Introduction

Accurately forecasting expected volume plays a fundamental role in the performance of execution algorithms, serving as a key input that guides trading decisions. A well-designed schedule enables an algorithm to execute the order in a way that aligns with the security's natural liquidity dynamics, ultimately reducing market impact and trading costs.

Schedules determine how child orders are distributed across trading hours. Widely utilized trading strategies like VWAP (Volume Weighted Average Price), Close (trading into the close), and Implementation Shortfall (IS) rely on schedules to execute orders accounting for stocks’ expected volume across a specified time window. For instance, consider a VWAP order for a European ADR trading in the US Equity market which is more “front-loaded” due to the overlapping European and American trading hours. If the volume profile used by the algorithm is incorrect, it will execute less (than the market volume) during the European hours and more after the European markets are closed (than the market volume). This will both create higher market impact as well as higher variance from the VWAP price of the day.  

While achieving perfect accuracy in matching each stock’s volume profile is unrealistic due to the noise in the volume profile itself, even incremental improvements in forecasting can enhance performance, leading to more effective execution and better cost outcomes. In this paper, we explain the theory and development of a new methodology using empirical volume distributions to predict minute-by-minute volume more accurately. This analysis covers the universe of roughly 8,300 stocks in the U.S. equity market. The sample period is Q4 2024.

To effectively capture the intraday volume patterns of this universe of stocks, we propose a hybrid approach, combining machine learning techniques with deep market microstructure understanding. In this analysis, we exclude auction volumes and focus only on estimating intraday minute-by-minute volume distribution during continuous trading from 9:30 am to 4:00 pm ET.