Inspecting Portfolio Covariance and Risk Factors with Eigenvalue Decomposition

Summary

This installment extends a portfolio-risk analysis by turning a covariance matrix into an inspectable object. It describes calculating logarithmic returns from closing prices, arranging assets as rows and observations as columns, and using MQL5’s covariance operation to build a matrix of pairwise relationships. A reusable class stores the matrix alongside symbol labels, checks its symmetry, and prints a labeled grid so the relationships among instruments can be examined directly.

The article then applies eigenvalue decomposition to the covariance matrix. Eigenvalues and eigenvectors are presented as a way to describe independent risk factors and show how instruments load on them, adding interpretation beyond a single portfolio-variance figure. The examples are implementation-focused and use a small multi-asset illustration; they do not provide empirical validation that the extracted factors predict returns or improve trading. Results depend on the chosen instruments, timeframe, lookback, and input data, and the discussion is part of a broader coding series.

Key ideas

• Logarithmic returns from multiple assets form the input to the covariance calculation.
• The matrix must be arranged with assets as rows and observations as columns for the described MQL5 method.
• A reusable class can store, label, print, and check the covariance matrix before further analysis.
• Eigenvalues and eigenvectors offer a factor-oriented view of portfolio risk and instrument loadings.
• The tutorial demonstrates matrix analysis in code but does not establish predictive or trading performance.

Tags

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