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Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization

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  • Papp, Gábor
  • Caccioli, Fabio
  • Kondor, Imre

Abstract

The optimization of a large random portfolio under the expected shortfall risk measure with an ℓ 2 regularizer is carried out by analytical calculation for the case of uncorrelated Gaussian returns. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition where this error would otherwise blow up. In the data-dominated region, where the number N of di?erent assets in the portfolio is much less than the length T of the available time series, the regularizer plays a negligible role even if its strength η is large, while in the opposite limit, where the size of samples is comparable to, or even smaller than the number of assets, the optimum is almost entirely determined by the regularizer. We construct the contour map of estimation error on the N/T versus η plane and find that for a given value of the estimation error the gain in N/T due to the regularizer can reach a factor of about four for a suffciently strong regularizer.

Suggested Citation

  • Papp, Gábor & Caccioli, Fabio & Kondor, Imre, 2019. "Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization," LSE Research Online Documents on Economics 100294, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:100294
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. G'abor Papp & Imre Kondor & Fabio Caccioli, 2021. "Optimizing Expected Shortfall under an $\ell_1$ constraint -- an analytic approach," Papers 2103.04375, arXiv.org.

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    More about this item

    Keywords

    cavity and replica method; quantitative finance; risk measure and management;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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