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Which portfolio is better? A discussion of several possible comparison criteria

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  • Henryk Gzyl
  • Alfredo Rios

Abstract

During the last few years, there has been an interest in comparing simple or heuristic procedures for portfolio selection, such as the naive, equal weights, portfolio choice, against more "sophisticated" portfolio choices, and in explaining why, in some cases, the heuristic choice seems to outperform the sophisticated choice. We believe that some of these results may be due to the comparison criterion used. It is the purpose of this note to analyze some ways of comparing the performance of portfolios. We begin by analyzing each criterion proposed on the market line, in which there is only one random return. Several possible comparisons between optimal portfolios and the naive portfolio are possible and easy to establish. Afterwards, we study the case in which there is no risk free asset. In this way, we believe some basic theoretical questions regarding why some portfolios may seem to outperform others can be clarified.

Suggested Citation

  • Henryk Gzyl & Alfredo Rios, 2018. "Which portfolio is better? A discussion of several possible comparison criteria," Papers 1805.06345, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:1805.06345
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    References listed on IDEAS

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    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
    3. James Thompson & L. Baggett & William Wojciechowski & Edward Williams, 2006. "Nobels for nonsense," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 29(1), pages 3-18.
    4. Philip Ernst & James Thompson & Yinsen Miao, 2016. "Portfolio Selection: The Power of Equal Weight," Papers 1602.00782, arXiv.org, revised Aug 2017.
    5. Kirby, Chris & Ostdiek, Barbara, 2012. "It’s All in the Timing: Simple Active Portfolio Strategies that Outperform Naïve Diversification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(2), pages 437-467, April.
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