Measuring Traded Market Risk: Value-at-risk and Backtesting Techniques

The proposed market-risk capital-adequacy framework, to be implemented at the end of 1997, requires Australian banks to hold capital against market risk. A fundamental component of this framework is the opportunity for banks to use their value-at-risk (VaR) models as the basis of the market-risk capital charge. Value-at-risk measures the potential loss on a portfolio for a specified level of confidence if adverse movements in market prices were to occur. This paper examines the VaR measure and some of the techniques available for assessing the performance of a VaR model. The first section of the paper uses a simple portfolio of two spot foreign exchange positions to illustrate three of the approaches used in the calculation of a VaR measure: variance-covariance, historical simulation and Monte-Carlo simulation. It is concluded that, although VaR is a very useful tool, it is not without its shortcomings and so should be supplemented with other risk-management techniques. The second section of the paper focuses on the use of backtesting – the comparison of model-generated VaR numbers with actual profits and losses z– for assessing the accuracy of a VaR model. Several statistical tests are demonstrated by testing daily VaR and profit and loss data obtained from an Australian bank. The paper concludes that, although the tests are not sufficiently precise to form the basis of regulatory treatment of banks’ VaR results, the tests do provide useful diagnostic information for evaluating model performance.