Efficient estimation of large scale Markowitz portfolios

This paper focuses on treating the estimation problem of the Markowitz portfolio in a large market. Several methods that have been introduced to solve this problem are investigated. The first method comes from Chen and Yuan (2016), who propose the so called subspace mean-variance portfolio, which introduces a trade-off between optimality and estimability. Another way solution for the estimation problem comes in the form of shrinkage estimation. Shrinkage estimators for the mean and variance of the asset returns have been introduced by Jorion (1986) and Ledoit and Wolf (2003) respectively. Furthermore, a combination of shrinkage estimation and the subspace mean-variance portfolio is made. Consequently, it is found through simulation that these methods are beneficial in terms of Sharpe ratio. However, these benefits were only seen in large markets when studying real return data. Furthermore, the combination of shrinkage estimation and the subspace mean-variance portfolio didn’t result in a better or worse portfolio rule, which implies a robustness of the subspace method towards the quality of the in-put sample estimates.