Value at Risk: A Comparative Analysis

study develops a comparative analysis concerning Value at Risk measure for a portfolio consisting of three stocks traded at Bucharest Stock Exchange. The analysis set out from 1-day, 1% VaR and has been extended in two directions: the volatility models and the distributions which are used when computing VaR. Thus, the historical volatility, the EWMA volatility model, GARCHtype models for the volatility of the stocks and of the portfolio and a dynamic conditional correlation (DCC) model were considered while VaR was computed using, apart from the standard normal distribution, different approaches for taking into account the non-normality of the returns (such as the Cornish-Fisher approximation, the modeling of the empirical distribution of the standardized returns and the Extreme Value Theory approach). The results indicate that using conditional volatility models and distributional tools that account for the non-normality of the returns leads to a better VaR-based risk management. For the considered portfolio VaR computed on the basis of a GARCH (1,1) model for the volatility of the portfolio returns where the standardized returns are modeled using the generalized hyperbolic distribution seems to be the best compromise between precision, capital coverage levels and the required amount of calculations. Moreover, the Expected Shortfall risk measure offers very good precision results in all approaches, but at the cost of rather high capital coverage levels.