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|Abstract: In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense of maximizing with probability 1 the asymptotic out-of-sample expected utility, i.e., mean-variance objective function for different values of risk aversion coefficient which in particular leads to the maximization of the out-of-sample expected utility and to the minimization of the out-of-sample variance. One of the main features of our estimator is the inclusion of the estimation risk related to the sample mean vector into the high-dimensional portfolio optimization. The asymptotic properties of the new estimator are investigated when the number of assets p and the sample size $n$ tend simultaneously to infinity such that p/n --> c ∈ (0,+∞). The results are obtained under weak assumptions imposed on the distribution of the asset returns, namely the existence of the 4+ε moments is only required. Thereafter we perform numerical and empirical studies where the small- and large-sample behavior of the derived estimator is investigated. The suggested estimator shows significant improvements over the existent approaches including the nonlinear shrinkage estimator and the two-fund portfolio rule when the portfolio dimension is comparable to the sample size. Moreover, it is robust to deviations from normality.|
The aim of this special issue is to feature research papers on theory, methodology, and applications of models and methods for recent advances in statistical finance. We encourage submissions presenting original works on statistical, computational, and mathematical approaches to modelling and analysis of financial data. Innovative applications and case studies in financial statistics are welcome, especially related to novel methodological challenges in the treatment of big data and high-frequency data.
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