This article develops a framework that applies to single securities to test whether asset pricing models can explain the size, value, and momentum anomalies. Stock level beta is allowed to vary with firm-level size and book-to-market as well as with macroeconomic variables. With constant beta, none of the models examined capture any of the market anomalies. When beta is allowed to vary, the size and value effects are often explained, but the explanatory power of past return remains robust. The past return effect is captured by model mispricing that varies with macroeconomic variables.

This article proposes a trading-based explanation for the asymmetric effect in daily volatility of individual stock returns. Previous studies propose two major hypotheses for this phenomenon: leverage effect and time-varying expected returns. However, leverage has no impact on asymmetric volatility at the daily frequency and, moreover, we observe asymmetric volatility for stocks with no leverage. Also, expected returns may vary with the business cycle, that is, at a lower than daily frequency. Trading activity of contrarian and herding investors has a robust effect on the relationship between daily volatility and lagged return. Consistent with the predictions of the rational expectation models, the non-informational liquidity-driven (herding) trades increase volatility following stock price declines, and the informed (contrarian) trades reduce volatility following stock price increases. The results are robust to different measures of volatility and trading activity.

This article develops a framework that applies to single securities to test whether asset pricing models can explain the size, value, and momentum anomalies. Stock level beta is allowed to vary with firm-level size and book-to-market as well as with macroeconomic variables. With constant beta, none of the models examined capture any of the market anomalies. When beta is allowed to vary, the size and value effects are often explained, but the explanatory power of past return remains robust. The past return effect is captured by model mispricing that varies with macroeconomic variables.

This article proposes a trading-based explanation for the asymmetric effect in daily volatility of individual stock returns. Previous studies propose two major hypotheses for this phenomenon: leverage effect and time-varying expected returns. However, leverage has no impact on asymmetric volatility at the daily frequency and, moreover, we observe asymmetric volatility for stocks with no leverage. Also, expected returns may vary with the business cycle, that is, at a lower than daily frequency. Trading activity of contrarian and herding investors has a robust effect on the relationship between daily volatility and lagged return. Consistent with the predictions of the rational expectation models, the non-informational liquidity-driven (herding) trades increase volatility following stock price declines, and the informed (contrarian) trades reduce volatility following stock price increases. The results are robust to different measures of volatility and trading activity.