A mixed Sharpe ratio

Abstract

Recent results in optimal stopping theory have shown that a ‘bang-bang’ (buy or sell immediately) style of trading strategy is in some sense optimal provided the asset's price dynamics follow certain familiar stochastic processes. This paper constructs a reward-to-variability ratio (the mixed Sharpe ratio) that is sufficient for this strategy's implementation. The use of this ratio for optimal portfolio selection is discussed and evidence for it varying over time is found. The performances of the ‘bang-bang’ and ‘buy-and-hold’ trading strategies are compared and the former is found to be significantly more profitable.

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