Statistical Arbitrage in Rank Space

Y. -F. Li and G. Papanicolaou

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Abstract: Equity market dynamics are conventionally investigated in name space, where stocks are indexed by company names. However, this perspective often suffers from high volatility and a low signal-to-noise ratio, which poses challenges for effective learning by deep neural networks (DNNs). In contrast, by indexing stocks by their ranks in capitalization, we gain a distinct and more structured view of market behavior in rank space. In this work, we demonstrate that DNNs achieve superior performance in statistical arbitrage when operating in rank space compared to name space. This performance gain is driven by more robust market representations and enhanced mean-reverting properties of residual returns in rank space, which facilitate more efficient learning. Our findings highlight the critical role of domain-informed data transformation in improving deep learning performance in noisy financial environments.

Date: 2024-10, Revised 2026-06
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