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The Linear Fractional Portfolio Selection Problem

Author

Listed:
  • Bruce H. Faaland

    (University of Washington)

  • Nancy L. Jacob

    (University of Washington)

Abstract

A simplified portfolio selection criterion suggested by Sharpe and Mao involves choosing at most n securities from a universe of m securities in order to maximize the portfolio's excess-return-to-beta ratio. This paper examines alternative solution procedures to achieve this objective, including a gradient procedure whose continuous Knapsack subproblems in m bounded variables are solved in O(m) time. The effect on the optimal portfolio of increasing n is discussed, as well as the relationship between the excess-return-to-beta ratio of an individual security and that of the optimal portfolio. The paper concludes with computational experience on problems with n ranging from 10 to 200 and m from 500 to 1,245.

Suggested Citation

  • Bruce H. Faaland & Nancy L. Jacob, 1981. "The Linear Fractional Portfolio Selection Problem," Management Science, INFORMS, vol. 27(12), pages 1383-1389, December.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:12:p:1383-1389
    DOI: 10.1287/mnsc.27.12.1383
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