Expectancy

A summary statistic computed over a completed sample of trades. The proportion that won is multiplied by the average winning amount, the proportion that lost is multiplied by the average losing amount, and the second is subtracted from the first. The result is one number in money per trade, and its sign is the point of the exercise: a rule can win most of the time and still produce a negative figure if the losses are large enough, and win rarely and still produce a positive one.

It is a description of a sample, not a property of a method. The figure inherits every characteristic of the trades it was computed from: the period they cover, the instruments, the position sizes and whether costs were deducted. Commission, spread and financing move a computed expectancy directly, and a figure calculated before costs is not comparable with one calculated after them. Practitioners also disagree about the unit: some compute it in money, others in multiples of the amount risked on each trade, which makes samples of different position sizes comparable but hides how much money the rule actually produced.

The reliable error is treating it as a forecast. A positive average over a sample says nothing about the next trade and nothing about the order in which results arrive, and a run of losses long enough to be uncomfortable is consistent with a positive average. Sample size is the usual weakness, since a handful of trades produces a figure that a single outlier dominates. And a figure computed on a backtest carries whatever assumptions the test made about fills, which is why backtested and realised expectancy are reported separately.