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The numeraire portfolio: a new perspective on financial theory

  • I. Bajeux-Besnainou
  • R. Portait
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    The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the 'true' (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.

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    Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

    Volume (Year): 3 (1997)
    Issue (Month): 4 ()
    Pages: 291-309

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    Handle: RePEc:taf:eurjfi:v:3:y:1997:i:4:p:291-309
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    1. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    2. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    3. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
    4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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