The FRTB P&L Attribution Test

The Fundamental Review of the Trading Book (FRTB) is a set of post-2008 regulatory reforms tightening how banks calculate capital for trading risk, and one of its requirements is the P&L attribution test, applied desk by desk. The test compares two P&L figures computed for the same trading desk over the same period: the "risk-theoretical" P&L, which is what the bank's own risk model predicts should have happened given the day's market moves and the desk's risk factor sensitivities, and the "hypothetical" (or actual) P&L, which is what the desk's positions genuinely produced. If a desk's risk model is accurate, these two numbers should track each other closely day after day.

The test formalizes "closely" using two statistics computed over a rolling window: the mean and standard deviation of the difference between the two P&L series (checking they aren't systematically biased or too noisy relative to each other) and a correlation-like measure of how well the two series co-move. A desk whose model fails these thresholds too often is downgraded from using its own internal model for regulatory capital, forcing it onto a standardized, typically far more capital-punitive approach instead, which makes trading materially less economical for that desk.

The test exists because a risk model can look fine in isolation (correctly sized VaR, passing backtests) while still failing to actually explain the desk's day-to-day P&L, meaning the model is missing risk factors or mis-specifying sensitivities that don't show up in a simple VaR exceedance count but do show up when you compare full P&L series directly.