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Portfolio Size in Stochastic Portfolio Networks Using Digital Portfolio Theory

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DOI: 10.4236/jmf.2013.32028    6,155 Downloads   10,761 Views   Citations


The investment portfolio with stochastic returns can be represented as a maximum flow generalized network with stochastic multipliers. Modern portfolio theory (MPT) [1] provides a myopic short horizon solution to this network by adding a parametric variance constraint to the maximize flow objective function. MPT does not allow the number of securities in solution portfolios to be specified. Integer constraints to control portfolio size in MPT results in a nonlinear mixed integer problem and is not practical for large universes. Digital portfolio theory (DPT) [2] finds a non-myopic long-term solution to the nonparametric variance constrained portfolio network. This paper discusses the long horizon nature of DPT and adds zero-one (0-1) variables to control portfolio size. We find optimal size constrained allocations from a universe of US sector indexes. The feasible size of optimal portfolios depends on risk. Large optimal portfolios are infeasible for low risk investors. High risk investors can increase portfolio size and diversification with little effect on return.

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The authors declare no conflicts of interest.

Cite this paper

C. Jones, "Portfolio Size in Stochastic Portfolio Networks Using Digital Portfolio Theory," Journal of Mathematical Finance, Vol. 3 No. 2, 2013, pp. 280-290. doi: 10.4236/jmf.2013.32028.


[1] H. M. Markowitz, “Portfolio Selection,” Journal of Finance, Vol. 7 No. 1, 1952, pp. 77-91.
[2] C. K. Jones, “Digital Portfolio Theory,” Journal of Computational Economics, Vol. 18, No. 3, 2001, pp. 287-316. doi:10.1023/A:1014824005585
[3] C. K. Jones, “Fixed Trading Costs, Signal Processing and Stochastic Portfolio Networks,” European Journal of Industrial Engineering, Vol. 1, No. 1, 2007, pp. 5-21. doi:10.1504/EJIE.2007.012651
[4] C. K. Jones, “Portfolio Selection in the Frequency Domain,” American Institute of Decision Sciences Proceedings, 1983.
[5] F. Glover and C. K. Jones, “A Stochastic Generalized Network Model and Large-Scale Mean-Variance Algorithm for Portfolio Selection,” Journal of Information and Optimization Sciences, Vol. 9, No. 3, 1988, pp. 299-316.
[6] C. K. Jones, “Portfolio Management: New Model for Successful Investment,” McGraw-Hill, London, 1992.
[7] S. M. Kay, “Fundamentals of Statistical Signal Processing: Volume II Detection Theory,” Prentice-Hall, New Jersey, 1998.
[8] P. A. Samuelson, “The Backward Art of Investing Money,” The Journal of Portfolio Management, Vol. 30, No. 5, 2004, pp. 30-33.
[9] C. K. Jones, “Calendar Based Risk, Firm Size, and the Random Walk Hypothesis,” Working Paper, 2004.
[10] M. N. Broadie, “Portfolio Management: New Models for Successful Investment Decisions,” Journal of Finance, Vol. 49, No. 1, 1994, pp. 361-364. doi:10.2307/2329151
[11] C. K. Jones, “PSS Release 2.0: Digital Portfolio Theory,” Portfolio Selection Systems, Gainesville, 1997.

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