Clustering Digital Assets Using Path Signatures: Application to Portfolio Construction

We propose a new way of building portfolios of cryptocurrencies that provide good diversification properties to investors. First, we seek to filter these digital assets by creating some clusters based on their path signature. The goal is to identify similar patterns in the behavior of these highly volatile assets. Once such clusters have been built, we propose "optimal" portfolios by comparing the performances of such portfolios to a universe of unfiltered digital assets. Our intuition is that clustering based on path signatures will make it easier to capture the main trends and features of a group of cryptocurrencies, and allow parsimonious portfolios that reduce excessive transaction fees. Empirically, our assumptions seem to be satisfied.