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Motivated by the problem of computing investment portfolio weightings weinvestigate various methods of clustering as alternatives to traditionalmean-variance approaches. Such methods can have significant benefits from apractical point of view since they remove the need to invert a samplecovariance matrix, which can suffer from estimation error and will almostcertainly be non-stationary. The general idea is to find groups of assets whichshare similar return characteristics over time and treat each group as a singlecomposite asset. We then apply inverse volatility weightings to these newcomposite assets. In the course of our investigation we devise a method ofclustering based on triangular potentials and we present associated theoreticalresults as well as various examples based on synthetic data.

Real time clustering of time series using triangular potentials