IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v282y2019i1d10.1007_s10479-018-2896-x.html
   My bibliography  Save this article

Managing portfolio diversity within the mean variance theory

Author

Listed:
  • Anatoly B. Schmidt

    (Kensho Technologies, Inc, One World Trade Center
    NYU School of Engineering)

Abstract

It is well documented that the classical mean variance theory (MVT) may yield portfolios (MVTP) that are highly concentrated and/or are outperformed by equal weight portfolios (EWP). In this work, it is proposed to expand the MVT minimizing objective function with an additional term that explicitly controls portfolio diversity (diversity booster DB). DB decreases with growing number of non-zero portfolio weights and has a minimum when all weights are equal. As a result, high values of DB yield EWP. For performance analysis, portfolio constructed with 12 major US equity ETFs is considered. Out-of-sample performance of maximum Sharpe portfolios is tested using statistics of bootstrapped Sharpe ratios for monthly rebalancing periods. It is found that for the 3-year calibrating window, the diversified MVT portfolio (DMVTP) outperformed both MVTP and EWP in 2012–2015. While the MVTP weights were highly concentrated and had sharp jumps between rebalancing periods, the DMVTP weights slowly changed with time.

Suggested Citation

  • Anatoly B. Schmidt, 2019. "Managing portfolio diversity within the mean variance theory," Annals of Operations Research, Springer, vol. 282(1), pages 315-329, November.
    • Handle: RePEc:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-2896-x
    DOI: 10.1007/s10479-018-2896-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2896-x
    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/s10479-018-2896-x?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. 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. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    3. Pérignon, Christophe & Smith, Daniel R., 2010. "Diversification and Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 55-66, January.
    4. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    5. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    6. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    7. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    8. Denvir, Emily & Hutson, Elaine, 2006. "The performance and diversification benefits of funds of hedge funds," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 16(1), pages 4-22, February.
    9. repec:dau:papers:123456789/4688 is not listed on IDEAS
    10. DeMiguel, Victor & Plyakha, Yuliya & Uppal, Raman & Vilkov, Grigory, 2013. "Improving Portfolio Selection Using Option-Implied Volatility and Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(6), pages 1813-1845, December.
    11. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
    12. Sankaran, Jayaram K. & Patil, Ajay A., 1999. "On the optimal selection of portfolios under limited diversification," Journal of Banking & Finance, Elsevier, vol. 23(11), pages 1655-1666, November.
    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. Francisco Fernández-Navarro & Luisa Martínez-Nieto & Mariano Carbonero-Ruz & Teresa Montero-Romero, 2021. "Mean Squared Variance Portfolio: A Mixed-Integer Linear Programming Formulation," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    2. Chen, Wei & Zhang, Haoyu & Jia, Lifen, 2022. "A novel two-stage method for well-diversified portfolio construction based on stock return prediction using machine learning," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    3. Syed Kumail Abbas Rizvi & Bushra Naqvi & Nawazish Mirza, 2022. "Is green investment different from grey? Return and volatility spillovers between green and grey energy ETFs," Annals of Operations Research, Springer, vol. 313(1), pages 495-524, June.
    4. Naqvi, Bushra & Rizvi, Syed Kumail Abbas & Hasnaoui, Amir & Shao, Xuefeng, 2022. "Going beyond sustainability: The diversification benefits of green energy financial products," Energy Economics, Elsevier, vol. 111(C).
    5. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    6. Naqvi, Bushra & Mirza, Nawazish & Rizvi, Syed Kumail Abbas & Porada-Rochoń, Małgorzata & Itani, Rania, 2021. "Is there a green fund premium? Evidence from twenty seven emerging markets," Global Finance Journal, Elsevier, vol. 50(C).

    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. Hwang, Inchang & Xu, Simon & In, Francis, 2018. "Naive versus optimal diversification: Tail risk and performance," European Journal of Operational Research, Elsevier, vol. 265(1), pages 372-388.
    2. 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.
    3. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    4. Haotian Cai & Anatoly B. Schmidt, 0. "Comparing mean–variance portfolios and equal-weight portfolios for major US equity indexes," Journal of Asset Management, Palgrave Macmillan, vol. 0, pages 1-7.
    5. Huang, Wei & Liu, Qianqiu & Ghon Rhee, S. & Wu, Feng, 2012. "Extreme downside risk and expected stock returns," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1492-1502.
    6. Yang, Junmin & Cao, Zhiguang & Han, Qiheng & Wang, Qiyu, 2019. "Tactical asset allocation on technical trading rules and data snooping," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    7. Stein, Tobias, 2024. "Forecasting the equity premium with frequency-decomposed technical indicators," International Journal of Forecasting, Elsevier, vol. 40(1), pages 6-28.
    8. Qi Xu & Ying Wang, 2021. "Managing volatility in commodity momentum," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 758-782, May.
    9. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    10. Hsu, Po-Hsuan & Han, Qiheng & Wu, Wensheng & Cao, Zhiguang, 2018. "Asset allocation strategies, data snooping, and the 1 / N rule," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 257-269.
    11. Byers, J.W. & Popova, I. & Simkins, B.J., 2021. "Robust estimation of conditional risk measures using machine learning algorithm for commodity futures prices in the presence of outliers," Journal of Commodity Markets, Elsevier, vol. 24(C).
    12. Haotian Cai & Anatoly B. Schmidt, 2020. "Comparing mean–variance portfolios and equal-weight portfolios for major US equity indexes," Journal of Asset Management, Palgrave Macmillan, vol. 21(4), pages 326-332, July.
    13. Peralta, Gustavo & Zareei, Abalfazl, 2016. "A network approach to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 157-180.
    14. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    15. Gourieroux, C. & Monfort, A., 2005. "The econometrics of efficient portfolios," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 1-41, January.
    16. Dan Anghel, 2013. "How Reliable is the Moving Average Crossover Rule for an Investor on the Romanian Stock Market?," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 5(2), pages 089-115, December.
    17. Yi Huang & Wei Zhu & Duan Li & Shushang Zhu & Shikun Wang, 2023. "Integrating Different Informations for Portfolio Selection," Papers 2305.17881, arXiv.org.
    18. Jun Yuan & Qi Xu & Ying Wang, 2023. "Probability weighting in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(4), pages 516-548, April.
    19. Shynkevich, Andrei, 2013. "Time-series momentum as an intra- and inter-industry effect: Implications for market efficiency," Journal of Economics and Business, Elsevier, vol. 69(C), pages 64-85.
    20. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.

    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:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-2896-x. 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.