Portfolio Management and the Shrinking Knapsack Algorithm

Bernell K. Stone and Ned C. Hill

Journal of Financial and Quantitative Analysis, 1979, vol. 14, issue 5, 1071-1083

Abstract: Since the formulation of the portfolio selection problem by Markowitz [12] as a parametric quadratic programming problem, considerable effort has been devoted to obtaining operational portfolio management models. Research has involved: (1) characterizing the return generating process in terms of index models; (2) specifying special-purpose algorithms such as the critical-line method of Markowitz [13] or the solution procedure of Jucker and de Faro [11]; (3) using linear programming formulations to approximate solutions to the nonlinear programming problems such as Sharpe [20, 22] and Stone [25]; and (4) converting portfolio selection models into portfolio management models designed to revise an existing protfolio subject to transaction costs using heuristics such as Smith [24] or revision formulations such as Pogue [16, 17] and Stone and Reback [27].

Date: 1979
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