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How efficient is naive portfolio diversification? an educational note

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  • Tang, Gordon Y. N.

Abstract

Standard textbooks of Investment/Financial Management teach that although portfolio diversification can help reduce investment risk without sacrificing the expected rate of return, the benefit of diversification is exhausted with a portfolio size of 10-15. Since by then, most of the diversifiable risk is eliminated, leaving only the portion of systematic risk. How valid is this "common" knowledge? What is the exact value of "most" in the above statement? This paper examines the issue on naive (equal weight) diversification and analytically shows that for an infinite population of stocks, a portfolio size of 20 is required to eliminate 95% of the diversifiable risk on average. However, an addition of 80 stocks (i.e., a size of 100) is required to eliminate an extra 4% (i.e., 99% total) of diversifiable risk. This result depends neither on the investment horizons, sampling periods nor the markets involved.

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  • Tang, Gordon Y. N., 2004. "How efficient is naive portfolio diversification? an educational note," Omega, Elsevier, vol. 32(2), pages 155-160, April.
    • Handle: RePEc:eee:jomega:v:32:y:2004:i:2:p:155-160
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    1. Florian Methling & Rüdiger Nitzsch, 2019. "Naïve diversification in thematic investing: heuristics for the core satellite investor," Journal of Asset Management, Palgrave Macmillan, vol. 20(7), pages 568-580, December.
    2. K. Liagkouras & K. Metaxiotis, 2018. "A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem," Annals of Operations Research, Springer, vol. 267(1), pages 281-319, August.
    3. Luo, Cuicui & Seco, Luis & Wu, Lin-Liang Bill, 2015. "Portfolio optimization in hedge funds by OGARCH and Markov Switching Model," Omega, Elsevier, vol. 57(PA), pages 34-39.
    4. ALIU Florin & NUHIU Artor & KNAPKOVA Adriana & LUBISHTANI Ermal & TRAN Khang, 2021. "Do Cryptocurrencies Offer Diversification Benefits For Equity Portfolios?," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 16(2), pages 5-18, August.
    5. Vitali Alexeev & Mardi Dungey, 2015. "Equity portfolio diversification with high frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1205-1215, July.
    6. Azra Zaimovic & Adna Omanovic & Almira Arnaut-Berilo, 2021. "How Many Stocks Are Sufficient for Equity Portfolio Diversification? A Review of the Literature," JRFM, MDPI, vol. 14(11), pages 1-30, November.
    7. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    8. Vitali Alexeev & Katja Ignatieva, 2021. "Biases in variance of decomposed portfolio returns," International Review of Finance, International Review of Finance Ltd., vol. 21(4), pages 1152-1178, December.
    9. Gasser, Stephan M. & Rammerstorfer, Margarethe & Weinmayer, Karl, 2017. "Markowitz revisited: Social portfolio engineering," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1181-1190.
    10. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    11. Vitali Alexeev & Mardi Dungey & Wenying Yao, 2016. "Continuous and Jump Betas: Implications for Portfolio Diversification," Econometrics, MDPI, vol. 4(2), pages 1-15, June.
    12. Hyung, Namwon & de Vries, Casper G., 2012. "Simulating and calibrating diversification against black swans," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1162-1175.
    13. Adeola Oyenubi, 2019. "Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1443-1471, December.
    14. Florin Aliu & Besnik Krasniqi & Adriana Knapkova & Fisnik Aliu, 2019. "Interdependence and Risk Comparison of Slovak, Hungarian and Polish Stock Markets: Policy and Managerial Implications," Acta Oeconomica, Akadémiai Kiadó, Hungary, vol. 69(2), pages 273-287, June.
    15. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.
    16. Florian Methling & Rüdiger Nitzsch, 2020. "Tailor-made thematic portfolios: a core satellite optimization," Journal of Global Optimization, Springer, vol. 76(2), pages 317-331, February.
    17. K. Liagkouras & K. Metaxiotis & G. Tsihrintzis, 2022. "Incorporating environmental and social considerations into the portfolio optimization process," Annals of Operations Research, Springer, vol. 316(2), pages 1493-1518, September.
    18. Francesco Cesarone & Jacopo Moretti & Fabio Tardella, 2016. "Optimally chosen small portfolios are better than large ones," Economics Bulletin, AccessEcon, vol. 36(4), pages 1876-1891.
    19. K. Liagkouras & K. Metaxiotis, 2019. "Improving the performance of evolutionary algorithms: a new approach utilizing information from the evolutionary process and its application to the fuzzy portfolio optimization problem," Annals of Operations Research, Springer, vol. 272(1), pages 119-137, January.
    20. Alexeev, Vitali & Tapon, Francis, 2013. "Equity Portfolio Diversification: How Many Stocks are Enough? Evidence from Five Developed Markets," Working Papers 2013-16, University of Tasmania, Tasmanian School of Business and Economics, revised 20 Nov 2013.
    21. Vitali Alexeev & Francis Tapon, 2014. "The number of stocks in your portfolio should be larger than you think: diversification evidence from five developed markets," Published Paper Series 2014-4, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    22. Syed Zakir Abbas ZAIDI*, 2017. "Determinants Of Stocks For Optimal Portfolio," Pakistan Journal of Applied Economics, Applied Economics Research Centre, vol. 27(1), pages 1-27.
    23. Namwon Hyung & Casper G. de Vries, 2010. "The Downside Risk of Heavy Tails induces Low Diversification," Tinbergen Institute Discussion Papers 10-082/2, Tinbergen Institute.

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