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In this article we introduce a portfolio optimisation framework, in which theuse of rough path signatures (Lyons, 1998) provides a novel method ofincorporating path-dependencies in the joint signal-asset dynamics, naturallyextending traditional factor models, while keeping the resulting formulaslightweight and easily interpretable. We achieve this by representing a tradingstrategy as a linear functional applied to the signature of a path (which werefer to as "Signature Trading" or "Sig-Trading"). This allows the modeller toefficiently encode the evolution of past time-series observations into theoptimisation problem. In particular, we derive a concise formulation of thedynamic mean-variance criterion alongside an explicit solution in our setting,which naturally incorporates a drawdown control in the optimal strategy over afinite time horizon. Secondly, we draw parallels between classical portfoliostategies and Sig-Trading strategies and explain how the latter leads to apathwise extension of the classical setting via the "Signature EfficientFrontier". Finally, we give examples when trading under an exogenous signal aswell as examples for momentum and pair-trading strategies, demonstrated both onsynthetic and market data. Our framework combines the best of both worldsbetween classical theory (whose appeal lies in clear and concise formulae) andbetween modern, flexible data-driven methods that can handle more realisticdatasets. The advantage of the added flexibility of the latter is that one canbypass common issues such as the accumulation of heteroskedastic and asymmetricresiduals during the optimisation phase. Overall, Sig-Trading combines theflexibility of data-driven methods without compromising on the clarity of theclassical theory and our presented results provide a compelling toolbox thatyields superior results for a large class of trading strategies.

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