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Portfolio choice under transitory price impact

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  • Isaenko, Sergei

Abstract

We consider a portfolio optimization problem for a short-term investor who faces an illiquid stock market. The illiquidity of this market results from a transitory price impact that is captured by the transaction costs that are convex in the number of shares traded by an investor. The linear component in these costs defines a no-trading zone, while the nonlinear component does not allow trading the stock at an arbitrary rate. The portfolio choice problem is solved when the stock path is continuous and when the stock may crash. We find that an economy could be in states where the conditional liquidity premium is of the same order of magnitude as the historical risk premium of the stock market. If the illiquid stock undergoes crashes, then in many states, an investor demands a premium for crashes that is much higher than that in the liquid market. Finally, we study the shape of the no-trading zone when the nonlinearity in the transitory price impact is strong or moderate. We find that this shape is significantly different from that when the transitory price impact is linear.

Suggested Citation

  • Isaenko, Sergei, 2010. "Portfolio choice under transitory price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2375-2389, November.
    • Handle: RePEc:eee:dyncon:v:34:y:2010:i:11:p:2375-2389
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    2. Astrup Jensen, Bjarne & Marekwica, Marcel, 2011. "Optimal portfolio choice with wash sale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1916-1937.
    3. Kraft, Holger & Kühn, Christoph, 2011. "Large traders and illiquid options: Hedging vs. manipulation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1898-1915.
    4. Isaenko, Sergey, 2023. "Transaction costs, frequent trading, and stock prices," Journal of Financial Markets, Elsevier, vol. 64(C).
    5. Du, Bian & Zhu, Hongliang & Zhao, Jingdong, 2016. "Optimal execution in high-frequency trading with Bayesian learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 767-777.
    6. Sergey Isaenko & Rui Zhong, 2015. "Liquidity premium in the presence of stock market crises and background risk," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 79-90, January.
    7. Isaenko, Sergey, 2015. "Equilibrium theory of stock market crashes," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 73-94.

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