This paper investigates fractional share trading. We develop a latency-based method for identifying a large sample of fractional share trades. We find that high-priced stocks, meme stocks, IPOs, SPACs, and popular retail stocks exhibit considerable numbers of these tiny trades. We surmise that this reflects dollar-based order entry, with many tiny trades being fractional components of larger orders. We show that our fractional trade measure is predictive of future liquidity and volatility, suggesting a new metric to capture the information in retail trades. We identify how data and reporting protocols preclude knowing the extent of fractional share trading, inflate volume data, and provide censured samples of these off-exchange trades.

We show current market practices relating to odd-lot quotes create a large “inside” market where better prices routinely exist relative to the National Best Bid or Offer. We show that odd-lot quotes play a price discovery role, and these quotes provide valuable information to traders with access to proprietary data feeds. Using a XGBoost machine learning algorithm that uses odd-lot data to predict future prices, we demonstrate a simple and profitable trading strategy. We argue the SEC’s proposed round-lot redefinition reduces—but does not eliminate—the high incidence of superior odd-lot quotes within the NBBO.

In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on Stock and Yogo (2005), we introduce the tF critical value function, leading to a standard error adjustment that is a smooth function of the first-stage F-statistic. For one-quarter of specifications in 61 AER papers, corrected standard errors are at least 49 and 136 percent larger than conventional 2SLS standard errors at the 5 percent and 1 percent significance levels, respectively. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded.