Module 8 · Advanced
Backtesting the margin model
A margin model is a forecast, and forecasts get audited. At a prime broker, margin backtesting asks one question, client by client: on how many days did the realized P&L move exceed the margin we held? Each such day is an exception — a day the buffer would have been fully consumed if the client had defaulted.
This is structurally identical to VaR backtesting (covered on the VaR backtesting page):
- Exception counting — a 99% model over 250 trading days should produce about 2.5 exceptions. Far more means the model under-margins; far fewer means it over-margins (which costs clients and business).
- Kupiec's proportion-of-failures test — a likelihood-ratio test of whether the observed exception count is statistically consistent with the promised coverage.
- Christoffersen's independence test — are exceptions arriving independently, or in clusters? Five exceptions in one crisis week is far worse than five spread over a year: clustering says the model fails to adapt exactly when it matters.
- Traffic-light zones — the Basel convention: green (0–4 exceptions per 250 days), yellow (5–9, add-on multiplier and model review), red (10+, model rejected).
🎛 Exception counter
One year of client P&L vs the margin you held
Amber dashed line = margin held. Red bars are exceptions — days the realized loss ate through the entire margin.
Exceptions / 250d
1
Expected if model right
2.5
Traffic light
green
Green zone — model accepted
Margin backtesting is structurally identical to VaR backtesting: count the days realized losses exceeded the margin held, and compare against what the model promised (2.33σ ≈ 99% → about 2.5 exceptions a year). Kupiec's proportion-of-failures test formalizes “too many exceptions”; Christoffersen adds “are they clustered?” — exceptions that arrive back-to-back in a crisis are far worse than the same count spread out. Turn fat tails on at 2.33σ: the Gaussian promise breaks precisely when it matters. Educational tool — not investment advice.
Things to try
- • Hold 2.33σ in the Gaussian world and resample a few years — mostly green, occasionally yellow. That's honest sampling noise, and why the yellow zone exists.
- • Turn fat tails on at the same 2.33σ: exceptions multiply, and they cluster. The model's promise broke, not your luck.
- • Now raise margin until fat-tailed exceptions go green again — note how much extra σ the tails cost. That premium is what the gap-risk add-on (Module 4) was charging for all along.
Test yourself
Two margin models both show exactly 5 exceptions last year. Model A's exceptions were spread across four months; Model B's all fell in one week in March. Which model do you trust less, which test formalizes that intuition, and what does the answer imply for a 24/7 crypto book where crises don't wait for the close?
End of the track
You've now seen the full arc: the default-and-liquidate question, the scenario grids that answer it, the add-ons that patch the grids' blind spots, the correlation traps in cross-margining, what digital assets break, how the engine is built, and how the model is audited. The natural next stops are VaR & expected shortfall, ISDA SIMM and repo & secured funding in the Fixed Income track.