Robustifying Markowitz

Wolfgang Härdle, Yegor Klochkov, Alla Petukhina and Nikita Zhivotovskiy

No 2021-018, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: 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 sen- sitivity 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 conse- quently 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 con- struct 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.

Date: 2021
New Economics Papers: this item is included in nep-cwa, nep-ecm, nep-fmk, nep-ore and nep-rmg
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2021018

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