Marginal value of an aggregate

Three uncorrelated bottom-level residuals (95% confidence ellipsoid), and how much adding one aggregate shrinks it — per the rank-one Sherman–Morrison update V⁺ = V − VaaᵗV / (ω + aᵗVa).

Interactive 3D visualization showing how adding an aggregate with its own forecast noise shrinks the joint residual ellipsoid of three uncorrelated bottom-level forecast errors, with sliders for each series' noise and the aggregate's own noise, and checkboxes to choose which series the aggregate sums.

σ₁ 1.00
σ₂ 1.30
σ₃ 0.80
0.50

Risk before, tr(V)

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Risk after, tr(V⁺)

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Reduction ΔR

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% reduction

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