Hierarchical risk parity

Hierarchical Risk Parity (HRP) allocates using López de Prado's algorithm: it clusters the assets by the correlation structure of the covariance matrix, then shares risk down the resulting hierarchy. Unlike the Markowitz methods, it needs no expected-return estimate—only the covariance, measured over the lookback window—so it avoids the noisiest input in portfolio optimisation. For where it sits among the six methods, see Portfolio optimisation.

HRP suits a universe with clear cluster structure—equities, bonds, and commodities, say—where the allocation should respect those groups rather than concentrate in a few names. Because it does not rely on expected returns, it tends to be steadier than the Markowitz methods when return estimates are unreliable, which makes it a common choice for the Hedge Portfolio.

The linkage method sets how the clustering step measures the distance between clusters:

• Single: nearest-neighbour distance, the default.
• Complete: farthest-neighbour distance.
• Average: mean pairwise distance between clusters.
• Ward: minimises within-cluster variance.

HRP allocates through its clustering logic rather than by solving against bounds. The per-asset allocation constraints therefore do not apply to it, and when Cash is on, the cash share is held at the minimum of the Cash Allocation range rather than optimised within it.