Data-driven Portfolio Optimization with Signatures

Traditionally, portfolio optimization has focused on balancing expected return and risk. In this study, we propose a data-driven portfolio optimization framework that simultaneously incorporates a predefined expected return and a signature-based risk measure. Without assuming a specific distribution for market data, we construct an uncertainty set using the signature of price sequences, ensuring coverage through exchangeability. Defining risk as the worst-case realized return, we formulate the portfolio optimization problem as a data-driven robust optimization. A numerical experiment on single-period portfolio optimization for NASDAQ 100 components demonstrates the coverage capability of the signature-based uncertainty set and shows that the optimized portfolio achieves diversification, thereby reducing risk.