Signature-Based Portfolio Allocation: A Network Approach

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Abstract
Portfolio allocation represents a significant challenge within financial markets, traditionally relying on correlation or covariance matrices to delineate relationships among stocks. However, these methodologies assume time stationarity and only capture linear relationships among stocks. In this study, we propose to substitute the conventional Pearson's correlation or covariance matrix in portfolio optimization with a similarity matrix derived from the signature. The signature, a concept from path theory, provides a unique representation of time series data, encoding their geometric patterns and inherent properties. Furthermore, we undertake a comparative analysis of network structures derived from the correlation matrix versus those obtained from the signature-based similarity matrix. Through numerical evaluation on the Standard & Poor's 500, we assess that portfolio allocation utilizing the signature-based similarity matrix yielded superior results in terms of cumulative log-returns and Sharpe ratio compared to the baseline network approach based on Pearson's correlation. This assessment was conducted across various portfolio optimization strategies. This research contributes to portfolio allocation and financial network representation by proposing the use of signature-based similarity matrices over traditional correlation or covariance matrices.

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