Tail Risk

The backtest proposed in this section is of complementary nature with the Basel mandated counting test. Our goal is to somehow quantify how extreme each VaR violation is in relation to its forecast distribution. The approach can be intuitively described as an extension of the “hit” time series concept, wherein each of the “1” values are modified so as to measure the distance between each violation and its corresponding VaR threshold.

This involves placing each VaR violation within its corresponding forecast distribution to obtain its location within the forecast distribution to obtain the corresponding PIT value (p-value). However, an additional exponential transform is performed. The resulting “hit” value is the difference between this exponentially transformed percentile value and the exponentially transformed VaR threshold percentile value.

When the counting test indicates a result in the “yellow” zone for a portfolio (five to nine VaR violations) we propose to use the tail risk backtest to indicate if the hypothesized model does account for the tail risk of the underlying portfolio over the sample period. The tail risk backtest helps to place the results of the simple Basel II mandated counting scheme into a more balanced and complete context.

The tail risk backtest is able to provide risk management with a better level of feedback about their portfolio behavior, and is also able to guide them in the identification of both type I and type II errors stemming from the counting test.

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