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

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.