Efficient Funds in a Financial Market with Options: a New Irrelevance Proposition

  • Author(s): KOSE JOHN
  • Published: Apr 30, 2012
  • Pages: 685-695
  • DOI: 10.1111/j.1540-6261.1981.tb00653.x


Under the same assumptions that Ross used to assert the existence of an efficient fund (on which a spanning set of options can be written) we prove that almost any portfolio is an efficient fund. From a constructive point of view, a randomly chosen vector of portfolio weights yields an efficient fund. When the Ross assumptions are relaxed, a limited notion of efficiency—maximal efficiency—is the best attainable. The maximally efficient funds are also everywhere dense in the portfolio space. Some implications are discussed and illustrative examples given.

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