A return rescaled to a one-year equivalent, which is essential for comparison and routinely abused on short samples.
From a total return over n years: (ending / beginning)^(1/n) - 1. An account going from $30,000 to $52,000 over three years annualises to (52/30)^(1/3) - 1 = 20.1%.
The abuse is in the extrapolation. A 6% month annualised is 101% a year, and quoting it that way implies a repeatability that no month of data supports. Annualising anything shorter than a year is a projection, not a measurement, and annualising a good quarter is the oldest trick in performance marketing. If you must do it, state the period it came from in the same sentence.
Compounding in reverse deserves equal care. A minus 8% month annualises to minus 63.2%, which is equally unrealistic. The honest presentation of short records is the raw period return plus the number of trades behind it - see sample-size-for-edge.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.
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