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

Authors


  • I am deeply grateful to Fred D. Arditti who introduced me to this area and provided many valuable insights. For discussions and suggestions, I am also indebted to Sudipto Bhattacharya, Avner Kalay, Stanley Kon, Antal Majthay and Marti Subrahmanyam. Helpful comments by Michael Brennan of this journal are also acknowledged. This work was supported by a Faculty Research Grant from the Graduate School of Business Administration. New York University.

ABSTRACT

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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