Wolfgang Karl Härdle, Yegor Klochkov, Alla Petukhina, Nikita Zhivotovskiy
arXiv 28 Dec 2022 · Econometrics · publishedJournal of Econometrics (2023) · 13 citations (OpenAlex)
arXiv:2212.13996 · PDF · DOI · OpenAlex · Extracted main text
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 the lowest turnover compared to shrinkage-based and constrained portfolios while preserving or slightly improving out-of-sample performance.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Mendelson \ Zhivotovskiy (2020) Robust covariance estimation under $L_4$-$L_2 $ norm equivalence, Annals of Statistics 48(3): 1648–1664 | 0.874 | 6 | 3 | 67% |
| 2 | Ledoit \ Wolf (2008) Robust performance hypothesis testing with the sharpe ratio, Journal of Empirical Finance 15(5): 850–859 | 0.843 | 5 | 3 | 60% |
| 3 | Ledoit \ Wolf (2011) Robust performances hypothesis testing with the variance, Wilmott 2011(55): 86–89 | 0.843 | 5 | 3 | 60% |
| 4 | Hopkins, Li \ Zhang (2020) Robust and heavy-tailed mean estimation made simple, via regret minimization, arXiv preprint arXiv:2007.15839 | 0.830 | 14 | 4 | 57% |
| 5 | Ledoit \ Wolf (2004) A well-conditioned estimator for large-dimensional covariance matrices, Journal of Multivariate Analysis 88(2): 365–411 | 0.811 | 4 | 2 | 100% |
| 6 | Ledoit \ Wolf (2017) Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks, The Review of Financial Studie… | 0.811 | 4 | 2 | 100% |
| 7 | Lugosi \ Mendelson (2019) Sub-Gaussian estimators of the mean of a random vector, Annals of Statistics 47(2): 783–794 | 0.754 | 7 | 3 | 43% |
| 8 | Depersin \ Lecué (2022) Robust sub-Gaussian estimation of a mean vector in nearly linear time, Annals of Statistics 50(1): 511–536 | 0.737 | 4 | 3 | 50% |
| 9 | Cherapanamjeri, Hopkins, Kathuria, Raghavendra \ Tripuraneni (2020) Algorithms for heavy-tailed statistics: Regression, covariance estimation, and beyond, Proceedings of the 52nd Annual ACM SIGACT… | 0.737 | 3 | 2 | 100% |
| 10 | DeMiguel \ Nogales (2009) Portfolio selection with robust estimation, Operations Research 57(3): 560–577 | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 62 scored citations.