Methodology: Correlation Matrix Visualizer

Scope

Computes pairwise Pearson correlations across a wide-format returns CSV, renders them as a heatmap, and reports portfolio-diagnostic statistics that summarize how redundant the strategies are to each other.

Input format

date,strategy_1,strategy_2,strategy_3,strategy_4
2024-01-02,0.0012,0.0008,-0.0003,0.0015
2024-01-03,-0.0005,-0.0002,0.0004,-0.0006
...

The date column (or timestamp / time) is optional and ignored for correlation computation. All remaining numeric columns are treated as return series and assumed aligned row-by-row.

Algorithms

Pearson correlation

ρ(x, y) = Σ_i (x_i − x̄)(y_i − ȳ) / ((n − 1) · σ_x · σ_y)

Sample standard deviation (divide by n − 1). Columns with zero variance produce ρ = 0 to avoid division by zero.

Eigenvalue decomposition

The correlation matrix R is real-symmetric. Eigenvalues are computed with the classical Jacobi rotation method: iterate through all off-diagonal entries, annihilating the largest with a planar rotation, until the sum of squared off-diagonals drops below 10⁻¹⁰. For the matrix sizes this tool targets (typically 2–20 strategies), Jacobi is accurate and simple.

Diagnostics

Average absolute off-diagonal correlation: mean of |ρ_ij| for i < j. A single scalar summary of redundancy.
Condition number: κ(R) = λ_max / λ_min. Large κ indicates a near-singular matrix; mean-variance optimization becomes unstable. κ > 100 is ill-conditioned; κ > 1000 is effectively singular.
Explained by first PC: λ_max / m. Because trace(R) = m, this is the share of total variance captured by the first principal component. Values above 0.6 indicate the portfolio is essentially one bet.
Effective number of axes (participation ratio): N_eff = (Σ λ_i)² / Σ λ_i². A smooth analogue to "how many independent strategies do you actually have." For the identity matrix N_eff = m; for a rank-1 matrix N_eff = 1.

Assumptions + limitations

Aligned rows. Column i and column j are assumed to refer to the same time point in each row. Misaligned data produces spurious low correlations.
Simple returns, not log returns. Pearson correlation is identical under linear rescaling, so mixing return conventions across columns changes scale but not the correlation structure. Still, prefer consistency.
IID observations. Standard Pearson assumes independent rows. Autocorrelated returns (common in slow-moving or overlapping strategies) inflate the effective sample size. For dense clusters of autocorrelated series, treat the reported correlations as upper-bound confidence.
Sample size. A minimum of 30 rows is enforced. Stable estimates typically require 200+ observations; 500+ for m > 10 columns.
Heatmap legibility. The rendering comfortably handles up to ~20 columns. For larger universes, pre-cluster before uploading.
Tail behaviour. Pearson captures linear co-movement only. Under regime changes (crashes), non-linear tail dependence can spike even when Pearson ρ looks moderate. Combine with a tail-dependence estimator for stress-regime analysis.

Privacy

All parsing and computation run in the browser. The CSV is never uploaded. No cookies, no tracking. Reload the page and the data is gone.

References

Pearson, K. (1895). "Notes on Regression and Inheritance in the Case of Two Parents." Proceedings of the Royal Society.
Press, W. H. et al. (2007). Numerical Recipes, 3rd ed., §11.1 (Jacobi rotations).
Laloux, L., Cizeau, P., Potters, M., & Bouchaud, J.-P. (2000). "Random Matrix Theory and Financial Correlations." International Journal of Theoretical and Applied Finance 3(3).
Meucci, A. (2009). "Managing Diversification." Risk 22(5).

Connects to

Risk-Adjusted Returns Calculator — per-strategy metrics complement the cross-strategy picture.
Backtest Overfitting Score — if the correlation matrix is near-singular, your "20 strategies" are probably one overfitted signal.
Fractional Kelly Sizer — correlation determines whether per-strategy Kelly sizes compose into a sane portfolio.

Changelog

2026-04-20 — Initial release with Pearson correlation, Jacobi eigenvalues, participation ratio, and condition number.