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In this paper we construct a shrinkage estimator of the global minimumvariance (GMV) portfolio by a combination of two techniques: Tikhonovregularization and direct shrinkage of portfolio weights. More specifically, weemploy a double shrinkage approach, where the covariance matrix and portfolioweights are shrunk simultaneously. The ridge parameter controls the stabilityof the covariance matrix, while the portfolio shrinkage intensity shrinks theregularized portfolio weights to a predefined target. Both parameterssimultaneously minimize with probability one the out-of-sample variance as thenumber of assets $p$ and the sample size $n$ tend to infinity, while theirratio $p/n$ tends to a constant $c>0$. This method can also be seen as theoptimal combination of the well-established linear shrinkage approach of Ledoitand Wolf (2004, JMVA) and the shrinkage of the portfolio weights by Bodnar etal. (2018, EJOR). No specific distribution is assumed for the asset returnsexcept of the assumption of finite $4+\varepsilon$ moments. The performance ofthe double shrinkage estimator is investigated via extensive simulation andempirical studies. The suggested method significantly outperforms itspredecessor (without regularization) and the nonlinear shrinkage approach interms of the out-of-sample variance, Sharpe ratio and other empirical measuresin the majority of scenarios. Moreover, it obeys the most stable portfolioweights with uniformly smallest turnover.

Two is better than one: Regularized shrinkage of large minimum variance portfolio