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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.

##### MSC:
 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
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