{"title":"How Many Losing Months Are Normal for a Trading Strategy?","published":"2026-09-17","measure":"Probability of at least one run of consecutive negative monthly excess returns","method":"Monthly loss probability q = Φ(-S / sqrt(12)); exact finite-state recurrence for run probability.","assumptions":{"returnProcess":"Independent, Normally distributed monthly arithmetic excess returns","sharpeRatio":"Known true annualized Sharpe ratio","benchmark":"Risk-free rate"},"monthlyLossProbabilities":[{"annualizedSharpe":0.5,"probabilityNegativeMonthlyExcessReturn":0.442616957237},{"annualizedSharpe":1.0,"probabilityNegativeMonthlyExcessReturn":0.386414996342},{"annualizedSharpe":1.5,"probabilityNegativeMonthlyExcessReturn":0.332502771051},{"annualizedSharpe":2.0,"probabilityNegativeMonthlyExcessReturn":0.281851430825}],"streakProbabilityGrid":[{"annualizedSharpe":0.5,"years":1,"months":12,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.842784451444},{"annualizedSharpe":0.5,"years":1,"months":12,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.462238223576},{"annualizedSharpe":0.5,"years":1,"months":12,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.203492219451},{"annualizedSharpe":0.5,"years":1,"months":12,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.032665395722},{"annualizedSharpe":0.5,"years":3,"months":36,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.996974166248},{"annualizedSharpe":0.5,"years":3,"months":36,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.871103877984},{"annualizedSharpe":0.5,"years":3,"months":36,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.550221066832},{"annualizedSharpe":0.5,"years":3,"months":36,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.127726205265},{"annualizedSharpe":0.5,"years":5,"months":60,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999941763603},{"annualizedSharpe":0.5,"years":5,"months":60,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.969104917652},{"annualizedSharpe":0.5,"years":5,"months":60,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.746015358212},{"annualizedSharpe":0.5,"years":5,"months":60,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.213446599953},{"annualizedSharpe":0.5,"years":10,"months":120,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999999997007},{"annualizedSharpe":0.5,"years":10,"months":120,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.999131013316},{"annualizedSharpe":0.5,"years":10,"months":120,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.939140508257},{"annualizedSharpe":0.5,"years":10,"months":120,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.392681261749},{"annualizedSharpe":1.0,"years":1,"months":12,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.754680592785},{"annualizedSharpe":1.0,"years":1,"months":12,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.345527651052},{"annualizedSharpe":1.0,"years":1,"months":12,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.129393676773},{"annualizedSharpe":1.0,"years":1,"months":12,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.015585107163},{"annualizedSharpe":1.0,"years":3,"months":36,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.987848283126},{"annualizedSharpe":1.0,"years":3,"months":36,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.75440773665},{"annualizedSharpe":1.0,"years":3,"months":36,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.386880734156},{"annualizedSharpe":1.0,"years":3,"months":36,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.063303475997},{"annualizedSharpe":1.0,"years":5,"months":60,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999398073654},{"annualizedSharpe":1.0,"years":5,"months":60,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.90784095145},{"annualizedSharpe":1.0,"years":5,"months":60,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.568214569122},{"annualizedSharpe":1.0,"years":5,"months":60,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.108708933066},{"annualizedSharpe":1.0,"years":10,"months":120,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999999671294},{"annualizedSharpe":1.0,"years":10,"months":120,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.992050382466},{"annualizedSharpe":1.0,"years":10,"months":120,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.820288637006},{"annualizedSharpe":1.0,"years":10,"months":120,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.212825228576},{"annualizedSharpe":1.5,"years":1,"months":12,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.647632609217},{"annualizedSharpe":1.5,"years":1,"months":12,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.243238349697},{"annualizedSharpe":1.5,"years":1,"months":12,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.076695820625},{"annualizedSharpe":1.5,"years":1,"months":12,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.006763542966},{"annualizedSharpe":1.5,"years":3,"months":36,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.962280759689},{"annualizedSharpe":1.5,"years":3,"months":36,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.603818263477},{"annualizedSharpe":1.5,"years":3,"months":36,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.246647506785},{"annualizedSharpe":1.5,"years":3,"months":36,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.028159209512},{"annualizedSharpe":1.5,"years":5,"months":60,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.995962336149},{"annualizedSharpe":1.5,"years":5,"months":60,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.792589960177},{"annualizedSharpe":1.5,"years":5,"months":60,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.385316377669},{"annualizedSharpe":1.5,"years":5,"months":60,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.049094002021},{"annualizedSharpe":1.5,"years":10,"months":120,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999984862707},{"annualizedSharpe":1.5,"years":10,"months":120,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.958869112178},{"annualizedSharpe":1.5,"years":10,"months":120,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.630354714171},{"annualizedSharpe":1.5,"years":10,"months":120,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.099479207216},{"annualizedSharpe":2.0,"years":1,"months":12,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.530073638314},{"annualizedSharpe":2.0,"years":1,"months":12,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.161089732304},{"annualizedSharpe":2.0,"years":1,"months":12,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.04232955873},{"annualizedSharpe":2.0,"years":1,"months":12,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.002661492863},{"annualizedSharpe":2.0,"years":3,"months":36,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.90706715223},{"annualizedSharpe":2.0,"years":3,"months":36,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.443069394658},{"annualizedSharpe":2.0,"years":3,"months":36,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.142993263731},{"annualizedSharpe":2.0,"years":3,"months":36,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.011262095741},{"annualizedSharpe":2.0,"years":5,"months":60,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.981621558423},{"annualizedSharpe":2.0,"years":5,"months":60,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.630268325397},{"annualizedSharpe":2.0,"years":5,"months":60,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.23307589802},{"annualizedSharpe":2.0,"years":5,"months":60,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.019788532095},{"annualizedSharpe":2.0,"years":10,"months":120,"losingStreakMonths":2,"probabilityAtLeastOneStreak":0.999680362833},{"annualizedSharpe":2.0,"years":10,"months":120,"losingStreakMonths":3,"probabilityAtLeastOneStreak":0.867229805685},{"annualizedSharpe":2.0,"years":10,"months":120,"losingStreakMonths":4,"probabilityAtLeastOneStreak":0.419004506639},{"annualizedSharpe":2.0,"years":10,"months":120,"losingStreakMonths":6,"probabilityAtLeastOneStreak":0.040784322652}],"limitations":["A losing month means negative excess return relative to the risk-free rate, not necessarily a nominal dollar loss.","Serial correlation changes both Sharpe scaling and streak clustering.","Normality, stationarity, and known-true-Sharpe assumptions are simplifying benchmarks rather than forecasts."]}