Estimating portfolio value at risk by a conditional copula approach in BRICS countries

Abstract

Abstract : This thesis used daily log returns of indices of BRICS countries from the period of March 11th 2013 to May 16th 2017. Its main focus was to estimate the value at risk (VaR) of a portfolio of the BRICS financial markets using a conditional copula approach. A useful starting point was to apply the model of AR (1)-GARCH (1,1) with t-distribution and AR (1)-GARCH (1,1), using returns of the normal errors for the marginal distribution models in the copula framework. Two copulas, the normal and the symmetric Joe Clayton (SJC) copulas, were estimated as both constant and time-varying. The log likelihood of the time-varying copula was significantly more suitable than the constant copula. The comparison of the performance of the copula models to the benchmark AR (1)-GARCH (1,1) was done using the Christoffersen test. The 99% VaR appeared fairly accurate, suggesting that the VaR models were dependable. The standard level of comparison AR (1)-GARCH (1,1) did not perform well compared to the SJC copula; i.e. the time-varying SJC copula performed better than the benchmark model. The time-varying SJC copula model used to estimate the portfolio VaR also showed a minimum number of exceptions in the back-test. This copula thus meets regulatory capital requirement for investors as stipulated in Basel II.M.Com. (Financial Economics