The Model That Passed Validation but Fails Stress
A bank uses an internal model to compute market risk capital for its trading book. The model passed annual validation with a 99% one-day VaR of $18M. Backtesting over the last 250 trading days shows 6 exceptions against an expected 2.5 at 99%. A regulator's traffic-light approach places 5 or more exceptions in the yellow-to-red zone, triggering a capital multiplier add-on. Separately, a stress test using 2008-like correlations produces a loss of $95M, far above the VaR figure. The model's assumptions include normal distributions and stable historical correlations, and the trading book has grown 40% in complex credit-sensitive positions over the year. The head of trading argues the exceptions are 'bad luck' and the model is validated.
1. Interpret the backtesting result and assess the model's validity.
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At 99% one-day VaR over 250 days, the expected number of exceptions is 2.5. Observing 6 is more than double the expectation and falls in the regulatory yellow/red zone, which under a traffic-light framework triggers an increase in the capital multiplier (often from 3 to 3.5 or higher depending on the zone). The probability of 6 or more exceptions when the true rate is 1% is small, so 'bad luck' is not a persuasive explanation, especially with the clustering and the 40% growth in complex positions.
The deeper issue is model validity. Normal-distribution and stable-correlation assumptions understate tail risk and correlation breakdown, which is exactly what the $95M stress loss reveals - more than five times the VaR. The model is not 'wrong' in the sense of failing validation arithmetic, but it is mis-specified for the current portfolio. The correct judgement is that backtesting exceptions plus a large stress-to-VaR gap are evidence the model understates risk, and capital should be adjusted upward via the multiplier add-on and possibly a stressed-VaR or add-on charge until the model is recalibrated.
2. What should risk management do before the next reporting date?
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First, escalate the backtesting result and the stress gap to the model risk committee and the regulator as required; do not let the trading head's framing delay action. Second, apply the traffic-light multiplier add-on to capital immediately and consider a temporary add-on reflecting the stress loss, since regulatory capital based on the understated VaR is inadequate. Third, investigate the exceptions: identify which positions and risk factors drove them, and whether they cluster around the credit-sensitive additions. Fourth, recalibrate or replace the model - introduce fat-tailed distributions, stressed correlations, and a stressed-VaR measure alongside the normal VaR. Fifth, impose position limits or reduce the complex credit-sensitive exposure until the model is fit for purpose. Sixth, document the remediation plan and timeline for the regulator.
The exam judgement is that passing validation is not a permanent certificate; backtesting and stress testing are ongoing challenges to the model, and a large stress-to-VaR gap is a signal to act before losses materialize, not after. The trading head's argument should be met with the quantitative evidence, and the model risk function must retain independence from the front office.