Dependence and Distance Matrices for Asset Returns

Summary

This documentation describes tools for measuring relationships among asset-return series. A dependence matrix computes pairwise codependence using alternatives such as mutual information, variation of information, distance correlation, Spearman rank correlation, and GPR or GNPR distance. A separate distance-matrix function converts a codependence matrix into pairwise distances, with angular, squared-angular, and absolute-angular metrics listed.

The example applies distance correlation to a dataframe of asset returns and contrasts it with a conventional Pearson correlation matrix, then illustrates deriving absolute angular distance from Pearson correlations. These matrices can provide different views of asset similarity and dependence for downstream analysis, such as grouping assets or studying portfolio structure. The excerpt documents available measures and a basic workflow, but does not compare their empirical performance, specify parameter choices, or provide guidance on estimation uncertainty. Results will depend on the data and metric selected, and the page refers readers to separate presentation material for deeper treatment.

Key ideas

• Dependence matrices summarize pairwise relationships among asset-return series using several statistical measures.
• Listed measures include mutual information, variation of information, distance correlation, rank correlation, and GPR or GNPR distance.
• Distance matrices transform codependence values into angular-based measures of dissimilarity.
• The example contrasts distance correlation with Pearson correlation for asset returns.
• The documentation describes functions and an example but does not establish which metric performs best.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.