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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.

has been cited by the following article:

• TITLE: Portfolio Size in Stochastic Portfolio Networks Using Digital Portfolio Theory

  AUTHORS: C. Kenneth Jones

  KEYWORDS: Finance; Portfolio Optimization; Portfolio Networks; Asset Allocation; Investment Diversification; Digital Signal Processing; Mixed Integer Programming

  JOURNAL NAME: Journal of Mathematical Finance, Vol.3 No.2, May 24, 2013

  ABSTRACT: 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.