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

Published online by Cambridge University Press:  19 October 2009

Rowland R. Hill
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Extract

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, and

2. A functional relationship which acts as a constraint on the weights.

The following is a heuristic algorithm without a rigorous, generalized proof.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 11 , Issue 3 , September 1976 , pp. 479 - 480
Copyright
Copyright © School of Business Administration, University of Washington 1976

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References

REFERENCES

[1]Frankfurter, George M.; Phillips, Herbert E.; and Seagle, John P.. “Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances.” Journal of Financial and Quantitative Analysis, vol. 6 (December 1971), pp. 1251–1262.Google Scholar
[2]Frankfurter, George M. “Performance of the Sharpe Portfolio Selection Model: A Comparison.” Journal of Financial and Quantitative Analysis (June 1976).Google Scholar
[3]Markowitz, Harry M. “Portfolio Selection.” Journal of Finance, vol. 1 (March 1952), pp. 77–91.Google Scholar
[4]Sharpe, William F. “A Simplified Model for Portfolio Analysis.” Management Science, vol. 9 (January 1963), pp. 277–293.CrossRefGoogle Scholar