Expected Versus Realised PnL Bands

A backtest doesn't just produce an expected daily return — it also implies how much that return should bounce around from day to day. A strategy with an annualized volatility of 12% is expected to have plenty of days that lose money even while performing exactly as designed; the question in live trading is never "did we make money today" but "did today's outcome fall inside the range the backtest said was normal." Expected-versus-realised bands make that comparison explicit by drawing a confidence band — typically one and two standard deviations around the expected daily return — around the backtested distribution, and then plotting live P&L against it day by day.

A day that lands inside the one-standard-deviation band is unremarkable; that's what "working as designed" looks like most of the time. A day outside two standard deviations is not automatically a problem — markets do produce outliers — but it is a prompt to ask why, especially if it keeps happening. The value of the band is that it turns a vague feeling ("that was a bad week") into a specific, falsifiable check: is the strategy still behaving like the model that was backtested, or has something about its risk profile changed?

A concrete example: a strategy's backtest implies a daily standard deviation of $8,000 around an expected daily P&L of $1,000, so the one-sigma band runs from roughly −$7,000 to $9,000. In live trading, the strategy posts three consecutive days at −$15,000, −$18,000, and −$12,000 — each individually outside the two-sigma band. A single such day might be shrugged off as noise, but three in a row is a strong signal that either the volatility assumption baked into the backtest is stale or the strategy's behavior in the current market regime has genuinely shifted, and it warrants investigation before a fourth day happens.

Bands are most useful when they are watched continuously rather than reviewed only after a bad month, since the whole point is catching a divergence early — while it is still one anomalous week rather than a fully realized drawdown.