We show that queue rationing under price controls is one driver of high-frequency trading. Uniform tick sizes constrain price competition and create rents for liquidity provision, particularly for securities with lower prices. The time priority rule allocates rents to high-frequency traders (HFTs) because of their speed advantage. An increase in relative tick size, defined as uniform tick sizes divided by security prices, increases the fraction of liquidity provided by HFTs but harms liquidity. We find that the message-to-trade ratio is a poor cross-sectional proxy for HFTs’ liquidity provision: stocks with more liquidity provided by HFTs have lower message-to-trade ratios. Received September 15, 2015; editorial decision October 7, 2017 by Editor Robin Greenwood.

We examine how fragmentation is affecting market quality in US equity markets. We use newly available trade reporting facilities (TRFs) data to measure fragmentation, and we use a variety of empirical approaches to compare execution quality and efficiency of stocks with more and less fragmented trading. We find that fragmentation affects all stocks; more fragmented stocks have lower transactions costs and faster execution speeds; and fragmentation is associated with higher short-term volatility but greater market efficiency, in that prices are closer to being a random walk. Our results that fragmentation does not appear to harm market quality are consistent with US markets being a single virtual market with multiple points of entry.

To prevent issuers from inflating their share prices, SEC Rule 10b-18 sets price ceilings on share repurchases through open markets. We find that market-structure reforms in the 1990s and 2000s dramatically increased share repurchases because they relaxed constraints on issuers competing with other buyers under price ceilings. The Tick Size Pilot Program, a controlled experiment that partially reversed previous reforms, significantly reduced share repurchases. We estimate that price ceilings and reduced market-structure frictions explain 18% of the secular increase in share repurchases. Meanwhile, these two frictions still exist, which explains why share repurchases have not crowded out dividends entirely.

The Regulation National Market System (Reg NMS) links fragmented stock exchanges by routing orders to the National Best Bid and Offer (NBBO). As the NBBO ignores exchange fees, 62% of routings lead to worse net prices. An increase in fee differences increases the market share captured by orders that refuse Reg NMS routings, particularly for stocks whose fees account for a large portion of transaction costs. Heterogeneous opportunity costs rationalize routing choices: non-routable orders entail lower non-execution costs than routable orders. Our results indicate that fees and clientele segmentation drive the proliferation of order types in the Reg NMS era.

We investigate the effect of tick size, a key feature of market microstructure, on managerial learning from stock prices. Using a randomized controlled tick-size experiment, the 2016 Tick Size Pilot Program, we find that a larger tick size increases a firm's investment sensitivity to stock prices, suggesting that managers glean more new information from stock prices to guide their investment decisions as the tick size increases. Consistently, we also find that changes in managerial beliefs, as reflected in adjustments of forecasted capital expenditures, respond more strongly to market feedback under a larger tick size. Additional evidence suggests the following mechanism through which tick size affects managerial learning: a larger tick size reduces algorithmic trading, in turn encouraging fundamental information acquisition. Increased fundamental information acquisition generates incremental information about growth opportunities, macroeconomic factors, and industry factors, with respect to which the market has a comparative information advantage over management.

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.

The second special issue on big data in finance showcases advancements in research related to data of large size, high dimension, and complex structure since the first NBER/RFS big data conference. The papers published in this next chapter address some questions that were proposed in the initial special issue in 2021. Other papers are more directly connected to recent developments in the markets. We discuss some new research directions, following on the papers published here. They include evaluating market microstructure reforms, understanding medium-frequency trading, improving missing data imputations, and deepening data valuation. We look forward to more developments to follow.

Big data is revolutionizing the finance industry and has the potential to significantly shape future research in finance. This special issue contains papers following the 2019 NBER-RFS Conference on Big Data. In this introduction to the special issue, we define the “big data” phenomenon as a combination of three features: large size, high dimension, and complex structure. Using the papers in the special issue, we discuss how new research builds on these features to push the frontier on fundamental questions across areas in finance—including corporate finance, market microstructure, and asset pricing. Finally, we offer some thoughts for future research directions.

Security trading now fragments into more than ten almost identical stock exchanges in the United States. We show that discrete pricing is one economic force that prevents the consolidation of trading volume. The uniform one-cent tick size (minimum price variation), imposed by the SEC's Rule 612, leads to more dispersed trading for lower priced securities. When a security reverse splits, its price increases and relative tick size (one cent divided by the price) decreases. We find that reverse splits consolidate trading of securities, using securities with identical underlying fundamentals that do not reverse split as the control group.