Efficient cluster-based portfolio optimization

Abstract

The sample mean and covariance matrix of historical data provide a disappointing out-of-sample performance in mean-variance portfolio rules. This poor performance is certainly due to the high estimation error incurred in the optimization model. Our purpose in this article is to find a method that enhances the out-of-sample performance of the portfolio weights. Using hierarchical clustering, we propose an alternative cluster-based portfolio to obtain a sequence of cluster assets. On the basis of Gram-Schmidt orthogonalization, the estimation risk of the data set becomes the sum of the estimations of the clusters in the sequence. The performance of our method and its competitors is compared empirically and via some simulations in high dimension.

Keywords:

• Covariance matrix
• Sharpe ratio
• Clustering
• Portfolio theory