The correlations between daily returns show, sometimes, surprising relationships. Looking at relationships on 5-day cumulative returns produced clusters more in line with the traditional view.

This is not surprising as weekly returns will have less “noise” than daily. A more robust measure than correlation needs to be used to determine whether relationships seen on daily or higher-frequency are bona fide.

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This series on your portfolio algo and your development of the spanning trees visualization is very nice. The visualizations themselves look very cool and evince some interesting relations. The algo you described didn’t mention sectors and yet the results are so cleanly segmented by same; safe to assume that you’re collecting your trees by sector?

More general question: to what degree do such visualizations play a part in your development?

Thanks for sharing this bit of work; compelling stuff!

Actually, there is no “manual” intervention in the algorithm. The sectors are clusters detected solely by the algorithm. To get an idea as to how this works, consider the simplest case amongst 5 assets with the following correlations:

A B: 0.8

A C: 0.55

A D: 0.58

A E: 0.77

B C: 0.62

B D: 0.35

B E: 0.66

C D: 0.72

C E: 0.57

Would produce the following graphs on the first pass:

E — A — B, C — D

The algorithm will combine subgraphs with less than the minimum number of nodes on subsequent passes.

Your second comment is interesting. For me visualizations help with ideas and/or are a rough validatation of numerical data, but all of my models are purely numerical and/or machine learning based.

A difficultly for me is that much of the data I deal with is high-dimensional. Understanding it can be very difficult. Visualizing slices of it is useful, but I still struggle.

In the case of these graphs, was useful for me, as I’ve spent most of my career in the fixed income and FX space, so providing some overview of the equity space.

As for the relations, yeah, some surprising stuff there …

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