Filtered clustering for exchange traded fund

Abstract

In this work, we show how time series of Exchange Traded Funds (i.e., ETF) returns can be clustered by reflecting the classification per investment class provided by the Borsa Italiana. We use the random matrix theory (RMT) filter to “clean” noise from a correlation matrix and we then use the reconstructed filtered correlation matrix to draw the hierarchical tree associated with the single linkage clustering algorithm (minimum spanning tree). The main goal of the paper is to show that RMT as a filter for correlation matrices enables the construction of trees that are easier to interpret with respect to large matrices, even for ETF returns.