The False Strategy Theorem: A Financial Application of Experimental Mathematics

Abstract

The False Strategy theorem tells us that the optimal outcome of an unknown number of historical simulations is right-unbounded — with enough trials, there is no Sharpe ratio sufficiently enough to reject the hypothesis that a strategy is false. Given the ease with which one can use a computer to explore many trials or variations of given strategy and only select the optimal variation, it follows that it is very easy to find impressive-looking strategy variations that are nothing more than false positives. This is the essence of selection bias under multiple testing.

Keywords: Selection bias, multiple testing, False Strategy theorem, experimental mathematics

JEL Classification: G0, G1, G2, G15, G24, E44