What's in a Name? A Cautionary Tale of Profitability Anomalies and Limits to Arbitrage

The recent literature investigating profitability anomalies defines profitability in various ways (i.e., gross, operating, and cash based). We show that limits to arbitrage are associated with returns of gross and cash-based operating profitability anomalies, suggesting mispricing. In contrast, returns from the operating profitability strategy have no relation with barriers to arbitrage and exhibit no evidence of mispricing. Additionally, we show that the differential effects of limited arbitrage-related mispricing of gross and cash-based operating profitability anomalies are attributable to their respective correlations with selling, general, and administrative (SG&A) expense and accruals anomalies. We find that SG&A return predictability, like that of accruals, is related to limits to arbitrage. These findings suggest that investors and researchers should proceed with caution when searching for return predictability by redefining profitability measures.