The dynamics of exchange traded funds: a geometrical and topological approach

Using a metric related to the returns correlation, a method is applied to the reconstruction of an economic space from Exchange-Traded Funds (ETFs) data. In the past, the same method was used in a geometrical analysis of times series of stock returns implying that the most of the systematic information of that market is contained in a space of small dimension. The same dimensional reduction was obtained using daily returns of 85 ETF securities in a time frame of more than 16 years. Having a metric defined in the space of ETF securities, a topological approach is used to define a complete network of ETFs and its corresponding Minimum Spanning Tree (MST). An outstanding separation of the two main classes of securities over the MST is uncovered. The dimensional reduction as well as the uncovered pattern in the topological structure, they both emerge from the data itself rather than from any modelling resolution.