When volatility is not enough: classical and quantum behaviors in stock investment

We introduce two novel metrics —the Zero Bin Ratio (ZBR) and algorithmic price variance ( λ )— to analyze investor behavior in high-frequency equity markets. Using nanosecond-level trading data from Nasdaq-100 stocks, we distinguish between classical and quantum patterns of investor behavior. In the classical case, bid-ask spreads are primarily driven by realized volatility, while in the quantum case, they are better explained by algorithmic variance and central distribution dynamics. The ZBR complements this distinction by capturing the role of zero-price-change trades in shaping liquidity. Our framework offers a new lens on market microstructure and investor heterogeneity. We apply it to twelve Nasdaq-100 firms—selected for their structural diversity, trading intensity, and exposure to stock splits—and uncover both persistent behavioral types and sharp regime shifts directly linked to those stock splits. The findings, derived through two empirical specifications tailored to each regime, reveal systematic behavioral heterogeneity with implications for market design, liquidity modeling, and trading strategy.