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Replica approach to mean-variance portfolio optimization

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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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    References listed on IDEAS

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    1. repec:eee:phsmap:v:502:y:2018:i:c:p:534-544 is not listed on IDEAS
    2. 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.
    3. repec:eee:phsmap:v:515:y:2019:i:c:p:671-681 is not listed on IDEAS
    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. 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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    JEL classification:

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

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