Aplicação da Metodologia de Componentes Principais na Análise da Estrutura a Termo de Taxa de Juros Brasileira e no Cálculo de Valor em Risco

The identification of the main factors affecting interest rate securities has been researchedby several academics and financial practitioners. This work applies an importanttechnique of factor decomposition, named Principal Component Analysis (PCA), intwo brazilian interest rate derivatives: DI Futuro and SWAP DI x Pré. Its objective isto identify the main attributes that govern changes in returns, giving subsidies to theimprovement of the assessment of the risk associated with such type of investment.Like previous studies, three principal components were responsible for more than95% of the variance of the original data. They were respectively associated withchanges in level, inclination and curvature of the brazilian interest rate term structure.Based on the previous results, the one-day Value-at-Risk (VaR), with significancelevels of 95%, 97.5% and 99%, were calculated using PCA in conjunction with MonteCarlo Simulation. For the purpose of comparing this method with the most famousone, named Riskmetrics, the confidence intervals defined by Kupiec (1995) wereused. Besides, a general performance measure was applied which showed close values,although PCA was slightly better. However, due to the high variance of this measure, wecame to the conclusion that no unambiguous conclusions have been identified. Theresults were very sensitive to the size of the test window what makes it necessary toapply further researches in the subject.