Discussing the article: "Measuring What Matters (Part 3): The Reconstruction Engine — Validating Risk Footprints with Matrix Algebra"

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Check out the new article: Measuring What Matters (Part 3): The Reconstruction Engine — Validating Risk Footprints with Matrix Algebra.

This article performs a numerical verification of MQL5 eigendecomposition for a covariance matrix using the spectral theorem A = V Λ Vᵀ. It reconstructs the matrix with Diag(), Transpose(), and MatMul(), computes the residual and its Frobenius norm, and shows that deviations remain at floating‑point precision, with results printed to the Experts journal.

Part 2 of this series ended with a striking number: 91.24%. That was the share of total portfolio variance held by Factor 1 in the eigenvalue spectrum — a single underlying driver, almost entirely Gold, consuming nine tenths of the portfolio's entire risk budget. The CovarianceMatrix class built in Part 2 produced that figure by calling the native MQL5 .Eig() method on the covariance matrix, which returned a set of eigenvectors V and eigenvalues λ that described the portfolio's risk in terms of independent, orthogonal factors.

But here is a question worth asking before building anything further on top of that decomposition: how do you know the eigenvectors and eigenvalues are correct? How do you know that the three factors extracted by .Eig() genuinely capture the complete risk structure of the portfolio — not an approximation of it, but its exact representation in exact arithmetic and its numerical equivalent within floating-point precision?

Author: Kayode Michael Oyetunde