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