Why does my risk limit miss disasters?
A 99% limit says a loss this big should happen on one day in a hundred. This lesson asks whether a limit was honest, and what the evidence can and cannot tell you about it. Every number is synthetic, and every chart states its units.
Model contract
- Objective
- A one-day 99% loss limit, fitted on a calibration window and then frozen.
- Observed
- The calibration days, the frozen limit, and the evaluation days once they are read.
- Hidden
- Which process generated the days. Revealed only at stage 5.
- Assumptions
- Days are independent once the process is fixed. The limit is not refitted during evaluation.
- Parameters
- Mean and volatility are estimated from calibration. Confidence is chosen, not estimated.
- Units
- Loss in % of portfolio per day. Positive is a loss. Horizon: one trading day.
- Benchmark
- A correct limit for the scenario, which the count is compared against.
- Failure
- A breach count outside the 95% range of a correct limit, sustained across fresh days.
1. Predict before you look
Your 99% limit was fitted on 250 quiet days and is now frozen. Over the next 1,000 trading days, how many breaches do you expect if the model is right?
Synthetic iid scenarios only. Nothing here is historical market data, and a result on these processes does not establish that a limit would have worked on a real book.