We examine the relation between stock returns, measures of risk, and several non-risk security characteristics, including the book-to-market ratio, firm size, the stock price, the dividend yield, and lagged returns. Our primary objective is to determine whether non-risk characteristics have marginal explanatory power relative to the arbitrage pricing theory benchmark, with factors determined using, in turn, the Connor and Korajczyk (CK; 1988) and the Fama and French (FF; 1993b) approaches. Fama–MacBeth-type regressions using risk adjusted returns provide evidence of return momentum, size, and book-to-market effects, together with a significant and negative relation between returns and trading volume, even after accounting for the CK factors. When the analysis is repeated using the FF factors, we find that the size and book-to-market effects are attenuated, while the momentum and trading volume effects persist. In addition, Nasdaq stocks show significant underperformance after adjusting for risk using either method.