Cross-Impact of Order Flow Imbalance in Equity Markets
Cross-Impact of Order Flow Imbalance in Equity Markets
This paper investigates the cross-impact of order flow imbalance (OFI) on equity prices using high-frequency data for 100 S&P 500 stocks. The authors first propose a novel method to aggregate multi-level OFIs (from the top 10 levels of the limit order book) into a single integrated OFI via principal component analysis (PCA). This integrated OFI captures the common variation across levels and is shown to explain contemporaneous price impact as effectively as using all ten levels individually. The study then revisits the role of cross-impact—the effect of one stock's order flow on another's returns. For contemporaneous returns, they find that once integrated OFI is used, adding cross-asset OFI terms does not improve explanatory power, suggesting that commonality in order flows already accounts for cross-sectional return correlations. However, for forecasting future returns, lagged cross-asset OFIs provide significant predictive content over short horizons (up to 5 minutes), though this predictability decays rapidly. The results are robust across various stock characteristics and time periods. The findings have implications for optimal execution, market microstructure modeling, and high-frequency trading strategies, highlighting that cross-impact is primarily a short-term predictive phenomenon rather than a contemporaneous one.
Highlights
- 1Proposes a systematic method to combine multi-level order flow imbalances (OFIs) into an integrated OFI variable using PCA, which better explains price impact than best-level OFI alone.
- 2Shows that once multi-level OFI information is integrated, cross-impact terms do not improve contemporaneous return models, suggesting a parsimonious model suffices.
- 3Demonstrates that lagged cross-asset OFIs significantly improve short-term return forecasts (up to several minutes), but predictive power decays rapidly.
- 4Provides comprehensive empirical analysis on 100 S&P 500 stocks using high-frequency Nasdaq ITCH data over three years.
Methods
- MPrincipal Component Analysis (PCA) to aggregate multi-level OFIs into an integrated OFI.
- MLinear regression models for contemporaneous price impact, comparing single-asset vs. multi-asset (cross-impact) specifications.
- MPredictive regression models with lagged cross-asset OFIs to forecast future returns, evaluated via out-of-sample R-squared and economic gains.
- MCross-sectional analysis of PCA weights across stock characteristics (volume, volatility, spread).
Results
- RIntegrated OFI explains contemporaneous returns as well as multi-level OFI models, with R-squared around 0.3-0.4 for 1-minute returns.
- RAdding cross-impact terms to contemporaneous models yields negligible improvement (R-squared increase < 0.01) when integrated OFI is used.
- RLagged cross-asset OFIs improve 1-minute-ahead return forecasts by up to 10% in R-squared relative to a model with only own-asset OFIs.
- RPredictive power of cross-impact decays quickly: significant for horizons up to 5 minutes, but negligible beyond 10 minutes.
- RFirst principal component of multi-level OFIs explains over 89% of total variance, with best-level OFI having the smallest weight.
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