TY - JOUR
T1 - Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?
AU - Bodnar, Taras
AU - Parolya, Nestor
AU - Thorsén, Erik
PY - 2023
Y1 - 2023
N2 - The main contribution of this paper is the derivation of the asymptotic behavior 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→∞, 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 and for the two shrinkage estimators introduced by Frahm and Memmel (2010) and Bodnar et al. (2018). We show that the behavior of the empirical out-of-sample variance may be misleading in many practical situations, leading, for example, to a comparison of zeros. 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 the out-of-sample variance can safely be used in practice for portfolios constructed from a large asset universe.
AB - The main contribution of this paper is the derivation of the asymptotic behavior 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→∞, 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 and for the two shrinkage estimators introduced by Frahm and Memmel (2010) and Bodnar et al. (2018). We show that the behavior of the empirical out-of-sample variance may be misleading in many practical situations, leading, for example, to a comparison of zeros. 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 the out-of-sample variance can safely be used in practice for portfolios constructed from a large asset universe.
KW - Shrinkage estimator
KW - High-dimensional covariance matrix
KW - Random matrix theory
KW - Minimum variance portfolio
KW - Parameter uncertainty
UR - http://www.scopus.com/inward/record.url?scp=85150762027&partnerID=8YFLogxK
U2 - 10.1016/j.frl.2023.103807
DO - 10.1016/j.frl.2023.103807
M3 - Article
SN - 1544-6123
VL - 54
JO - Finance Research Letters
JF - Finance Research Letters
M1 - 103807
ER -