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Optimal Portfolio Revision with a Proportional Transaction Cost

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  • Jules H. Kamin

    (Dart Industries and the University of California, Los Angeles)

Abstract

The theory of the optimal investment decision is reexamined for a case in which the portfolio initialization problem is trivial but the portfolio adjustment decision presents some new and important problems. The investor is assumed to be a risk-averse expected utility maximizer whose portfolio consists of two risky assets. His objective is to maximize his expected utility at some time horizon, and there is a transaction cost for intermediate adjustment of the portfolio proportional to the value of assets traded. The solution for the optimum adjustment strategy consists of a set of pairs of control limits for the ratio of the amounts of the assets in the portfolio, one pair for each decision opportunity. The model falls naturally into the class of "cash balance" and dynamic portfolio selection models. The most important departure from both of these subclasses of models is the explicit consideration of more than one risky asset in the portfolio together with the transaction cost. The introduction of the transaction cost implies investor behavior which is systematically different from that implied by the no-transaction-cost dynamic portfolio selection models. The implied behavior is, however, quite similar in form to that implied by the cash-balance models, in which the objective is expected cost minimization.

Suggested Citation

  • Jules H. Kamin, 1975. "Optimal Portfolio Revision with a Proportional Transaction Cost," Management Science, INFORMS, vol. 21(11), pages 1263-1271, July.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:11:p:1263-1271
    DOI: 10.1287/mnsc.21.11.1263
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    Cited by:

    1. Jagriti Srivastava & Pankaj Kumar Baag, 2019. "Positive Accounting Theory, Agency Costs And Accountng Regulation," Working papers 346, Indian Institute of Management Kozhikode.
    2. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    3. Peter Schober & Julian Valentin & Dirk Pflüger, 2022. "Solving High-Dimensional Dynamic Portfolio Choice Models with Hierarchical B-Splines on Sparse Grids," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 185-224, January.
    4. Reuven Glick, 1984. "The Geometry Of Asset Adjustment With Adjustment Costs," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 7(4), pages 303-314, December.
    5. Yongyang Cai & Kenneth L. Judd & Rong Xu, 2013. "Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs," NBER Working Papers 18709, National Bureau of Economic Research, Inc.
    6. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.
    7. Jongbin Jung & Seongmoon Kim, 2017. "Developing a dynamic portfolio selection model with a self-adjusted rebalancing method," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 766-779, July.
    8. Girlich, Hans-Joachim, 2003. "Transaction costs in finance and inventory research," International Journal of Production Economics, Elsevier, vol. 81(1), pages 341-350, January.
    9. Framstad, Nils Chr., 2014. "The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model," Memorandum 25/2014, Oslo University, Department of Economics.

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