VaR Backtesting Exceptions and a New Product Nobody Modelled
Meridian Markets, the trading subsidiary of a $40bn bank, reports 99% one-day VaR of $4.8m on a $2.3bn fixed-income portfolio. The model uses equally weighted historical simulation over a 500-day window. Backtesting over the last 250 trading days shows seven losses exceeding VaR, against an expected 2.5. The exceptions cluster in two periods: the March rate shock and a September spread widening. Separately, the desk has added $150m of inflation-linked bonds whose risk is mapped to nominal government bonds because the inflation factor has less than 250 days of history. The desk hedges mortgage-backed securities with 10-year Treasury futures and reports residual basis risk of $0.6m per 10bp. Model validation last reviewed the model 26 months ago, and the VaR limit is $5.0m. The head of trading says seven exceptions in 250 days is 'within noise' and notes that the model passed last year.
1. Test whether seven exceptions in 250 days is acceptable at the 99% level. What does the clustering tell you?
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At 99% one-day VaR over 250 days, the expected number of exceptions is 2.5. Seven is nearly three times that. Under a binomial or Poisson approximation, the probability of observing seven or more exceptions when the true rate is 1% is about 1.4%. A standard Kupiec test therefore rejects the null hypothesis of correct coverage at the 5% level. Under a Basel-style traffic-light approach, seven exceptions fall in the yellow zone, which requires investigation and generally a capital multiplier add-on rather than automatic model rejection.
The clustering matters as much as the count. Kupiec assumes independent exceptions; here they arrive in two bursts, which suggests the model is slow to react to volatility regime changes. A Christoffersen independence test would likely reject as well. Clustering also means the bank's worst losses are occurring together, which is exactly when liquidity and capital are most strained. The head of trading's 'within noise' claim is wrong: seven is outside normal sampling variation and the pattern indicates model misspecification, not bad luck.
2. Assess the model weaknesses created by the inflation-linked position, the MBS hedge, and the model's calibration window.
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The inflation-linked position is mapped to nominal government bonds because the inflation factor lacks history. That mapping ignores real-rate risk and breakeven inflation risk. A rise in real yields or a fall in inflation expectations can produce losses that the nominal mapping does not capture. The position is $150m, which is material relative to a $2.3bn portfolio and a $4.8m VaR.
The MBS hedge uses 10-year Treasury futures. That hedges the rate component but leaves negative convexity, spread duration, and basis risk. The desk itself reports $0.6m of residual basis risk per 10bp; a 50bp spread widening would produce roughly $3m of unhedged loss, which is large relative to daily VaR.
The 500-day equally weighted window gives stale observations the same weight as recent ones. After a low-volatility period, the model understates current risk. A 26-month gap since validation is too long for a model with new products and a poor backtest. The VaR limit of $5.0m against reported VaR of $4.8m leaves almost no headroom, so any model understatement puts the desk over limit without warning.
3. Recommend immediate and structural actions. Should the bank raise the VaR limit?
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The bank should not simply raise the limit to accommodate a model that is failing backtests. Immediate actions: reduce or hedge the inflation-linked and MBS basis exposures; apply a conservative add-on or overlay to reported VaR until the model is fixed; escalate to the model risk committee and, if required by policy, to the regulator; and set a remediation timetable with named owners.
Structural actions: replace or supplement equally weighted historical simulation with a volatility-weighted or filtered approach; add a real-rate risk factor and an explicit MBS basis factor; introduce expected shortfall and stressed VaR alongside VaR; backtest at desk level as well as firm level; and strengthen P&L attribution so that unexplained P&L is detected early. Independent validation should be repeated within a defined cycle, not left for 26 months.
Temporarily reducing the VaR limit is defensible if the model understates risk, because the limit is calibrated to a model the bank no longer trusts. Any limit change should be approved by risk committee with the model limitations documented. The goal is to make the limit reflect measured risk, not to make the breach disappear.