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Liquidity Risk And Instabilities In Portfolio Optimization

Author

Listed:
  • FABIO CACCIOLI

    (Department of Computer Science, University College London, London WC1E 6BT, UK2Systemic Risk Centre, London School of Economics and Political Sciences, London, UK)

  • IMRE KONDOR

    (Parmenides Foundation, Kirchplatz 1, Pullach, 82049, Germany)

  • MATTEO MARSILI

    (Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste, 34151, Italy)

  • SUSANNE STILL

    (Information and Computer Sciences, University of Hawai’i at Mānoa, 1680 East-West Road, Honolulu, 96822, Hawai’i, USA)

Abstract

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm ℓp with p > 1 makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with p < 1 do not. The ℓ1 norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

Suggested Citation

  • Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:05:n:s0219024916500357
    DOI: 10.1142/S0219024916500357
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    References listed on IDEAS

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    Cited by:

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    2. Zhao, Longfeng & Wang, Gang-Jin & Wang, Mingang & Bao, Weiqi & Li, Wei & Stanley, H. Eugene, 2018. "Stock market as temporal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1104-1112.
    3. 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.
    4. Longfeng Zhao & Chao Wang & Gang-Jin Wang & H. Eugene Stanley & Lin Chen, 2021. "Community detection and portfolio optimization," Papers 2112.13383, arXiv.org.
    5. 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.
    6. Masoud Rahiminezhad Galankashi & Farimah Mokhatab Rafiei & Maryam Ghezelbash, 2020. "Portfolio selection: a fuzzy-ANP approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-34, December.
    7. 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.
    8. Axel Pruser & Imre Kondor & Andreas Engel, 2021. "Aspects of a phase transition in high-dimensional random geometry," Papers 2105.04395, arXiv.org, revised Jun 2021.
    9. 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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