Title: Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?
Authors: Nestor Parolya - Delft University of Technology (Netherlands) [presenting]
Taras Bodnar - Stockholm University (Sweden)
Erik Thorsen - Stockholm University (Sweden)
Abstract: The main contribution 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 $m$ and $n$ approach infinity, where $p$ is the portfolio dimension, $n$ 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 GMV portfolio, for two previous shrinkage estimators, 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 in 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 set-up. As a result, an important question arises if this risk measure can be safely used in practice for portfolios constructed from a large asset universe.