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Replica approach to mean-variance portfolio optimization

Author

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  • Varga-Haszonits, Istvan
  • Caccioli, Fabio
  • Kondor, Imre
Abstract
We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for r = N/T

Suggested Citation

  • Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:68955
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    File URL: http://eprints.lse.ac.uk/68955/
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    References listed on IDEAS

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    Cited by:

    1. Imre Kondor & G'abor Papp & Fabio Caccioli, 2017. "Analytic approach to variance optimization under an $\ell_1$ constraint," Papers 1709.08755, arXiv.org, revised Jul 2018.
    2. Papp, Gábor & Kondor, Imre & Caccioli, Fabio, 2021. "Optimizing expected shortfall under an ℓ1 constraint—an analytic approach," LSE Research Online Documents on Economics 111051, London School of Economics and Political Science, LSE Library.
    3. Li, Yan & Jiang, Xiong-Fei & Tian, Yue & Li, Sai-Ping & Zheng, Bo, 2019. "Portfolio optimization based on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 671-681.
    4. Nava, Noemi & Di Matteo, Tiziana & Aste, Tomaso, 2018. "Financial time series forecasting using empirical mode decomposition and support vector regression," LSE Research Online Documents on Economics 91028, London School of Economics and Political Science, LSE Library.
    5. Noemi Nava & Tiziana Di Matteo & Tomaso Aste, 2018. "Financial Time Series Forecasting Using Empirical Mode Decomposition and Support Vector Regression," Risks, MDPI, vol. 6(1), pages 1-21, February.
    6. Jerome Garnier-Brun & Michael Benzaquen & Stefano Ciliberti & Jean-Philippe Bouchaud, 2021. "A new spin on optimal portfolios and ecological equilibria," Post-Print hal-03378915, HAL.
    7. Nava, Noemi & Di Matteo, T. & Aste, Tomaso, 2018. "Dynamic correlations at different time-scales with empirical mode decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 534-544.
    8. Tomaso Aste & T. Di Matteo, 2017. "Sparse Causality Network Retrieval from Short Time Series," Complexity, Hindawi, vol. 2017, pages 1-13, November.
    9. Imre Kondor & G'abor Papp & Fabio Caccioli, 2016. "Analytic solution to variance optimization with no short-selling," Papers 1612.07067, arXiv.org, revised Jan 2017.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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