Hierarchical clustering and the portfolio selection problem
Abstract
Classical portfolio selection techniques measure risk through the variance of asset returns, which investors wants to minimise. These methods only work well in practice if the covariance (or correlation) matrix of the returns is properly de-noised. A good de-noising (or filtering) method conserves only the useful and informative parts of the matrix' structure. Since stock markets may also be viewed as hierarchical structures (Simon 1991), we can use hierarchical clustering to identify this hierarchy and use the detected structure to filter the covariance matrix. In this work we show possible applications of hierarchical clustering both for using it as a matrix filtering technique in the Markowitz portfolio model and directly as a way to assemble portfolios. We perform our experiments on real world data and evaluate using different performance indicators. We work with a data set containing daily closing prices and transform these into daily logarithmic returns from which we create the covariance matrix. We model the following situation: the investor decides the length T of the investment. On day t0 they create a portfolio based on the previous T days of returns and then they wait for T days, selling all of their assets afterwards.
