Path-Dependent Portfolio Optimization with Rough Path Signatures
Summary
This article presents Signature Trading, a portfolio optimization method that represents a strategy as a linear function of a path signature. Signatures encode the history of joint signal and asset movements, allowing the framework to include path dependence while extending traditional factor models. The authors derive a dynamic mean-variance criterion and an explicit finite-horizon solution that incorporates drawdown control, and relate the resulting strategies to a signature-based efficient frontier.
The article illustrates the approach using exogenous signals, momentum, and pairs trading, with examples on synthetic and market data. It argues that the method can retain interpretable formulas while handling richer time-series patterns than classical models. The supplied description does not give details of the datasets, evaluation design, or quantitative performance, so it is not possible to assess the claimed advantages or their robustness from this text alone. The examples and framework describe a modeling approach; they do not establish that signature-based strategies will outperform in live trading.
Key ideas
- A path signature can encode the history of joint signal and asset movements in an optimization model.
- Signature Trading represents strategies as linear functionals of path signatures.
- The framework extends dynamic mean-variance optimization and includes finite-horizon drawdown control.
- Examples cover exogenous signals, momentum, and pairs trading on synthetic and market data.
- The description provides limited information for judging comparative performance or live robustness.
Tags
Full text
# Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals # Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals 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.
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