  Motivated by the problem of computing investment portfolio weightings we
investigate various methods of clustering as alternatives to traditional
mean-variance approaches. Such methods can have significant benefits from a
practical point of view since they remove the need to invert a sample
covariance matrix, which can suffer from estimation error and will almost
certainly be non-stationary. The general idea is to find groups of assets which
share similar return characteristics over time and treat each group as a single
composite asset. We then apply inverse volatility weightings to these new
composite assets. In the course of our investigation we devise a method of
clustering based on triangular potentials and we present associated theoretical
results as well as various examples based on synthetic data.
