Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization

ArXiv ID: 2402.08108 “View on arXiv”

Authors: Unknown

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.

Keywords: Statistical Arbitrage, Convex-Concave Procedure, Sequential Convex Programming, Portfolio Optimization, Volatility, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical optimization using convex-concave procedures and non-convex formulations (high math), while providing structured numerical experiments with backtest-ready metrics like profit and out-of-sample periods (moderate-high rigor).

  flowchart TD
    A["Research Goal:<br>Find multi-asset statistical arbitrages"] --> B{"Data & Inputs"}
    B --> C["Asset Price Data<br>Lev. Constraint Bound<br>Band Width Parameters"]
    
    C --> D["Formulate NCCP<br>Maximize Volatility<br>Subject to Band & Lev."]
    
    D --> E["Sequential Convex<br>Optimization"]
    E --> F{"Convex-Concave<br>Procedure"}
    F -->|Converges| G["Optimal Portfolio<br>Moving-Band Arb. Strategy"]
    F -->|Iterate| E
    
    G --> H["Outcomes:<br>Generalizes pair trading to N assets<br>Efficient moving-band solver<br>Volatility scaling identified"]