Dynamic portfolio optimization with liquidity cost and market impact

a simulation-and-regression approach

Rongju Zhang, Nicolas Langrené, Yu Tian, Zili Zhu, Fima Klebaner, Kais Hamza

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. 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 impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method 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.

Original languageEnglish
Pages (from-to)519-532
Number of pages14
JournalQuantitative Finance
Volume19
Issue number3
DOIs
Publication statusPublished - 2019

Keywords

  • Dynamic portfolio optimization
  • Least squares Monte Carlo
  • Liquidity cost
  • Multi-period asset allocation
  • Permanent market impact
  • Transaction cost

Cite this

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title = "Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach",
abstract = "We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. 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 impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method 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.",
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Dynamic portfolio optimization with liquidity cost and market impact : a simulation-and-regression approach. / Zhang, Rongju; Langrené, Nicolas; Tian, Yu; Zhu, Zili; Klebaner, Fima; Hamza, Kais.

In: Quantitative Finance, Vol. 19, No. 3, 2019, p. 519-532.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Tian, Yu

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AU - Klebaner, Fima

AU - Hamza, Kais

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AB - We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. 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 impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method 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.

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