Correlation alone rebuilds the GICS sectors

Sort every pairwise correlation of daily returns, then merge the k strongest edges using union-find. Small k leaves almost everything a singleton. Large k collapses the index into one blob. The interesting behaviour is in between.

At k = 400 the largest cluster is 36 stocks, and every one of them is a Financial. The algorithm is never shown a sector label. It recovers the sector purely from how the returns move together.

Push k to 3,000 and purity falls to 28% as genuinely unrelated names get merged through chains of intermediate correlations. That degradation is the honest part of the result: single-linkage clustering is fragile to exactly that kind of chaining.

If correlation structure reproduces the sector taxonomy, then sector labels are largely redundant for risk purposes, and a portfolio that diversifies across sector names may not be diversified at all. That is the same mistake the macro book made in a different asset class.