A financial Rayleigh criterion: How long must we wait to detect outperformance?
In physics, the Rayleigh criterion answers the question: how close must we get before we can resolve two objects optically? A similar question can be posed in finance: how long must we wait before we can resolve – in this case, statistically – the performance of a fund from its benchmark. We will explore this question using a simple mathematical model. The answers will shed light on whether we can detect “skill” from luck, and whether fund management fees can be empirically justified.