A Linear Programming Algorithm for Mutual Fund Portfolio Selection

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Abstract
The portfolio selection problem faced by a mutual fund manager can be formulated following the Markowitz approach: find those portfolios that are efficient in terms of predicted expected return and standard deviation of return, subject to legal constraints in the form of upper bounds on the proportion of the fund invested in any single security. This paper suggests that such problems be re-formulated as parametric linear-programming problems, utilizing a linear approximation to the true (quadratic) formula for a portfolio's risk. Limited empirical evidence suggests that the approximation is acceptable. Moreover, it allows the use of an extremely simple and efficient special-purpose solution algorithm. With appropriate modifications, this algorithm may prove useful to the managers of mutual funds with a wide variety of objectives.

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