Finding Moving-Band Statistical Arbitrage Portfolios with Convex-Concave Optimization

Summary

The document presents an optimization approach for identifying statistical arbitrages that can include more than two assets. It frames the task as finding a portfolio with high volatility while keeping its price within a specified band and respecting a leverage constraint. The band defines a bounded price path, and the method extends the usual fixed-band setup to cases where the band midpoint changes over time.

Because the portfolio optimization is nonconvex, the proposed solution uses the convex-concave procedure, a sequential method that repeatedly solves convex approximations. The document describes the method and its generalization, but gives no empirical results, performance comparisons, or details about transaction costs and robustness. Accordingly, it establishes a formulation and computational approach rather than evidence that the resulting portfolios are profitable in live trading. Any practical use would depend on how the band, leverage limit, and changing midpoint are specified and validated.

Key ideas

• The method searches for statistical arbitrages that can combine more than two assets.
• It maximizes portfolio volatility subject to a price-band condition and a leverage limit.
• The resulting optimization problem is nonconvex and is approximately solved with sequential convex programming.
• A moving-band version allows the price-band midpoint to vary over time.
• The document gives no reported trading results or assessment of real-world implementation costs.

Tags

# Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization


# Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.