Efficient Portfolio Selection in a Large Market

The Markowitz estimated mean-variance portfolio is proven to not work well in markets in which the number of assets is relatively high compared to the number of historical observations, which can be attributed to the large estimation error in the sample estimates of the expected return and covariance matrix. Chen & Yuan (2016) introduce a method that reduces the investment universe to the subspace, spanned by the leading eigenvectors of the sample covariance matrix. In this paper, it is shown that the sample mean and covariance matrix can be well used in this so-called subspace mean-variance analysis. These restricted subspace mean-variance portfolios theoretically outperform the usual unrestricted Markowitz mean-variance portfolios, even when more sophisticated, shrinkage estimators are used to estimate the mean and variance. However, empirical analysis does not support these observations. It is shown that in the real market, the subspace method does not necessarily outperform the estimated mean-variance porfolio which is why its practical application is not unchallenged.