An Algorithm for Counting the Number of Possible Portfolios Given Linear Restrictions on the Weights

Rowland R. Hill

Journal of Financial and Quantitative Analysis, 1976, vol. 11, issue 3, 479-480

Abstract: In application of portfolio selection algorithms [3,4] and in tests of the effectiveness of these approaches [1,2], it is sometimes useful to know, a priori, the size of the set of possible portfolios that may be encountered. Given a set of linear restrictions such as that worked by Frankfurter, Phillips, and Seagle [1,2], the set of possible portfolios is finite. This note presents a simple algorithm for determining the size of this set. Only two inputs are required:1. The size of the universe of securities under study, and2. A functional relationship which acts as a constraint on the weights.The following is a heuristic algorithm without a rigorous, generalized proof.

Date: 1976
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