This paper discusses the practical aspects of working with high-dimensional shrinkage portfolios. It presents the R package HDShOP which provides a comprehensive framework for such work. In particular, we cover the construction of portfolios using shrinkage-based estimators for the mean vector, covariance matrix, and precision matrix of asset returns, as well as the shrinkage estimators derived directly for the weights of optimal portfolios. Moreover, shrinkage-based tests on the mean-variance efficiency of a given portfolio are discussed. Aspects related to programming, such as classes and methods used in the construction of optimal portfolios, are described. The description of the software is preceded by underlying theory and it is accompanied by several empirical illustrations based on the data consisting of returns on stocks from the S&P 500 index.

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets p increases at the same rate as the sample size n such that their ratio p/n approaches a positive constant cin (0,1) as nto infty. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S&P 500 constituents.

In this paper, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets p depends on the sample size n such that p/n → c ϵ (0, 1) as n tends to infinity. In the case of a singular covariance matrix with rank equal to q we assume that q/n → c ϵ (0, 1) as n → ∞. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of c close to one.