Value at Risk (VaR) Backtesting Techniques and P-Value Risk Decomposition Analysis

This paper presents a methodology to analyze the Value at Risk (VaR) backtesting probability values to detect the soundness of the VaR model, the integrity of the VaR input and output as well as providing information about the type of the risk that a subportfolio is exposed to in every trading day. The paper presets statistical methods to back test the number of VaR breaches when there is no or some autocorrelation in the P&L daily values. It illustrates a method to evaluate the model by backtesting all quintiles. It also presents a methodology to test the integrity of the P&L and consequently the p-values using the run test. Finally a model is presented to decompose the subportfolios' P&L risk into systematic and idiosyncratic risk using a Gaussian Copula model. The risk decomposition can be used to detect any unusual subportfolio exposures to specific risk or detect the unusual rise in the systematic risk across different subportfolios