Three Correlations Passed Validation. The Matrix Was Impossible.
A risk dashboard can look completely convincing while displaying numbers from a model that should never have accepted its inputs. Imagine a UI with three correlation sliders: Asset A and asset B: +0.90 Asset A and asset C: +0.90 Asset B and asset C: -0.90 Every input fits the permitted range. The diagonal of the resulting matrix is 1. The matrix is symmetric. A naïve form validator gives it a…
A risk dashboard can appear entirely credible with inputs that have no business being there. Picture a UI featuring three correlation sliders: Asset A linked to Asset B at +0.90, Asset A to Asset C at +0.90, and Asset B to Asset C at -0.90. Despite each input falling within permissible bounds, the matrix produced by these sliders fails the validation test.
The diagonal of the resulting matrix is 1, and it is symmetric. Although a basic form validator would give it a green checkmark, common sense tells us that three random variables cannot exhibit all three of these pairwise correlations simultaneously. This isn't a report of a production malfunction; it's an example of a design flaw we deliberately guarded against while creating a browser-based portfolio-risk visualization. The problem lies entirely in the inputs, prior to any rendering code executing.
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