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...

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...

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...

We incorporate discrete tick size and allow non-high-frequency traders (non-HFTs) to supply liquidity in the framework of Budish, Cramton, and Shim (2015). When adverse selection risk is low or tick size is large, the bid-ask spread is typically below one tick, and HFTs dominate liquidity...

Stock exchange operators compete for order flow by setting "make" fees for limit orders and "take" fees for market orders. When traders quote continuous prices, they can choose prices that perfectly neutralize any fee division, and traders stream to the exchange with the lowest total fee. The...

We argue that a one-penny minimum tick size for all stocks priced above $1 (SEC rule 612) encourages high-frequency trading and taker/maker–fee markets. We find that non-high frequency traders (non-HFTers) are 2.62 times more likely than HFTers to provide best prices, thereby establishing...

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...