Testing the household Euler equation with consumption data faces econometric challenges caused by large measurement errors in the data and a short time span. We adopt a framework to test the Euler equation with stock market data to alleviate the measurement error and short time span issues. Utilizing a data-driven group panel data method, we identify a heterogeneous pattern of Euler equation failure among different groups of listed firms. The identified degree of Euler equation failure is significantly related to firm characteristics that are associated with famous stock anomalies. We show that the correlations between the degree of Euler equation failure and firm characteristics provide a new set of stylized facts that can help us distinguish between different economic theories on Euler equation failures and asset pricing anomalies, and identify challenges facing current theories.

Using a comprehensive factor zoo, we document a notable factor MAX premium in the Chinese market. Factors with high maximum daily returns consistently outperform those with low maximum returns by 0.82% per month in the future, on a risk-adjusted basis. This premium remains robust controlling for various factor characteristics, and is not sensitive to the selection of factors. The factor MAX anomaly stands apart from lottery-type stock anomalies and contributes to elucidate most of these anomalies. The factor MAX premium concentrates in high-eigenvalue principal component factors, shedding light on the prevalent lottery preferences for factor investing in China’s A-share market. We document pronounced existence of factor MAX anomaly in the United States and other G7 countries.

Using a comprehensive factor zoo, we document a notable factor MAX premium in the Chinese market. Factors with high maximum daily returns consistently outperform those with low maximum returns by 0.82% per month in the future, on a risk-adjusted basis. This premium remains robust controlling for various factor characteristics, and is not sensitive to the selection of factors. The factor MAX anomaly stands apart from lottery-type stock anomalies and contributes to elucidate most of these anomalies. The factor MAX premium concentrates in high-eigenvalue principal component factors, shedding light on the prevalent lottery preferences for factor investing in China’s A-share market.