IDEAS home Printed from
   My bibliography  Save this article

Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification


  • Prayut Jain

    () (Department of Mathematics, Indian Institute of Science, Bengaluru 560012, India)

  • Shashi Jain

    () (Department of Management Studies, Indian Institute of Science, Bengaluru 560012, India)


The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance matrix, however, it does not require its invertibility. In this paper, we first study the impact of covariance misspecification on the performance of the different allocation methods. Next, we study under an appropriate covariance forecast model whether the machine learning based HRP outperforms the traditional risk-based portfolios. For our analysis, we use the test for superior predictive ability on out-of-sample portfolio performance, to determine whether the observed excess performance is significant or if it occurred by chance. We find that when the covariance estimates are crude, inverse volatility weighted portfolios are more robust, followed by the machine learning-based portfolios. Minimum variance and maximum diversification are most sensitive to covariance misspecification. HRP follows the middle ground; it is less sensitive to covariance misspecification when compared with minimum variance or maximum diversification portfolio, while it is not as robust as the inverse volatility weighed portfolio. We also study the impact of the different rebalancing horizon and how the portfolios compare against a market-capitalization weighted portfolio.

Suggested Citation

  • Prayut Jain & Shashi Jain, 2019. "Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification," Risks, MDPI, Open Access Journal, vol. 7(3), pages 1-27, July.
  • Handle: RePEc:gam:jrisks:v:7:y:2019:i:3:p:74-:d:245327

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Carlos Trucíos & Mauricio Zevallos & Luiz K. Hotta & André A. P. Santos, 2019. "Covariance Prediction in Large Portfolio Allocation," Econometrics, MDPI, Open Access Journal, vol. 7(2), pages 1-24, May.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. Martin Martens, 2002. "Measuring and forecasting S&P 500 index‐futures volatility using high‐frequency data," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 22(6), pages 497-518, June.
    4. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    5. David Ardia & Guido Bolliger & Kris Boudt & Jean-Philippe Gagnon-Fleury, 2017. "The impact of covariance misspecification in risk-based portfolios," Annals of Operations Research, Springer, vol. 254(1), pages 1-16, July.
    6. Philippe Bertrand & Vincent Lapointe, 2018. "Risk-based strategies: the social responsibility of investment universes does matter," Annals of Operations Research, Springer, vol. 262(2), pages 413-429, March.
    7. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    8. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    9. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    10. Goncalves, Silvia & de Jong, Robert, 2003. "Consistency of the stationary bootstrap under weak moment conditions," Economics Letters, Elsevier, vol. 81(2), pages 273-278, November.
    11. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    12. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Illya Barziy & Marcin Chlebus, 2020. "HRP performance comparison in portfolio optimization under various codependence and distance metrics," Working Papers 2020-21, Faculty of Economic Sciences, University of Warsaw.
    2. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2020. "Company classification using machine learning," Papers 2004.01496,, revised May 2020.

    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. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
    2. Massimiliano Caporin & Michael McAleer, 2011. "Ranking Multivariate GARCH Models by Problem Dimension: An Empirical Evaluation," Working Papers in Economics 11/23, University of Canterbury, Department of Economics and Finance.
    3. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    4. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Kim, Jong-Min & Jung, Hojin, 2016. "Linear time-varying regression with Copula–DCC–GARCH models for volatility," Economics Letters, Elsevier, vol. 145(C), pages 262-265.
    6. Yudong Wang & Chongfeng Wu & Li Yang, 2015. "Hedging with Futures: Does Anything Beat the Naïve Hedging Strategy?," Management Science, INFORMS, vol. 61(12), pages 2870-2889, December.
    7. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224, October.
    8. Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2015. "Testing for structural breaks in correlations: Does it improve Value-at-Risk forecasting?," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 135-152.
    9. Harris, Richard D.F. & Nguyen, Anh, 2013. "Long memory conditional volatility and asset allocation," International Journal of Forecasting, Elsevier, vol. 29(2), pages 258-273.
    10. Yudong Wang & Li Liu, 2016. "Crude oil and world stock markets: volatility spillovers, dynamic correlations, and hedging," Empirical Economics, Springer, vol. 50(4), pages 1481-1509, June.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    12. Marchese, Malvina & Kyriakou, Ioannis & Tamvakis, Michael & Di Iorio, Francesca, 2020. "Forecasting crude oil and refined products volatilities and correlations: New evidence from fractionally integrated multivariate GARCH models," Energy Economics, Elsevier, vol. 88(C).
    13. Audrino, Francesco, 2014. "Forecasting correlations during the late-2000s financial crisis: The short-run component, the long-run component, and structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 43-60.
    14. Clements, A. & Silvennoinen, A., 2013. "Volatility timing: How best to forecast portfolio exposures," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 108-115.
    15. Hung, Jui-Cheng, 2015. "Evaluation of realized multi-power variations in minimum variance hedging," Economic Modelling, Elsevier, vol. 51(C), pages 672-679.
    16. Becker, R. & Clements, A.E. & Doolan, M.B. & Hurn, A.S., 2015. "Selecting volatility forecasting models for portfolio allocation purposes," International Journal of Forecasting, Elsevier, vol. 31(3), pages 849-861.
    17. Erik Kole & Thijs Markwat & Anne Opschoor & Dick van Dijk, 2017. "Forecasting Value-at-Risk under Temporal and Portfolio Aggregation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(4), pages 649-677.
    18. Allen, David & Lizieri, Colin & Satchell, Stephen, 2020. "A comparison of non-Gaussian VaR estimation and portfolio construction techniques," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 356-368.
    19. Ruili Sun & Tiefeng Ma & Shuangzhe Liu, 2020. "Portfolio selection: shrinking the time-varying inverse conditional covariance matrix," Statistical Papers, Springer, vol. 61(6), pages 2583-2604, December.
    20. David Gabauer, 2020. "Volatility impulse response analysis for DCC‐GARCH models: The role of volatility transmission mechanisms," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(5), pages 788-796, August.

    More about this item


    machine learning for portfolio; covariance misspecification; superior predictive ability; NIFTY;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law


    Access and download statistics


    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:gam:jrisks:v:7:y:2019:i:3:p:74-:d:245327. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.