The impact of covariance misspecification in risk-based portfolios

Annals of Operations Research volume 254, pages1–16(2017)Cite this article

Abstract

The equal-risk-contribution, inverse-volatility weighted, maximum-diversification and minimum-variance portfolio weights are all direct functions of the estimated covariance matrix. We perform a Monte Carlo study to assess the impact of covariance matrix misspecification to these risk-based portfolios at the daily, weekly and monthly forecasting horizon. Our results show that the equal-risk-contribution and inverse-volatility weighted portfolio weights are relatively robust to covariance misspecification. In contrast, the minimum-variance portfolio weights are highly sensitive to errors in both the estimated variances and correlations, while errors in the estimated correlations can have a large effect on the weights of the maximum-diversification portfolio.

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Notes

  1. 1.

    Throughout the paper, we use (co)variance based risk measures. E.g., see Stoyanov et al. (2013) for a sensitivity study on risk estimates based on higher order co-moments, and Ardia and Boudt (2015) for a recent review on risk-based portfolios.

  2. 2.

    If a numerical solution is not found, we follow the recommendation in Maillard et al. (2010) and slightly modify the problem and optimize over the N-dimensional vector \(\mathbf {u} \) such that \(\mathbf {w} \equiv \mathbf {u}/ (\mathbf {u} '\varvec{\iota } _N)\), under the constraint that \(\mathbf {u} \ge \mathbf {0} _N\) and \(\mathbf {u} '\varvec{\iota } _N > 0\). This new optimization problem is easier to solve numerically as an inequality constraint is less restrictive than the full investment equality constraint.

  3. 3.

    Estimations are performed with an adapted version of the R package rmgarch (Ghalanos 2012).

  4. 4.

    Data are available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

  5. 5.

    The use of the DCC model to describe the daily returns in our six data setups is common in the academic literature and in practice. See in particular the real-time conditional variance and correlation estimates available on Robert Engle’s V-Lab available at https://vlab.stern.nyu.edu/. We use a parametric setup instead of a block bootstrap approach, since, for our analysis on the effect of covariance missspecification on the risk-based portfolios, we need the true covariance matrix of the data generating process.

  6. 6.

    Results for universes #1, #2 and #3 are available from the corresponding author. They are similar to those of universe #4, because, as can be seen in Table 2, the distributions of the variance, and especially the correlation statistic, is similar for the first four universes.

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Author information

Affiliations

  1. Institute of Financial Analysis, University of Neuchâtel, Rue A.-L. Breguet 2, 2000, Neuchâtel, Switzerland

    David Ardia & Guido Bolliger

  2. Département de Finance, Assurance et Immobilier, Université Laval, Québec, Canada

    David Ardia & Jean-Philippe Gagnon-Fleury

  3. Syz Asset Management (Suisse) SA, Geneva, Switzerland

    Guido Bolliger

  4. Solvay Business School, Vrije Universiteit Brussel, Bruxelles, Belgium

    Kris Boudt

  5. Faculty of Economics and Business, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Kris Boudt

Authors
  1. David Ardia
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  2. Guido Bolliger
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  3. Kris Boudt
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  4. Jean-Philippe Gagnon-Fleury
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Corresponding author

Correspondence to David Ardia.

Additional information

We thank the Editor (Endre Boros), two anonymous referees, Simon Keel and Enrico Schumann for useful comments. David Ardia is grateful to IFM2 and Industrielle-Alliance for financial support. All analyses have been performed in the R statistical language (R Core Team 2015) with the package RiskPortfolios (Ardia et al. 2017).

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Ardia, D., Bolliger, G., Boudt, K. et al. The impact of covariance misspecification in risk-based portfolios. Ann Oper Res 254, 1–16 (2017). https://doi.org/10.1007/s10479-017-2474-7

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Keywords

  • Covariance misspecification
  • Monte Carlo study
  • Risk-based portfolios