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Portfolio Return Relative to a Benchmark

Author

Listed:
  • Aleksandr Alekseev
  • Mikhail Sokolov

Abstract

Benchmarking is a universal practice in portfolio management and is well-studied in the optimal portfolio selection literature. This paper derives axiomatic foundations for a benchmark-based evaluation, which is generally grounded on the relative return. We show that the existence of a benchmark naturally arises from a few basic axioms and is tightly linked to the economic theory. Our method relies on the use of both axiomatic and economic approaches to index number theory. We also analyze the problem of optimal portfolio selection under complete uncertainty about a future price system, where the objective function is the relative return.

Suggested Citation

  • Aleksandr Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series 2016/04, European University at St. Petersburg, Department of Economics.
    • Handle: RePEc:eus:wpaper:ec2016_04
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    References listed on IDEAS

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    1. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    2. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    3. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
    4. Juan‐Pedro Gómez & Richard Priestley & Fernando Zapatero, 2009. "Implications of Keeping‐Up‐with‐the‐Joneses Behavior for the Equilibrium Cross Section of Stock Returns: International Evidence," Journal of Finance, American Finance Association, vol. 64(6), pages 2703-2737, December.
    5. Juan Enrique Martínez-Legaz & Alexander M. Rubinov & Siegfried Schaible, 2005. "Increasing quasiconcave co-radiant functions with applications in mathematical economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 261-280, June.
    6. Admati, Anat R & Pfleiderer, Paul, 1997. "Does It All Add Up? Benchmarks and the Compensation of Active Portfolio Managers," The Journal of Business, University of Chicago Press, vol. 70(3), pages 323-350, July.
    7. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, January.
    8. Kenneth B. Gray, Jr. & Robert B. K. Dewar, 1971. "Axiomatic Characterization of the Time-Weighted Rate of Return," Management Science, INFORMS, vol. 18(2), pages 32-35, October.
    9. David Promislow, S. & Spring, David, 1996. "Postulates for the internal rate of return of an investment project," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 325-361.
    10. Diana Barro & Elio Canestrelli, 2009. "Tracking error: a multistage portfolio model," Annals of Operations Research, Springer, vol. 165(1), pages 47-66, January.
    11. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    12. Gali, Jordi, 1994. "Keeping Up with the Joneses: Consumption Externalities, Portfolio Choice, and Asset Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 26(1), pages 1-8, February.
    13. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
    14. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    15. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    16. Alexeev, Alexander G. & Sokolov, Mikhail V., 2014. "A theory of average growth rate indices," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 101-115.
    17. Grossman, Sanford J & Zhou, Zhongquan, 1996. "Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
    18. 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.
    19. Sudhir A. Shah, 2007. "Dual Representations Of Strongly Monotonic Utility Functions," Working papers 161, Centre for Development Economics, Delhi School of Economics.
    20. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    21. Rothstein, Marvin, 1972. "On Geometric and Arithmetic Portfolio Performance Indexes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1983-1992, September.
    22. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-1090.
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    More about this item

    Keywords

    portfolio performance; compound annual growth rate; benchmarking; index number theory; portfolio choice under uncertainty;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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