Value at Risk Models in the Indian Stock Market

This paper provides empirical tests of different risk management models in the Value at Risk (VaR) framework in the Indian stock market. It is found that the GARCH-GED (Generalised Auto-Regressive Conditional Heteroscedasticity with Generalised Error Distribution residuals) performs exceedingly well at all common risk levels (ranging from 0.25% to 10%). The EWMA (Exponentially Weighted Moving Average) model used in J. P. Morgan’s RiskMetrics® methodology does well at the 10% and 5% risk levels but breaks down at the 1% and lower risk levels. The paper then suggests a way of salvaging the EWMA model by using a larger number of standard deviations to set the VaR limit. For example, the paper suggests using 3 standard deviations for a 1% VaR while the normal distribution indicates 2.58 standard deviations and the GED indicates 2.85 standard deviations. With this modification the EWMA model is shown to work quite well. Given its greater simplicity and ease of interpretation, it may be more convenient in practice to use this model than the more accurate GARCH-GED specification. The paper also provides evidence suggesting that it may be possible to improve the performance of the VaR models by taking into account the price movements in foreign stock markets.