Clustering Approaches for Global Minimum Variance Portfolio

Abstract: The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical data to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between in-sample volatility and out-of-sample volatility decreases, but also the out-of-sample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance.