  In this paper we construct a shrinkage estimator of the global minimum
variance (GMV) portfolio by a combination of two techniques: Tikhonov
regularization and direct shrinkage of portfolio weights. More specifically, we
employ a double shrinkage approach, where the covariance matrix and portfolio
weights are shrunk simultaneously. The ridge parameter controls the stability
of the covariance matrix, while the portfolio shrinkage intensity shrinks the
regularized portfolio weights to a predefined target. Both parameters
simultaneously minimize with probability one the out-of-sample variance as the
number of assets $p$ and the sample size $n$ tend to infinity, while their
ratio $p/n$ tends to a constant $c>0$. This method can also be seen as the
optimal combination of the well-established linear shrinkage approach of Ledoit
and Wolf (2004, JMVA) and the shrinkage of the portfolio weights by Bodnar et
al. (2018, EJOR). No specific distribution is assumed for the asset returns
except of the assumption of finite $4+\varepsilon$ moments. The performance of
the double shrinkage estimator is investigated via extensive simulation and
empirical studies. The suggested method significantly outperforms its
predecessor (without regularization) and the nonlinear shrinkage approach in
terms of the out-of-sample variance, Sharpe ratio and other empirical measures
in the majority of scenarios. Moreover, it obeys the most stable portfolio
weights with uniformly smallest turnover.
