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Portfolio Optimization with Concave Transaction Costs

Author

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  • Andriy Demchuk

    () (University of Lausanne and FAME)

Abstract

In this paper we study the optimal portfolio management for the constant relative-risk averse investor who maximizes an expected utility of his terminal wealth and who faces transaction costs during his trades. In our model the investor's portfolio consists of one risky and one risk-free asset, and we assume that the transaction cost is a concave function of the traded volume of the risky asset. We find that under such transaction cost formulation the optimal trading strategies and boundaries of the no-transaction region are different than those when transaction costs are proportional, i.e. when they are linear in the traded volume. When transaction costs are concave, we show that the no-transaction region is narrower than when transaction costs are proportional, and it is not a positive cone. Under our transaction cost formulation, when the investor's wealth is relatively high, the optimal trading strategy consists in bringing the post-trade portfolio position inside the no-transaction region, whereas proportional transaction costs induce the investor trading to the boundary of the no-transaction region. We also examine the impact of the risky asset volatility and the risk aversion parameter on the shape of the no-transaction region. When comparing different transaction cost structures, we show that the financial securities' market tends to be more liquid with concave transaction costs than with alternative cost specifications.

Suggested Citation

  • Andriy Demchuk, 2002. "Portfolio Optimization with Concave Transaction Costs," FAME Research Paper Series rp103, International Center for Financial Asset Management and Engineering.
  • Handle: RePEc:fam:rpseri:rp103
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    File URL: http://www.swissfinanceinstitute.ch/rp103.pdf
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    References listed on IDEAS

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    1. C. Atkinson & P. Wilmott, 1995. "Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 357-367.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 35-51, February.
    4. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    5. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters,in: Theory Of Valuation, chapter 7, pages 207-227 World Scientific Publishing Co. Pte. Ltd..
    6. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
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    Cited by:

    1. repec:spr:compst:v:62:y:2005:i:2:p:319-343 is not listed on IDEAS
    2. Valeri Zakamouline, 2005. "A unified approach to portfolio optimization with linear transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 319-343, November.
    3. Valeri Zakamouline, 2004. "A Unified Approach to Portfolio Optimization with Linear Transaction Costs," GE, Growth, Math methods 0404003, EconWPA, revised 28 Apr 2004.

    More about this item

    Keywords

    concave transaction costs; optimal trading strategy;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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