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Dominating estimators for minimum-variance portfolios. (English) Zbl 1441.62264
Summary: In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets \(d\geq 4\) and number of observations \(n\geq d+2\). The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed \(d\) but \(n\to \infty\) and \(n,d\to \infty\) but \(n/d\to q\leq \infty\) are investigated. Furthermore, we present a small-sample test for the question of whether it is better to completely ignore time series information in favor of naive diversification.

62P05 Applications of statistics to actuarial sciences and financial mathematics
62H12 Estimation in multivariate analysis
62G05 Nonparametric estimation
62G09 Nonparametric statistical resampling methods
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J07 Ridge regression; shrinkage estimators (Lasso)
91G10 Portfolio theory
Full Text: DOI
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