What Hierarchical Risk Parity Optimizes and What the Discussion Establishes

Summary

The question asks whether Hierarchical Risk Parity (HRP) has a clear mathematical problem statement behind its algorithm, including the roles of hierarchical clustering, quasi-diagonalization, and recursive bisection. It wonders whether HRP can be framed as an allocation problem constrained by a tree structure. The response does not state an objective function, constraints, or an inverse problem. Instead, it points to a video and chart as an explanation of the method.

As presented here, the exchange offers a reference rather than a mathematical derivation or a direct answer to the request for a precise formulation. It gives no evidence, equations, portfolio comparisons, or caveats about the method’s assumptions. Readers seeking a formal optimization interpretation cannot infer one from this exchange alone; they would need to consult the linked material or other technical sources. The useful takeaway is that the question distinguishes HRP’s procedural steps from the objective those steps might be understood to solve, while the reply leaves that distinction unresolved in the text.

Key ideas

• The question seeks a mathematical objective or inverse problem underlying HRP’s algorithmic steps.
• The discussion names clustering, quasi-diagonalization, and recursive bisection as parts of the method.
• The reply directs readers to explanatory material but does not provide a formal objective or constraints.
• No equations, empirical evidence, or assumptions are supplied in the exchange itself.

Tags

# Is there a clear mathematical statement of what problem Hierarchical Risk Parity is solving?


# Is there a clear mathematical statement of what problem Hierarchical Risk Parity is solving?












Prado's paper is really just an algorithm for solving some inverse problem. Has anyone seen a clear statement of that inverse problem? Or do you know how to write it simply?

The first step is just a linkage matrix (see scipy.linkage) so that is pretty clear and can probably be posed as a constrained DAG optimization in some continuous formulation. The quasi-diag and recursive bisection are some sort of inversion operation. But what is the precise statement of that problem? Prado just comes up with an algorithm without context.

Is this solving some optimal allocation with dag structure?

Is there really no statement of what this is actually doing or have I missed a reference in my reading?

## Answer by KaiSqDist (score 2)

https://quant.stackexchange.com/a/85352

I think this video and this chart effectively answers your question:

https://www.mathworks.com/videos/asset-allocation-hierarchical-risk-parity-1577957794663.html

Pardon the short solution, but I think the answer is clearly presented in the video.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.