Seven VaR exceptions in a bond trading book
Marlowe Securities is the trading subsidiary of an Australian bank. Its 99% one-day historical simulation VaR is built on 500 days of equally weighted data and averages A$4.2 million. The desk holds A$2.4 billion of government and semi-government bonds, A$300 million of subordinated bank paper and a A$60 million private credit position that is carried at a stale broker mark and is not modelled. Over the 250 business days to 30 June the model recorded seven exceptions, five of them inside a single two-week window in March when the central bank surprised the market; after each of those losses the desk cut risk. Actual P&L is used for backtesting, although a hypothetical clean P&L series is available and currently unused. The CRO must tell APRA whether the model can stay in use for regulatory capital while a replacement is built.
1. Interpret the seven exceptions. What zone is the model in, what are the capital consequences, and why might the count understate the problem?
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Zone classification. Under the Basel backtesting framework for a 99% VaR over 250 days, the zones are 0-4 exceptions green, 5-9 yellow and 10 or more red. Seven exceptions places the model in the yellow zone, and the plus factor applied to the base multiplier of 3.0 is 0.65, giving a multiplier of 3.65 for the capital calculation. Continued use is permitted; the model is not automatically rejected.
Why the count understates the problem
- Clustering. Five of seven exceptions fell in one two-week window. The binomial test behind the traffic light assumes independent exceptions; clustering indicates the model is not merely unlucky but systematically understates risk in a specific regime - a jump in volatility the 500-day equally weighted window had damped out. Supervisors treat correlated exceptions more seriously than the raw number implies.
- Contaminated test. The desk cut risk after each loss, so actual P&L was flattered relative to a static position. That understates the model's failure. The hypothetical (clean) P&L series should be the primary backtest, with actual P&L secondary - the difference between them is itself diagnostic of intraday trading, fees and reserve movements.
- Incomplete capture. A A$60 million private credit position sits outside the model at a stale mark. Its risk is real, unmeasured, and correlated with exactly the kind of credit spread widening that produced the March losses.
- Window length. 500 equally weighted days is slow to respond and gives a single stressed episode the same weight as any quiet day, so the model is both sluggish and insensitive to the tail.
Conclusion: 7 in yellow supports continued use with a capital add-on, but the clustering and the unmodelled position mean the true capital need is higher than the traffic light suggests.
2. Identify the structural weaknesses in the model and set out a remediation sequence.
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Weaknesses and remedies
| Weakness | Consequence | Remedy |
|---|---|---|
| 500-day equally weighted history | Slow response to volatility regime shifts; understates risk after a break | Use a shorter effective window or exponential weighting alongside stressed calibration |
| 1-day horizon applied to illiquid paper | Understates the loss for positions that cannot be exited in a day | Liquidity horizons per FRTB, with higher horizon multipliers for subordinated bank paper and private credit |
| Private credit excluded, stale mark | Unmeasured risk and an artificially low VaR | Bring into scope with a prudent valuation adjustment or model-based proxy until a proper valuation is available |
| Actual P&L backtest | Confounds model error with trading and reserve movements | Switch primary backtest to hypothetical clean P&L |
| VaR only | Silent on tail shape and on liquidity of hedges | Add 97.5% expected shortfall and stressed-period calibration |
Sequence
- Immediate (0-30 days): switch the primary backtest to hypothetical P&L, produce a re-run of the 250-day series against a static model to remove the risk-reduction contamination, and book the 3.65 multiplier. Impose a temporary internal limit reduction on the unmodelled private credit position.
- Short term (1-3 months): independent validation of the model, including cluster analysis and a stress-period recalibration; a documented overlay or capital add-on for the unmodelled exposure.
- Medium term (3-12 months): rebuild on expected shortfall with liquidity horizons and stressed calibration; add P&L attribution to separate risk-theoretical from hypothetical P&L.
- Governance: model risk committee sign-off at each stage, with the board risk committee seeing the validation report, not just the summary.
3. What would you put to APRA, and what interim conservatism would you offer while the replacement model is built?
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Substance of the notification
- State the fact first: 7 exceptions in 250 days, yellow zone, plus factor 0.65 applied, multiplier 3.65. Do not let the supervisor discover the number.
- Present the diagnosis, not just the count: five exceptions clustered in one window, the model's 500-day equally weighted calibration lagged the volatility shift, the actual P&L backtest was contaminated by post-loss de-risking, and a A$60 million private credit position is outside the model at a stale mark.
- Show the evidence you have generated: static re-run of the backtest, hypothetical P&L results, cluster analysis, and the independent validation scope.
- Remediation plan with dates and owners, including interim milestones - not a statement that a new model is coming.
Interim conservatism to offer
- The higher multiplier already applies; add a voluntary capital overlay for the unmodelled private credit exposure until it is in scope.
- Reduce the trading limit on illiquid and subordinated paper until liquidity horizons are implemented.
- Apply a conservative mark or valuation uncertainty reserve to the private credit position.
- Report exceptions and the overlay to APRA monthly, and notify immediately if another cluster occurs.
Framing for the CRO: supervisors distinguish between a bank that has a model failure and reports it with a plan, and a bank that reports it late or minimises it. The clustering is not a defence, but candour plus demonstrable conservatism is what supports continued model approval. The one thing not to do is argue the exceptions away because the desk de-risked after the losses.