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A Mean-Variance Analysis of Self-Financing Portfolios

Author

Listed:
  • 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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    Cited by:

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    3. Fang, Shuhong, 2007. "A Mean–variance analysis of arbitrage portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 625-632.
    4. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    5. Yan Liu & Ngai Hang Chan & Chi Tim Ng & Samuel Po Shing Wong, 2016. "Shrinkage Estimation Of Mean-Variance Portfolio," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-25, February.
    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    7. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2016. "Management Science, Economics and Finance: A Connection," Tinbergen Institute Discussion Papers 16-040/III, Tinbergen Institute.
    8. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    9. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Econometric Institute Research Papers 18-024/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Han, Yufeng & Zhou, Guofu & Zhu, Yingzi, 2016. "A trend factor: Any economic gains from using information over investment horizons?," Journal of Financial Economics, Elsevier, vol. 122(2), pages 352-375.
    11. Bodnar Taras & Schmid Wolfgang, 2011. "On the exact distribution of the estimated expected utility portfolio weights: Theory and applications," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 319-342, December.
    12. Frank Schuhmacher & Hendrik Kohrs & Benjamin R. Auer, 2021. "Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed," Management Science, INFORMS, vol. 67(12), pages 7812-7824, December.
    13. 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.
    14. 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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