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

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  • Hill, Rowland R.

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.

Suggested Citation

  • Hill, Rowland R., 1976. "An Algorithm for Counting the Number of Possible Portfolios Given Linear Restrictions on the Weights," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(3), pages 479-480, September.
    • Handle: RePEc:cup:jfinqa:v:11:y:1976:i:03:p:479-480_02
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