Efficient Portfolio Selection in a Large Market

The focus of this paper is on a portfolio rule that approaches the optimal Sharpe ratio in a large market with a realistic amount of historical data and a well-chosen subspace, named “subspaceP mean-variance analysis”. This portfolio rule carefully balances the tradeoff between the estimation error and the systematic error. A well-chosen subspace is the key extension on the paper of Chen and Yuan (2016). Also a mathematical comparison is given for the Markowitz (subspaceP) mean-variance portfolio with and without the constraint that the sum of the portfolio holdings sums up to one. Another comparison is made between the subspaces PΣ and PCorr, that are created with the eigenvectors of the covariance- or correlation matrix, by using the efficient frontier, the dimension of the subspaces and a comparison over different investment opportunities. To give the last comparison, a mathematical explanation needs to be given that an additional investment option could decrease the Sharpe ratio of the subspaceP mean-variance portfolio.