Variable Clustering Methods and Applications in Portfolio Selection

This thesis introduces three variable clustering methods designed in the context of diversified portfolio selection. The motivation is to cluster financial assets in order to identify a small set of assets to approximate the level of diversification of the whole universe of stocks. First, we develop a data-driven approach to variable clustering based on a correlation blockmodel, in which assets in the same cluster have the same correlations with all other assets. Under the correlation blockmodel, the assets in the same cluster are controlled by the same latent factor. In addition, each cluster forms an equivalent class among assets, in the sense that the portfolio consisting of one stock from each cluster will have the same correlation matrix, regardless of the specific stocks chosen. We devise an algorithm named ACC (Asset Clustering through Correlation) to detect the clusters, with theoretical analysis and practical guidance for tuning the parameter for the algorithm. Our second method studies a multi-factor block model, which is a generalization of the correlation blockmodel. Under this multi-factor block model, assets in the same cluster are governed by a set of multiple latent