Backtesting VaR Models: An Expected Shortfall Approach

Academics and practitioners have extensively studied Value-at-Risk (VaR) to propose a unique risk management technique that generates accurate VaR estimations for long and short trading positions and for all types of financial assets. However, they have not succeeded yet as the testing frameworks of the proposals developed, have not been widely accepted. A two-stage backtesting procedure is proposed to select a model that not only forecasts VaR but also predicts the losses beyond VaR. Numerous conditional volatility models that capture the main characteristics of asset returns (asymmetric and leptokurtic unconditional distribution of returns, power transformation and fractional integration of the conditional variance) under four distributional assumptions (normal, GED, Student-t, and skewed Student-t) have been estimated to find the best model for three financial markets, long and short trading positions, and two confidence levels. By following this procedure, the risk manager can significantly reduce the number of competing models that accurately predict both the VaR and the Expected Shortfall (ES) measures.