Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals

ArXiv ID: 2308.15135 “View on arXiv”

Authors: Unknown

Abstract

In this article we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending traditional factor models, while keeping the resulting formulas lightweight and easily interpretable. We achieve this by representing a trading strategy as a linear functional applied to the signature of a path (which we refer to as “Signature Trading” or “Sig-Trading”). This allows the modeller to efficiently encode the evolution of past time-series observations into the optimisation problem. In particular, we derive a concise formulation of the dynamic mean-variance criterion alongside an explicit solution in our setting, which naturally incorporates a drawdown control in the optimal strategy over a finite time horizon. Secondly, we draw parallels between classical portfolio stategies and Sig-Trading strategies and explain how the latter leads to a pathwise extension of the classical setting via the “Signature Efficient Frontier”. Finally, we give examples when trading under an exogenous signal as well as examples for momentum and pair-trading strategies, demonstrated both on synthetic and market data. Our framework combines the best of both worlds between classical theory (whose appeal lies in clear and concise formulae) and between modern, flexible data-driven methods that can handle more realistic datasets. The advantage of the added flexibility of the latter is that one can bypass common issues such as the accumulation of heteroskedastic and asymmetric residuals during the optimisation phase. Overall, Sig-Trading combines the flexibility of data-driven methods without compromising on the clarity of the classical theory and our presented results provide a compelling toolbox that yields superior results for a large class of trading strategies.

Keywords: rough path signatures, portfolio optimization, Sig-Trading, path-dependencies, mean-variance criterion, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced rough path theory (signatures, tensor algebra) and extends the mean-variance framework with path-dependent dynamics, indicating high mathematical complexity. It includes concrete implementation sections, numerical results on synthetic and market data for pairs trading, momentum, and exogenous signals, demonstrating strong empirical backing for a theoretical paper.

  flowchart TD
    A["Research Goal<br>Integrate Path-Dependencies<br>into Mean-Variance Framework"] --> B{"Methodology: Signature Trading"}
    B --> C["Represent Strategy as Linear Functional<br>of Rough Path Signature"]
    C --> D["Derive Dynamic Mean-Variance<br>Optimization Formulation"]
    D --> E["Compute Solution with<br>Integrated Drawdown Control"]
    E --> F["Construct Signature<br>Efficient Frontier"]
    F --> G["Outcomes: Unified Framework<br>Interpretable Formulas & Superior Performance"]