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Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

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  • Sait Tunc
  • Suleyman S. Kozat

Abstract

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.

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  • Sait Tunc & Suleyman S. Kozat, 2012. "Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach," Papers 1203.4156, arXiv.org.
    • Handle: RePEc:arx:papers:1203.4156
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    References listed on IDEAS

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    1. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    2. Garud Iyengar, 2005. "Universal Investment In Markets With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 359-371, April.
    3. David P. Helmbold & Robert E. Schapire & Yoram Singer & Manfred K. Warmuth, 1998. "On‐Line Portfolio Selection Using Multiplicative Updates," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 325-347, October.
    4. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    5. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
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    Cited by:

    1. Fotis Papailias & Dimitrios Thomakos, 2015. "Covariance averaging for improved estimation and portfolio allocation," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(1), pages 31-59, February.

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