Discussing the article: "Measuring What Matters (Part 4): Reading the Spectrum — What Eigenvalues Tell You About Risk"
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Check out the new article: Measuring What Matters (Part 4): Reading the Spectrum — What Eigenvalues Tell You About Risk.
We turn eigenvalues from a covariance matrix into a normalized spectral‑entropy score that measures how evenly variance is spread across factors. SpectralEntropyCalculator.mq5 compares two portfolios in one run, using native vector summation, ArraySort()-based ordering, element‑wise division, and the Shannon entropy formula. The report makes dominant factors visible and enables quick, repeatable checks of diversification quality.
When you decompose the covariance matrix of a three-symbol portfolio you get three eigenvalues. Each eigenvalue represents the amount of variance carried by one independent risk factor — a direction in the portfolio’s risk space along which the instruments tend to move together. The sum of all eigenvalues gives the total variance represented by the covariance matrix. That identity is useful, but the real information sits in how the total is split among the individual eigenvalues.
Consider two possible outcomes.
A concentrated spectrum might look something like 90 %, 8 %, 2 %. One factor is doing almost all the work. In practice this can mean that the instruments are heavily exposed to a common market force — dollar direction, broad risk sentiment, or commodity market tone. The other two factors are minor. Even though the portfolio holds three different instruments, they are mostly just different expressions of the same underlying bet. When that dominant factor moves sharply, the entire portfolio feels it. There is very little internal buffering.
A more distributed spectrum might look like 45 %, 35 %, 20 %. No single factor dominates. The variance is spread across three more evenly represented directions. When one factor jumps — a sudden dollar surge, for example — the other two can still remain relatively quiet and absorb some of the impact. That is closer to what genuine diversification looks like when viewed through eigenvalues. The portfolio has more than one engine, so a problem with one engine does not stop the whole machine.
You can often see the difference just by looking at the bars. One tall bar and two short ones versus three bars of roughly similar height. Most experienced traders develop an intuitive feel for this pattern after looking at enough portfolios. But visual inspection leaves a practical question: when does a dominant factor become excessive? Is 70 % acceptable? Is 80 % already dangerous? Spectral entropy is designed to answer that question with a single, comparable number instead of leaving the judgment entirely to the eye.
Author: Kayode Michael Oyetunde