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Multiperiod portfolio selection with transaction and market-impact costs

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  • Víctor de Miguel

    ()

  • Xiaoling Mei

    ()

  • Francisco J. Nogales

    ()

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    Abstract

    We carry out an analytical investigation on the optimal portfolio policy for a multiperiod mean-variance investor facing multiple risky assets. We consider the case with proportional, market impact, and quadratic transaction costs. For proportional transaction costs, we find that a buy-and-hold policy is optimal: if the starting portfolio is outside a parallelogram-shaped no-trade region, then trade to the boundary of the no-trade region at the first period, and hold this portfolio thereafter. For market impact costs, we show that the optimal portfolio policy at each period is to trade to the boundary of a state-dependent movement region. Moreover, we find that the movement region shrinks along the investment horizon, and as a result the investor trades throughout the entire investment horizon. Finally, we show numerically that the utility loss associated with ignoring transaction costs or investing myopically may be large

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    File URL: http://e-archivo.uc3m.es/bitstream/10016/16996/1/ws131615.pdf
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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws131615.

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    Date of creation: May 2013
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    Handle: RePEc:cte:wsrepe:ws131615

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    Related research

    Keywords: Portfolio optimization; Multiperiod utility; No-trade region;

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    1. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
    2. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
    3. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    4. 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.
    5. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    6. George M. Constantinides, 1979. "Multiperiod Consumption and Investment Behavior with Convex Transactions Costs," Management Science, INFORMS, vol. 25(11), pages 1127-1137, November.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
    8. Hong Liu, 2004. "Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets," Journal of Finance, American Finance Association, vol. 59(1), pages 289-338, 02.
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