Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization

TL;DR

The paper develops a scalable method for identifying stat-arbs by casting the search as a nonconvex portfolio optimization that maximizes price variation while enforcing a mean-reverting band and a leverage constraint, solvable approximately via the convex-concave procedure. It extends the framework to moving-band stat-arbs, where band midpoints adapt over time to recent price history, and demonstrates that the same CCP approach applies to this dynamic setting. Empirical results on a large CRSP dataset show moving-band stat-arbs outperform fixed-band counterparts in profitability and durability, with substantial multi-asset portfolios and long active periods. The work provides a practical, scalable tool for generating high-variance, mean-reverting portfolios without relying on co-integration tests, with clear implications for diversified stat-arb strategies and future research on trading portfolios of stat-arbs.

Abstract

We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex, but can be approximately solved using the convex-concave procedure, a specific sequential convex programming method. We show how the method generalizes to finding moving-band statistical arbitrages, where the price band midpoint varies over time.

Figures (8)

• Figure 1: Distribution of the number of assets per fixed-band stat-arb.
• Figure 2: Number of active fixed-band stat-arbs over time.
• Figure 3: A fixed-band stat-arb strategy that made money. Top. Price. Bottom. Cumulative profit.
• Figure 4: A fixed-band stat-arb strategy that lost money. Top. Price. Bottom. Cumulative profit.
• Figure 5: Distribution of the number of assets per moving-band stat-arb.