Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2021 018

Robustifying Markowitz

Wolfgang Karl Härdle
Yegor Klochkov
Alla Petukhina
Nikita Zhivotovskiy

Markowitz mean-variance portfolios with sample mean and covariance as input
parameters feature numerous issues in practice. They perform poorly out of
sample due to estimation error, they experience extreme weights together with
high sensitivity to change in input parameters. The heavy-tail characteristics
of  financial time series are in fact the cause for these erratic fluctuations
of weights that consequently create substantial transaction costs. In
robustifying the weights we present a toolbox for stabilizing costs and weights
for global minimum Markowitz portfolios. Utilizing a projected gradient descent
(PGD) technique, we avoid the estimation and inversion of the covariance
operator as a whole and concentrate on robust estimation of the gradient descent
increment. Using modern tools of robust statistics we construct a
computationally efficient estimator with almost Gaussian properties based on
median-of-means uniformly over weights. This robustified Markowitz approach is
confirmed by empirical studies on equity markets. We demonstrate that
robustified portfolios reach higher risk-adjusted performance and the lowest
turnover compared to shrinkage based and constrained portfolios.


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