An Empirical Study on Value-at-Risk and Backtesting VaR Models

In a risky financial environment, investors gradually realise the danger of potential risk and the importance of risk management. The theory of Value-at-Risk (VaR) has become popular along with the establishment of risk management system in the field of finance. This paper will start with introducing different types of risks existing in today’s market, which in general term can be categorised into business risk and financial risk. The latter is where VaR falls and what financial analysts try to minimise by performing VaR analysis. The concept of VaR and its measurement were explained in great detail. Three popular and representative approaches in estimating VaR, the Historical Simulation approach, Moving Average approach and GARCH approach, were introduced and applied as an empirical study. To test the accuracy of the VaR estimates, conditional and unconditional backtesting methods were established. At pre-determined level of confidence, models that produce reasonable and accurate results were accepted, while those failed to perform were rejected. Historical stock prices for ten major indices during January 2004 and December 2013 were obtained to calculate VaR forecasts and backtested to evaluate the accuracy of the models. The backtesting result shows that the forecasts at 99% level of confidence under all three approaches underestimate the risk, thereby allowing too many VaR breaks throughout the years. At 95% level of confidence, all three models performed better compared with themselves at 99%. However, Moving Average approach performed better than the Historical Simulation approach, while GARCH approach outperformed both of them and is a preferred choice according to our research