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Lemma 1 — HRP never sees the cross-block
At γ = 0 the recursion is hierarchical risk parity: it splits by the naive variances of the two diagonal blocks and never touches the cross-block. So noise in the cross-block cannot move the HRP weights at all, while any γ > 0 reads the noisy block and moves. The covariance is the paper's Family A: volatilities (1,1,2,2), within-block correlation ½, cross-block correlation 0.3, and the noise moves the cross-block correlation by ±τ.
What to look for: drag τ. The γ = 0 bars never
move (clean and perturbed weights are identical to machine precision); the
γ = 0.6 bars drift with the noise.
The widget runs the recursion of the paper's equation (4) with the naive fitness (5), ported directly from the reference implementations, live in your browser. Nothing is pre-baked.