On mutual funds-of-ETFs asset allocation with rebalancing: sample covariance versus EWMA and GARCH

  • Panos XidonasEmail author
  • Mike Tsionas
  • Constantin Zopounidis
Original Research


Our purpose in this article is to investigate the benefits of introducing quantitative strategies for the estimation of portfolio variance–covariance matrices, expecting that the stylized facts of asset returns and their economic impact will be effectively captured. More specifically, we are dealing with the process of portfolio optimization with rebalancing for ETFs portfolios, in a time-varying volatility environment. The aim of the analysis is to construct optimal portfolios, based on the econometric modelling and calculation of return covariances. Also, our target is to infer critical comparative insights, as far as the application of three popular quantitative frames: (a) the sample covariance or equal weighting model, (b) the EWMA model, and (c) the GARCH (1,1) model. The validity of the attempt is verified through an illustrative empirical testing procedure on an actively traded low-volatility momentum mutual fund-of-ETFs, consisting of a well-diversified investment universe of 150 ETFs. Additionally, we co-assess a set of non-convex investment policy restrictions, such as buy-in thresholds and compliance norms, modelling the corresponding portfolio selection process as a mixed-integer optimization problem. The qualitative and technical conclusions obtained, document superior out-of-sample returns for the portfolios constructed by means of the EWMA and GARCH (1,1) models. Moreover, other findings that confirm and expand the existing underlying research, are also reported.


Asset allocation Rebalancing Volatility modelling Portfolio optimization Non-convex policy constraints Mutual funds ETFs 


  1. Adcock, C., & Meade, N. (1994). A simple algorithm to incorporate transaction costs in quadratic optimization. European Journal of Operational Research, 79(1), 85–94.CrossRefGoogle Scholar
  2. Alexander, C. (2008). Practical financial econometrics: Market risk analysis (Vol. II). Hoboken: Wiley.Google Scholar
  3. Arshanapalli, B., Coggin, T., & Nelson, W. (2001). Is fixed-weight asset allocation really better. The Journal of Portfolio Management, 27, 27–38.CrossRefGoogle Scholar
  4. Bollerslev, T. (1986). Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–327.CrossRefGoogle Scholar
  5. Brinson, G., Singer, B., & Beebower, G. (1991). Determinants of portfolio performance II: An update. Financial Analysts Journal, 47(3), 40–48.CrossRefGoogle Scholar
  6. Brooks, C., Burke, S., & Persand, G. (2003). Multivariate GARCH models: Software choice and estimation issues. Journal of Applied Econometrics, 18, 725–734.CrossRefGoogle Scholar
  7. Brown, D., & Smith, J. (2011). Dynamic portfolio optimization with transaction costs: Heuristics and dual bounds. Management Science, 57(10), 1752–1770.CrossRefGoogle Scholar
  8. DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22, 1915–1953.CrossRefGoogle Scholar
  9. Dickson, J., Kwon, D., & Rowley, J. (2015). Choosing between ETFs and mutual funds: Strategy, then structure. Valley Forge: The Vanguard Group.Google Scholar
  10. Engle, R. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.CrossRefGoogle Scholar
  11. Fabozzi, F., Focardi, S., & Jonas, C. (2007). Trends in quantitative equity management: Survey results. Quantitative Finance, 7, 115–122.CrossRefGoogle Scholar
  12. Fabozzi, F., Huang, D., & Zhou, G. (2010). Robust portfolios: Contributions from operations research and finance. Annals of Operations Research, 176, 191–220.CrossRefGoogle Scholar
  13. Ibbotson, R., & Kaplan, P. (2000). Does asset allocation policy explain 40, 90, or 100 percent of performance? Financial Analysts Journal, 56(1), 26–33.CrossRefGoogle Scholar
  14. Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10, 603–629.CrossRefGoogle Scholar
  15. Leland, H. (1999). Beyond mean-variance: Performance measurement in a non-symmetrical World. Financial Analysts Journal, 55, 27–36.CrossRefGoogle Scholar
  16. Maginn, J., Tuttle, D., Pinto, D., & McLeavey, D. (2007). Managing investment portfolios (3rd ed.). New York: Wiley.Google Scholar
  17. Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.Google Scholar
  18. Markowitz, H. (1956). The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly, 3, 111–133.CrossRefGoogle Scholar
  19. Moallemi, C., & Saglam, M. (2017). Dynamic portfolio choice with linear rebalancing rules. Journal of Financial and Quantitative Analysis, 52(3), 1247–1278.CrossRefGoogle Scholar
  20. Morgan, J. P. (1996). RiskMetrics™ technical document. Accessed Nov 2014.
  21. Wallick, D., Shanahan, J., Tasopoulos, C., & Yoon, J. (2012). The global case for strategic asset allocation. Valley Forge: The Vanguard Group.Google Scholar
  22. Xidonas, P., & Mavrotas, G. (2014a). Multiobjective portfolio optimization with non-convex policy constraints: Evidence from the Eurostoxx 50. European Journal of Finance, 20(11), 957–977.CrossRefGoogle Scholar
  23. Xidonas, P., & Mavrotas, G. (2014b). Comparative issues between linear and non-linear risk measures for non-convex portfolio optimization: Evidence from the S&P 500. Quantitative Finance, 14(7), 1229–1242.CrossRefGoogle Scholar
  24. Xidonas, P., Mavrotas, G., Zopounidis, C., & Psarras, J. (2011). IPSSIS: An integrated multicriteria DSS for equity portfolio construction and selection. European Journal of Operational Research, 210(2), 398–409.CrossRefGoogle Scholar
  25. Zilbering, Y., Jaconetti, C., & Kinniry, F. (2015). Best practices for portfolio rebalancing. Valley Forge: The Vanguard Group.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Panos Xidonas
    • 1
    Email author
  • Mike Tsionas
    • 2
  • Constantin Zopounidis
    • 3
  1. 1.ESSCA Grande ÉcoleParisFrance
  2. 2.Lancaster UniversityLancasterUK
  3. 3.Audencia Business SchoolNantes Cedex 3France

Personalised recommendations