What is hierarchical clustering and how do I read a dendrogram?

Question

AcadiFi · Accepted Answer

Hierarchical clustering builds a tree of nested clusters without requiring K in advance. The agglomerative variant starts with each observation as its own cluster and iteratively merges the two closest clusters until one remains. The divisive variant works top-down. The result is a dendrogram, a tree diagram where the vertical axis shows linkage distance and horizontal cuts produce cluster partitions.

Choice of linkage matters. Single linkage uses the minimum pairwise distance and can produce chaining (long stringy clusters). Complete linkage uses maximum distance and tends to create compact clusters. Average linkage balances these. Ward's method minimizes within-cluster variance and is popular for financial data because clusters end up similar in size.

For a portfolio at a firm like Drayhollow Fixed Income, clustering 120 corporate bonds by duration, convexity, spread, and credit rating using Ward linkage might yield a dendrogram where a natural cut at distance 4.2 produces 7 clusters corresponding to short HY, short IG, intermediate IG, long IG, utilities, financials, and crossovers.

```mermaid
graph TD
    A[All bonds]
    A --> B[Cluster 1]
    A --> C[Cluster 2]
    B --> D[Sub 1a]
    B --> E[Sub 1b]
    C --> F[Sub 2a]
```

Read the dendrogram by identifying large vertical gaps between successive merges, which indicate stable cluster counts. For CFA candidates, hierarchical clustering is preferred when you lack prior knowledge of K and want a hierarchy of groupings rather than a flat partition.

What is hierarchical clustering and how do I read a dendrogram?

Master Level II with our CFA Course

Related Questions

Practice Questions