Telling P&L Noise From P&L Signal

A book with $1.2m of predicted daily volatility loses $700,000 on Tuesday, makes $900,000 on Wednesday, and loses $300,000 on Thursday. None of those three days, taken alone, means the strategy has stopped working — that's ordinary noise for a book with that much volatility, the kind of swing you'd expect several times a month by chance alone. But a trader who reacts to each daily number as if it were news will end up doing something on Tuesday, undoing it on Wednesday, and being confused on Thursday, having generated nothing but trading costs.

What "normal" looks like

Every book has a predicted daily volatility from the risk model — how much the P&L should typically move, day to day, given the positions held and their historical co-movement. A day's move sitting inside that predicted range is not information about the strategy; it is the strategy doing exactly what a strategy with that much risk is expected to do on a random day. The wobble is priced in before you ever look at the screen.

Signal is different. Signal is a P&L pattern that would be unlikely to occur if nothing had actually changed about the strategy, the market regime, or the positions — a string of days consistently on one side of predicted vol, a single day many multiples outside it, or a pattern that lines up with a specific, identifiable cause (a factor everyone is suddenly crowded into, a name where your edge just got arbitraged away).

Three questions before reacting to a run of P&L

Is the magnitude actually unusual, or does it just feel unusual? A losing day that's within one standard deviation of predicted vol is not unusual no matter how it feels sitting through it.

Is there a run, or is this one data point? Three losing days in a row on a book that loses money roughly 40 percent of days individually is not automatically a "run" in the statistical sense — check whether that sequence is more common than intuition suggests before treating it as a break.

Does the loss have an identifiable cause that maps to something changing, or is it diffuse across many uncorrelated positions? A loss concentrated in one factor bet that used to work is a candidate for signal. A loss spread thinly and randomly across forty positions, none individually notable, looks more like noise finding its way through a large book.

Worked contrast

Book A: predicted daily vol $1m, standard deviation of realized P&L over the last sixty days has actually been about $1.1m — close to the model's prediction. A -$1.4m day is roughly 1.3 standard deviations out. Unremarkable; file it and move on.

Book B: predicted daily vol $1m, but the last twelve trading days have all been negative, averaging -$180,000 each, and seven of those losses concentrate in the same value-factor bet. No single day looks alarming against the vol prediction, but the run itself — twelve losing days out of twelve, all pointing the same direction — is now the signal. The question isn't "was today a bad day" anymore; it's "has this factor stopped working," and that's a strategy-level review, not a daily-P&L one.

Why intuition is bad at this specific judgment

Human pattern recognition is tuned to spot runs and streaks as meaningful even when they're statistically unremarkable — three losing days in a row feels like a story is unfolding, because that's how the brain is built to process sequences. A book that loses money on 40 percent of days will, over a normal year, produce several three-day losing streaks purely by chance, with no change in the underlying strategy at all. This is exactly why the daily review needs the risk-model comparison as an anchor rather than relying on the feel of a run — the model doesn't get anxious watching three red days and doesn't get complacent watching three green ones, which is precisely the discipline a human reviewer has to import deliberately.

Setting the threshold in advance

The most useful version of this discipline is deciding, before a run of bad days ever happens, what would actually count as signal — for instance, "three consecutive days each individually outside one standard deviation of predicted vol, all on the same side" — and writing that threshold down. Deciding the threshold in the calm of a quiet week, rather than in the middle of a stretch that already feels alarming, is what keeps the review honest instead of being reverse-engineered to justify whatever action already feels tempting that day.