Correlation & Diversification

The correlation matrix tells a customer which strategies are independent bets. It is computed on the return series, not equity curves, and is exposed at GET /v1/correlation (and inside /v1/export).

Pearson on aligned returns

For each pair of strategies, standard Pearson correlation of their period-over-period returns over the periods they both have:

r(a,b) = Σ (aᵢ − ā)(bᵢ − b̄)  /  ( √Σ(aᵢ − ā)²  ·  √Σ(bᵢ − b̄)² )

• Pairwise-complete (inner join): correlation uses only the period labels present in both series (set(a) ∩ set(b)), sorted.
• Needs ≥ 2 overlapping periods, else the cell is null.
• Matrix is symmetric with a 1.0 diagonal; values rounded to 6 dp. The API also returns n_overlap — the number of shared periods behind each cell.
• Available daily or weekly (?period=), and for a subset of strategies (?ids=).

Why returns, not equity curves

:::warning Correlating equity curves is misleading Equity curves are trending, non-stationary series. Two strategies that both grow over years will show curve-correlation near +1 regardless of whether their bar-to-bar behaviour is independent — the shared upward drift dominates. Correlating returns (the period-over-period changes) removes that drift and measures genuine co-movement, which is what determines diversification. This dataset always correlates returns. :::

Risk-invariance

Pearson correlation is invariant under positive linear scaling: multiplying either return series by a constant (which is exactly what risk_pct does) leaves r unchanged. Therefore correlation is identical at any risk level — it is not affected by risk_pct and is returned the same in base and rescaled responses.

Effective bets

GET /v1/summary reports a single-number diversification gauge from the daily matrix:

mean_corr     = mean of the off-diagonal (i < j) non-null pairwise correlations
effective_bets = n / ( 1 + (n − 1) · mean_corr )

Interpretation: how many independent strategies the book behaves like. It equals n when all strategies are uncorrelated (mean_corr = 0) and collapses toward 1 as they become perfectly correlated. For the current dataset: n = 17, mean_corr ≈ 0.315 → ≈ 2.81 effective bets.

:::warning Effective-bets is a heuristic This formula depends only on the mean pairwise correlation. It ignores the structure of the correlation matrix (clusters, the eigenvalue spread, tail dependence). It is a quick, honest gauge of diversification — useful for comparison and a sanity check — not a portfolio-optimisation output or a substitute for the full matrix, which the API also provides. summary also reports the most- and least-correlated pairs so you can see the extremes behind the mean. :::

Performance Metrics

The per-strategy statistics this complements.

Provenance

Denomination, base risk, and why book_size = 1 here.