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Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

Author

Listed:
  • Rongju Zhang

    (Monash University [Melbourne])

  • Nicolas Langrené

    (CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra])

  • Yu Tian

    (Monash University [Melbourne])

  • Zili Zhu

    (CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra])

  • Fima Klebaner

    (Monash University [Melbourne])

  • Kais Hamza

    (Monash University [Melbourne])

Abstract

We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impacts. To do so, we improve the accuracy of the control randomization approach in the case of discrete controls, and propose a global iteration procedure to further improve the allocation estimates. We validate our numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We quantify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic allocation protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk-aversion level and investment horizon.

Suggested Citation

  • Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach," Post-Print hal-02909207, HAL.
    • Handle: RePEc:hal:journl:hal-02909207
    DOI: 10.1080/14697688.2018.1524155
    Note: View the original document on HAL open archive server: https://hal.science/hal-02909207
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    References listed on IDEAS

    as
    1. Jules Binsbergen & Michael Brandt, 2007. "Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 355-367, May.
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    Cited by:

    1. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Post-Print hal-02909342, HAL.
    2. repec:tin:wpaper:20230016 is not listed on IDEAS
    3. Ivan Guo & Nicolas Langrené & Gregoire Loeper & Wei Ning, 2020. "Robust utility maximization under model uncertainty via a penalization approach," Working Papers hal-02910261, HAL.
    4. Chen, Shun & Ge, Lei, 2021. "A learning-based strategy for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 936-942.

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