When price competition is constrained by tick size, speed allocates the resources due to the time priority rule. We demonstrate three implications of competition in speed. 1) We find more high frequency liquidity provision for lower price stocks with high market cap, where the one cent tick size...

Odd-lots are trades for less than 100 shares of stock. These trades are missing from the TAQ data because they are not reported to the consolidated tape. We investigate the systematic bias that arises from the exclusion of odd lots from TAQ data. In our sample, the median number of missing...

We investigate the systematic bias that arises from the exclusion of trades for less than 100 shares from TAQ data. In our sample, we find that the median number of missing trades per stock is 19%, but for some stocks missing trades are as high as 66% of total transactions. Missing trades are...

This paper applies the Least Absolute Shrinkage and Selection Operator (LASSO) to make rolling 1-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. And, this...

We model competition for liquidity provision between high-frequency traders (HFTs) and slower execution algorithms designed to minimize transaction costs for buy-side institutions (B-Algos). Under continuous pricing, B-Algos dominate liquidity provision by using aggressive limit orders to...

This paper uses wavelets to decompose each stock's trading-volume variance into frequency-specific components. We find that stocks dominated by short-run fluctuations in trading volume have abnormal returns that are 1% per month higher than otherwise similar stocks where short-run fluctuations...

How do arbitrageurs find variables that predict returns? If a predictor lasts 30 days or more, then a clever arbitrageur can use his intuition to get the job done. But, what's an arbitrageur supposed to do if a predictor lasts 30 minutes or less? An arbitrageur's intuition is useless if the...

We show that queueing rationing under price controls drives high-frequency trading. A one-cent uniform tick size (minimal price variation) creates rents and generates queues for liquidity provision, particularly for securities with lower prices (larger relative tick sizes). Speed rations the...

This paper introduces a new tool — the wavelet-variance estimator — that measures the fraction of trading activity at each investment horizon. We find substantial cross-sectional variation in horizons, even for stocks with the same volume, size, and liquidity. Moreover, the fraction of...