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Backtesting VaR models: Quantitative and Qualitative Tests
Carlos Blanco and Maksim Oks
This is the first article in a two-part series analyzing the accuracy of risk measurement models. In this first article, we will present an overview of backtesting methods and point out the importance of conducting regular backtests on the risk models being used. In the second article, we will present an alternative to measuring VaR using a top-down or “macro” approach as a complementary tool to traditional risk methodologies.
Should risk models be accurate?
Firms that use VaR as a risk disclosure or risk management tool are facing growing pressure from internal and external parties such as senior management, regulators, auditors, investors,*…show more content…*

It is always better to be approximately right than exactly wrong. Determining the accuracy of VaR models How can we assess the accuracy and performance of a VaR model? To answer this question, we first need to define what we mean by “accuracy.” By accuracy, we could mean: - How well does the model measure a particular percentile of or the entire profit-and-loss distribution? - How well does the model predict the size and frequency of losses? Many standard backtests of VaR models compare the actual portfolio losses for a given horizon vs. the estimated VaR numbers. In its simplest form, the backtesting procedure consists of calculating the number or percentage of times that the actual portfolio returns fall outside the VaR estimate, and comparing that number to the confidence level used. For example, if the confidence level were 95%, we would expect portfolio returns to exceed the VaR numbers on about 5% of the days. Backtesting can be as much an art as a science. It is important to incorporate rigorous statistical tests with other visual and qualitative ones. Simple Backtesting: VaR

It is always better to be approximately right than exactly wrong. Determining the accuracy of VaR models How can we assess the accuracy and performance of a VaR model? To answer this question, we first need to define what we mean by “accuracy.” By accuracy, we could mean: - How well does the model measure a particular percentile of or the entire profit-and-loss distribution? - How well does the model predict the size and frequency of losses? Many standard backtests of VaR models compare the actual portfolio losses for a given horizon vs. the estimated VaR numbers. In its simplest form, the backtesting procedure consists of calculating the number or percentage of times that the actual portfolio returns fall outside the VaR estimate, and comparing that number to the confidence level used. For example, if the confidence level were 95%, we would expect portfolio returns to exceed the VaR numbers on about 5% of the days. Backtesting can be as much an art as a science. It is important to incorporate rigorous statistical tests with other visual and qualitative ones. Simple Backtesting: VaR

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