VaR Backtesting Failure at a Korean Bank Trading Book
A Korean commercial bank's trading book uses a 1-day 99% historical simulation VaR model. Over the most recent 250 trading days, the model produced 14 exceptions. The bank's risk committee reviews the Basel traffic-light test: at 99% with 250 observations, 0-4 exceptions is green, 5-9 is yellow, and 10 or more is red. The market risk head proposes two fixes: recalibrate the model to a 99.9% confidence level so that fewer exceptions occur, and shorten the historical window from two years to 60 days to make the model more responsive. The front office argues the exceptions are caused by 'unusually volatile markets' and should be excluded from the backtest. The bank also reports standalone VaR of KRW 3.0 billion for the rates desk and KRW 4.0 billion for the credit desk, but total VaR of KRW 5.5 billion.
1. Compute the exception rate, classify the backtest result, and assess whether the model should be considered invalid.
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Exception rate = 14/250 = 5.6%. At 99% the expected number is 2.5, and the probability of 14 or more exceptions is very low under a correct model. Under the Basel traffic-light approach, 10 or more exceptions in 250 days is the red zone, so this is a red-zone result, not a borderline yellow. Red does not mathematically prove the model is invalid, but it is presumptive evidence of a problem and triggers supervisory attention, a higher capital multiplier, and model validation. The bank should investigate whether the exceptions are clustered, whether P&L is clean or dirty, whether the historical window missed a volatility regime, and whether the model captures nonlinear positions. It should not continue using the model for capital without remediation. The front office's 'unusually volatile markets' explanation may be partly true, but exceptions in volatile periods are exactly what a risk model should capture; that argument does not cure the backtest failure.
2. Critique the two proposed fixes and the front office's request to exclude volatile days.
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Raising the confidence level to 99.9% changes the test, not the model; it would mechanically reduce the exception count and make the backtest non-comparable. A 99.9% one-day VaR needs a much larger sample to backtest meaningfully, and the bank would still need a 99% test. Shortening the window to 60 days may make the model more responsive, but it also makes the 99% quantile noisy and can increase exceptions if volatility clusters; it is not a substitute for fixing the distribution or P&L. Excluding volatile days is data snooping and violates the purpose of backtesting; all realized P&L must be included, with clean P&L adjustments documented. A better response is to use expected shortfall, stressed VaR, volatility-weighted historical simulation, and a validated P&L attribution. The committee should reject both fixes as presented and require a model validation plan.
3. Explain the diversification benefit and how component VaR would be used to allocate the KRW 5.5 billion total VaR across the two desks.
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Standalone VaRs sum to KRW 7.0bn, but total VaR is KRW 5.5bn, so the diversification benefit is KRW 1.5bn, or 21.4% of the sum. The benefit arises because rates and credit positions are not perfectly correlated; in stress, correlations can rise and the benefit can shrink. Component VaR allocates the total by each desk's marginal contribution: CVaR_i = (marginal VaR_i) x (position_i), and the components sum to total VaR. It is not the same as standalone VaR. The rates desk should not be allocated its full KRW 3.0bn if its marginal contribution is lower; the allocation should reflect covariance. Use Euler allocation with the same model and report both standalone and component VaR. For limit-setting, component VaR is fairer, but stress tests should assume reduced diversification.