IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v54y2019i4d10.1007_s10614-016-9600-5.html
   My bibliography  Save this article

Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation

Author

Listed:
  • Adeola Oyenubi

    (University of Cape Town)

Abstract

This paper provides a plausible explanation for why the optimum number of stocks in a portfolio is elusive, and suggests a way to determine this optimal number. Diversification has a lot to do with the number of stocks in a portfolio. Adding stocks to a portfolio increases the level of diversification, and consequently leads to risk reduction up to a certain number of stocks, beyond which additional stocks are of no benefit, in terms of risk reduction. To explain this phenomenon, this paper investigates the relationship between portfolio diversification and concentration using a genetic algorithm. To quantify diversification, we use the portfolio Diversification Index (PDI). In the case of concentration, we introduce a new quantification method. Concentration is quantified as complexity of the correlation matrix. The proposed method quantifies the level of dependency (or redundancy) between stocks in a portfolio. By contrasting the two methods it is shown that the optimal number of stocks that optimizes diversification depends on both number of stocks and average correlation. Our result shows that, for a given universe, there is a set of Pareto optimal portfolios containing a different number of stocks that simultaneously maximizes diversification and minimizes concentration. The choice portfolio among the Pareto set will depend on the preference of the investor. Our result also suggests that an ideal condition for the optimal number of stocks is when variance reduction benefit of diversification is off-set by the variance contribution of complexity.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:4:d:10.1007_s10614-016-9600-5
    DOI: 10.1007/s10614-016-9600-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-016-9600-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-016-9600-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. K. J. Martijn Cremers & Antti Petajisto, 2009. "How Active Is Your Fund Manager? A New Measure That Predicts Performance," The Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3329-3365, September.
    2. Doherr, Thorsten & Czarnitzki, Dirk, 2002. "Genetic algorithms: a tool for optimization in econometrics - basic concept and an example for empirical applications," ZEW Discussion Papers 02-41, ZEW - Leibniz Centre for European Economic Research.
    3. Martijn Cremers & Antti Petajisto, 2006. "How Active is Your Fund Manager? A New Measure That Predicts Performance," Yale School of Management Working Papers amz2370, Yale School of Management, revised 01 May 2009.
    4. John L. Evans & Stephen H. Archer, 1968. "Diversification And The Reduction Of Dispersion: An Empirical Analysis," Journal of Finance, American Finance Association, vol. 23(5), pages 761-767, December.
    5. Erkin Diyarbakırlıoğlu & Mehmet H Satman, 2013. "The Maximum Diversification Index," Journal of Asset Management, Palgrave Macmillan, vol. 14(6), pages 400-409, December.
    6. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 353-363, September.
    7. Michael Maschek, 2016. "Economic Modeling Using Evolutionary Algorithms: The Influence of Mutation on the Premature Convergence Effect," Computational Economics, Springer;Society for Computational Economics, vol. 47(2), pages 297-319, February.
    8. Erkin Diyarbakirlioglu & Mehmet Hakan Satman, 2014. "The maximum diversification index," Post-Print hal-01134593, HAL.
    9. Tang, Gordon Y. N., 2004. "How efficient is naive portfolio diversification? an educational note," Omega, Elsevier, vol. 32(2), pages 155-160, April.
    10. Ben Cooper, 2000. "orignal paper: Modelling research and development: How do firms solve design problems?," Journal of Evolutionary Economics, Springer, vol. 10(4), pages 395-413.
    11. 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.
    12. Ulrich Kirchner & Caroline Zunckel, 2011. "Measuring Portfolio Diversification," Papers 1102.4722, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christos Alexakis & Michael Dowling & Konstantinos Eleftheriou & Michael Polemis, 2021. "Textual Machine Learning: An Application to Computational Economics Research," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 369-385, January.
    2. 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.
    3. Jiawen Xu & Yixuan Li & Kai Liu & Tao Chen, 2023. "Portfolio selection: from under-diversification to concentration," Empirical Economics, Springer, vol. 64(4), pages 1539-1557, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.
    4. 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.
    5. Pi‐Hsia Hung & Donald Lien & Yun‐Ju Chien, 2020. "Portfolio concentration and fund manager performance," Review of Financial Economics, John Wiley & Sons, vol. 38(3), pages 423-451, July.
    6. Vitali Alexeev & Mardi Dungey, 2015. "Equity portfolio diversification with high frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1205-1215, July.
    7. 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.
    8. Vitali Alexeev & Mardi Dungey & Wenying Yao, 2016. "Continuous and Jump Betas: Implications for Portfolio Diversification," Econometrics, MDPI, vol. 4(2), pages 1-15, June.
    9. 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.
    10. 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.
    11. 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.
    12. Libin Yang & William Rea & Alethea Rea, 2015. "Stock Selection with Principal Component Analysis," Working Papers in Economics 15/03, University of Canterbury, Department of Economics and Finance.
    13. 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.
    14. 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.
    15. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    16. Chang, Xiaochen & Guo, Songlin & Huang, Junkai, 2022. "Kidnapped mutual funds: Irrational preference of naive investors and fund incentive distortion," International Review of Financial Analysis, Elsevier, vol. 83(C).
    17. Mercedes Alda, 2021. "The dilemma between fund‐style consistency and active management over the economic cycle. Evidence from pension funds," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2219-2240, April.
    18. Andrea Flori & Fabrizio Lillo & Fabio Pammolli & Alessandro Spelta, 2021. "Better to stay apart: asset commonality, bipartite network centrality, and investment strategies," Annals of Operations Research, Springer, vol. 299(1), pages 177-213, April.
    19. Javier Vidal-García & Marta Vidal & Sabri Boubaker & Riadh Manita, 2019. "Idiosyncratic risk and mutual fund performance," Annals of Operations Research, Springer, vol. 281(1), pages 349-372, October.
    20. Cristina Cella & Andrew Ellul & Mariassunta Giannetti, 2013. "Investors' Horizons and the Amplification of Market Shocks," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1607-1648.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:54:y:2019:i:4:d:10.1007_s10614-016-9600-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.