A Note on Statistical Arbitrage and Long Term Market Efficiency

Market efficiency is a central topic in finance. The notion of statistical arbitrage is a suitable instrument to investigate market efficiency without the need to specify an equilibrium model. We introduce a new definition of statistical arbitrage (named Strong Statistical Arbitrage, SSA in the following) modifying the original definition in an apparently infinitesimal way. We show that some simple investment strategies, recognized as statistical arbitrages by the standard definition, do not test positive for SSA. We discuss the relations between the proposed definition and common definitions of arbitrage and prove that SSA is compatible with deviations from market efficiency in a “short term frame.” The idea is that if market anomalies are small, the markets do not deviate significantly from efficiency, while an SSA requires time persistent anomalies on asset prices.