Using CRSP stock and mutual fund data, we find strong evidence for reversals at the style level (e.g., large value, small growth, etc.). There are significant excess and risk-adjusted returns for stocks in styles characterized by the worst past returns and net inflows. We also find evidence for momentum and positive feedback trading at the style level. These value and momentum effects are driven neither by fundamental risk nor by stock-level reversals and momentum. Taken together, the results are consistent with the style-level positive feedback trading model of Barberis and Shleifer (2003).

This paper introduces the concept of statistical arbitrage, a long horizon trading opportunity that generates a riskless profit and is designed to exploit persistent anomalies. Statistical arbitrage circumvents the joint hypothesis dilemma of traditional market efficiency tests because its definition is independent of any equilibrium model and its existence is incompatible with market efficiency. We provide a methodology to test for statistical arbitrage and then empirically investigate whether momentum and value trading strategies constitute statistical arbitrage opportunities. Despite adjusting for transaction costs, the influence of small stocks, margin requirements, liquidity buffers for the marking-to-market of short-sales, and higher borrowing rates, we find evidence that these strategies generate statistical arbitrage.