Office of Research Statistical Arbitrage and Tests of Market Efficiency

Roughly speaking, statistical arbitrage is a long horizon trading strategy that generates a riskless profit. The concept of statistical arbitrage is motivated by numerous empirical studies that construct trading strategies to profit from persistent anomalies. However, we demonstrate by example that positive expected trading profits are not sufficient to reject market efficiency. Instead, this paper provides a methodology to test for statistical arbitrage whose existence is incompatible with market efficiency. Furthermore, statistical arbitrage circumvents the traditional joint hypothesis dilemma of traditional tests for market efficiency because its definition is independent of any equilibrium model. Instead, we replace a particular equilibrium model with a stochastic process that describes the dynamics of trading profits generated by trading strategies. The assumed stochastic process may be verified with a secondary goodness-of-fit test.