Agglomerative clustering builds a hierarchy from the bottom up: every asset begins alone, then the closest pair of current clusters is merged repeatedly until one cluster contains all assets. In hierarchical risk parity, the resulting linkage matrix records each merge and supports later asset ordering. section 11.2.4
For correlated assets, first derive a distance matrix from correlations, then compute distances between the resulting asset-distance profiles. At each iteration, select the smallest remaining distance, create a combined cluster, update its distances, and record the two children, merge distance, and cluster size. section 11.2.4
Eight-asset linkage
With VV, VB, AGG, VEA, BNDX, VWO, EMB, and DJP, the first recorded merge joins assets 0 and 1 at distance 0.2951. Later merges incorporate additional assets and clusters; the final row joins clusters 11 and 13 into an eight-asset cluster. section 11.2.4
