Reconciling P&L With What Risk Predicted

Before the market opens, your risk model gives you a number: given today's positions and the covariance matrix it's using, the book's daily P&L should have a standard deviation of roughly $400,000. That number is a forecast. At the close, you have an actual outcome. Reconciling the two — did the actual P&L look like a draw from that predicted distribution, or not — is the single best check on whether you should trust the risk model tomorrow.

Most desks skip this because it feels like busywork when the sign is right: you predicted risk, you made money, good day. But a model that predicts $400k of daily volatility and then routinely produces $900k swings isn't a good model that got lucky — it's underestimating risk, and it will eventually be wrong on the side that costs you your job.

The basic check

Every day, compute the standardized P&L:

$$z = \frac{\text{PnL}_{\text{actual}}}{\sigma_{\text{predicted}}}$$

In words: divide today's actual profit or loss by the risk model's predicted daily standard deviation for the book. If the model is well calibrated, $z$ should behave like a draw from something close to a standard normal — most days between $-2$ and $+2$, only rare days beyond $\pm 3$.

Worked example

The model predicts $\sigma = 400{,}000$ for Thursday. The book actually loses $950,000. That's $z = -950{,}000 / 400{,}000 = -2.375$ — a two-and-a-half sigma day. On its own, unremarkable; two-and-a-half sigma days happen more often than a normal distribution says they should, because real returns have fat tails.

The useful step is logging every $z$ for a quarter and looking at the distribution. If you see six days beyond $\pm 3\sigma$ in sixty trading days, when a well-calibrated model should give you roughly zero, the model is too tight — probably because the covariance matrix hasn't picked up correlations that only show up in stress, like two supposedly uncorrelated names both being long the same crowded factor.

What you do with the finding

If actual P&L is consistently narrower than predicted, the model is too conservative and you're probably under-risked relative to what you're being paid for — a case for taking more size, not less. If it's consistently wider, before you touch position size, look at whether the risk model is missing a specific driver: a correlation that spikes only under stress, a position whose volatility is stale, or a factor exposure the model doesn't even carry as a factor. Reconciliation tells you the model is wrong; chasing the individual bad days tells you why.