与 VaR 估计无关，因为在大多数投资组合中，适当的 copula 会导致显着的 VaR 估计。它发现拟合的最佳模型提供了保守的风险度量，估计为 5% 和 1%，在更激进的情况下。