Abstract
How should an active investor calibrate their investment decisions, when the goal is to reach an outperformance target over the long term, without succumbing to large drawdowns in the interim? Closed-form expressions for the probability of consistent long-term alpha are derived and show that maximizing this probability requires a thoughtful calibration of skill, volatility, decision frequency, and costs. The article derives the minimum skill level for which the probability of consistent long-term alpha trends to its maximum for long investment horizons. This minimum skill level is not typically large, at only marginally above a fair coin toss. Unfortunately, the maximum probability of consistent long-term alpha is also not very large, even when skill is high and the investment horizon is long. The reason is that, although the probability of reaching the long-term goal rises with the time horizon for sufficiently high skill, so does the probability of experiencing the intertemporal loss that can force a stop-out in the interim.
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