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


  • 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.


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.