Bubble Value at Risk: A Countercyclical Risk Management Approach, Revised Edition

Chapter 15

Acceptance Tests

The VaR models used in banks usually undergo the strict statistical tests found in Chapter 8. These goodness of model tests are a regulatory requirement. Passing all these tests proves that a bank’s value at risk (VaR) distribution is independent and identically distributed (i.i.d.) and hence the quantile estimate is not biased or understated. Under these peacetime conditions, the VaR model is a consistent metric. The great irony is that a risk manager should be more concerned about extreme conditions, which threaten the bank’s survival. But these are the exact conditions under which such statistical tests would fail.

Unsurprisingly, buVaR will fail these tests even under benign conditions since, by design, this metric is non-i.i.d. (its day-to-day distribution is conditional on the cycle). For example, one can apply standard statistical tests on the (inflated) buVaR return time series and show that it is not i.i.d. Without the convenience of i.i.d., we will need to rely on other less consistent (and less precise) tests. We will test the effectiveness of buVaR by assessing its historical performance covering major financial assets and indices, over a long history and over specific stressful episodes.

15.1 BuVaR VISUAL CHECKS

Our test is similar to the way a trader would test a trading system—it is subjective, performance-based, and not based on strict hypothesis testing. First, and perhaps most importantly, we check visually to ensure that buVaR is generally ...