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Dynamic Portfolio Cuts: A Spectral Approach to Graph-Theoretic Diversification

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Listed:
  • Alvaro Arroyo
  • Bruno Scalzo
  • Ljubisa Stankovic
  • Danilo P. Mandic

Abstract

Stock market returns are typically analyzed using standard regression, yet they reside on irregular domains which is a natural scenario for graph signal processing. To this end, we consider a market graph as an intuitive way to represent the relationships between financial assets. Traditional methods for estimating asset-return covariance operate under the assumption of statistical time-invariance, and are thus unable to appropriately infer the underlying true structure of the market graph. This work introduces a class of graph spectral estimators which cater for the nonstationarity inherent to asset price movements, and serve as a basis to represent the time-varying interactions between assets through a dynamic spectral market graph. Such an account of the time-varying nature of the asset-return covariance allows us to introduce the notion of dynamic spectral portfolio cuts, whereby the graph is partitioned into time-evolving clusters, allowing for online and robust asset allocation. The advantages of the proposed framework over traditional methods are demonstrated through numerical case studies using real-world price data.

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  • Alvaro Arroyo & Bruno Scalzo & Ljubisa Stankovic & Danilo P. Mandic, 2021. "Dynamic Portfolio Cuts: A Spectral Approach to Graph-Theoretic Diversification," Papers 2106.03417, arXiv.org.
    • Handle: RePEc:arx:papers:2106.03417
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    References listed on IDEAS

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    1. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    2. Guharay, Samar K. & Thakur, Gaurav S. & Goodman, Fred J. & Rosen, Scott L. & Houser, Daniel, 2013. "Analysis of non-stationary dynamics in the financial system," Economics Letters, Elsevier, vol. 121(3), pages 454-457.
    3. Jos'e Vin'icius de Miranda Cardoso & Jiaxi Ying & Daniel Perez Palomar, 2020. "Algorithms for Learning Graphs in Financial Markets," Papers 2012.15410, arXiv.org.
    4. Bruno Scalzo & Alvaro Arroyo & Ljubisa Stankovic & Danilo P. Mandic, 2021. "Nonstationary Portfolios: Diversification in the Spectral Domain," Papers 2102.00477, arXiv.org.
    5. Calkin, Neil J. & López de Prado, Marcos, 2014. "Stochastic flow diagrams," Algorithmic Finance, IOS Press, vol. 3(1-2), pages 21-42.
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