  The construction of minimum spanning trees (MSTs) from correlation matrices
is an often used method to study relationships in the financial markets.
However most of the work on this topic tends to use the Pearson correlation
coefficient, which relies on the assumption of normality and can be brittle to
the presence of outliers, neither of which is ideal for the study of financial
returns. In this paper we study the inference of MSTs from daily US, UK and
German financial returns using Pearson and two rank correlation methods,
Spearman and Kendall's $\tau$. MSTs constructed using these rank methods tend
to be more stable and maintain more edges over the dataset than those
constructed using Pearson correlation. The edge agreement between the Pearson
and rank MSTs varies significantly depending on the state of the markets, but
the rank MSTs generally show strong agreement at all times. Deviation from
univariate normality can be related to changes in the correlation matrices but
is more difficult to connect to changes in the MSTs. Irrelevant of coefficient,
the trees tend to have similar topologies. Portfolios constructed from the MST
correlation matrices have a smaller turnover than those from the full
covariance matrix for the larger markets, but not for the smaller German
market. Using a bootstrap method we find that the correlation matrices
constructed using the rank correlations are more robust, but there is little
difference between the robustness of the MSTs.
