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Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks

Author

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  • Nick James

    (School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia
    These authors contributed equally to this work.)

  • Max Menzies

    (Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing 101408, China
    These authors contributed equally to this work.)

  • Jennifer Chan

    (School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia)

Abstract

This paper proposes a new method for financial portfolio optimization based on reducing simultaneous asset shocks across a collection of assets. This may be understood as an alternative approach to risk reduction in a portfolio based on a new mathematical quantity. First, we apply recently introduced semi-metrics between finite sets to determine the distance between time series’ structural breaks. Then, we build on the classical portfolio optimization theory of Markowitz and use this distance between asset structural breaks for our penalty function, rather than portfolio variance. Our experiments are promising: on synthetic data, we show that our proposed method does indeed diversify among time series with highly similar structural breaks and enjoys advantages over existing metrics between sets. On real data, experiments illustrate that our proposed optimization method performs well relative to nine other commonly used options, producing the second-highest returns, the lowest volatility, and second-lowest drawdown. The main implication for this method in portfolio management is reducing simultaneous asset shocks and potentially sharp associated drawdowns during periods of highly similar structural breaks, such as a market crisis. Our method adds to a considerable literature of portfolio optimization techniques in econometrics and could complement these via portfolio averaging.

Suggested Citation

  • Nick James & Max Menzies & Jennifer Chan, 2023. "Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks," Econometrics, MDPI, vol. 11(1), pages 1-33, March.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:1:p:8-:d:1090337
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    References listed on IDEAS

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    1. Arthur A. B. Pessa & Matjaz Perc & Haroldo V. Ribeiro, 2023. "Age and market capitalization drive large price variations of cryptocurrencies," Papers 2302.12319, arXiv.org.
    2. Hussein Khraibani & Bilal Nehme & Olivier Strauss, 2018. "Interval Estimation of Value-at-Risk Based on Nonparametric Models," Econometrics, MDPI, vol. 6(4), pages 1-30, December.
    3. Enrique Ballestero, 2005. "Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 1-15.
    4. Ross, Gordon J., 2015. "Parametric and Nonparametric Sequential Change Detection in R: The cpm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i03).
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    Cited by:

    1. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Nick James & Max Menzies, 2023. "An exploration of the mathematical structure and behavioural biases of 21st century financial crises," Papers 2307.15402, arXiv.org, revised Sep 2023.
    3. James, Nick & Menzies, Max, 2023. "An exploration of the mathematical structure and behavioural biases of 21st century financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    4. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    5. Nick James & Max Menzies, 2023. "Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies," Papers 2304.08902, arXiv.org, revised Jun 2023.

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