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A Mean-Variance Analysis of Self-Financing Portfolios

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  • Bob Korkie

    (Department of Finance and Management Science, University of Alberta, Edmonton, Alberta, Canada T6G 2R6, and OPSEU Pension Trust, Adelaide Street E 1200, Toronto, Ontario, Canada M5C 3A7)

  • Harry J. Turtle

    (Department of Finance, Insurance, and Real Estate, College of Business and Economics, Washington State University, Pullman, Washington 99164-4746)

Abstract

This paper develops the analytics and geometry of the investment opportunity set (IOS) and the test statistics for self-financing portfolios. A self-financing portfolio is a set of long and short investments such that the sum of their investment weights, or net investment, is zero. This contrasts with a standard portfolio that has investment weights summing to one. Examples of self-financing portfolios are hedges, overlays, arbitrage portfolios, swaps, and long/short portfolios. A standard portfolio plus the IOS of self-financing portfolios form a restricted IOS hyperbola with restricted efficient set constants that differ from the usual constants. The restrictions affect statistical tests of portfolio efficiency, which are developed for the self-financing restrictions. As an application, we consider the self-financing portfolios formed by Fama and French (1992, 1993, 1995), based on market capitalization and value. In contrast to Fama and French (1992, 1993, 1995), we find that their restricted IOS is significantly different from the unrestricted IOS with the implication that the Fama-French tests are misspecified.

Suggested Citation

  • Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:3:p:427-443
    DOI: 10.1287/mnsc.48.3.427.7725
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    References listed on IDEAS

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    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    7. Bai, Zhidong & Li, Hua & Wong, Wing-Keung, 2013. "The best estimation for high-dimensional Markowitz mean-variance optimization," MPRA Paper 43862, University Library of Munich, Germany.
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    10. Joel M. Vanden, 2021. "Equilibrium asset pricing and the cross section of expected returns," Annals of Finance, Springer, vol. 17(2), pages 153-186, June.
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