We investigate odd‐lot trades in equity markets. Odd lots are increasingly used in algorithmic and high‐frequency trading, but are not reported to the consolidated tape or in databases such as TAQ. In our sample, the median number of odd‐lot trades is 24% but in some stocks odd lots are 60% or more of trading. Odd‐lot trades contribute 35% of price discovery, consistent with informed traders using odd lots to avoid detection. Omitting odd‐lot trades leads to inaccuracies in order imbalance measures and makes sentiment measures unreliable. Excluding odd lots from the consolidated tape raises important regulatory issues.

This paper applies the Least Absolute Shrinkage and Selection Operator (LASSO) to make rolling one‐minute‐ahead return forecasts using the entire cross‐section of lagged returns as candidate predictors. The LASSO increases both out‐of‐sample fit and forecast‐implied Sharpe ratios. This out‐of‐sample success comes from identifying predictors that are unexpected, short‐lived, and sparse. Although the LASSO uses a statistical rule rather than economic intuition to identify predictors, the predictors it identifies are nevertheless associated with economically meaningful events: the LASSO tends to identify as predictors stocks with news about fundamentals.