 Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?Taras Bodnar, Nestor Parolya and Erik Thors\'en Abstract: The main contribution of this paper is the derivation of the asymptotic behaviour of the out-of-sample variance, the out-of-sample relative loss, and of their empirical counterparts in the high-dimensional setting, i.e., when both ratios $p/n$ and $p/m$ tend to some positive constants as $m\to\infty$ and $n\to\infty$, where $p$ is the portfolio dimension, while $n$ and $m$ are the sample sizes from the in-sample and out-of-sample periods, respectively. The results are obtained for the traditional estimator of the global minimum variance (GMV) portfolio, for the two shrinkage estimators introduced by \cite{frahm2010} and \cite{bodnar2018estimation}, and for the equally-weighted portfolio, which is used as a target portfolio in the specification of the two considered shrinkage estimators. We show that the behaviour of the empirical out-of-sample variance may be misleading is many practical situations. On the other hand, this will never happen with the empirical out-of-sample relative loss, which seems to provide a natural normalization of the out-of-sample variance in the high-dimensional setup. As a result, an important question arises if this risk measure can safely be used in practice for portfolios constructed from a large asset universe. Date: 2021-11 Published in Finance Research Letters, Volume 54, June 2023, 103807 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2111.12532 Access Statistics for this paper More papers in Papers from arXiv.org |
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