Return Correlation — TWR
Pearson correlation of two reports’ daily returns over their overlapping period. +1 = move together, 0 = independent, −1 = move opposite. Lower is better for diversification.
- Computed from
- Equity curve
- Scope
- Across reports
- Range
- −1 to +1
- Direction
- Lower is better
Return correlation measures how closely two reports move together. It's the foundation of diversification — spreading your money across strategies that don't all win or lose at the same time, so one bad stretch doesn't sink everything. Combining strategies that don't rise and fall in lockstep smooths the combined equity curve far more than adding another copy of what you already have.
How it's calculated
ρ = covariance(rᵢ, rⱼ) / ( stdev(rᵢ) × stdev(rⱼ) )
- rᵢ, rⱼ
- the two reports’ per-period RETURNS (not curve levels) over the overlap
- ρ
- Pearson correlation coefficient, between −1 and +1
TWR basis (default): correlation of cashflow-neutral returns — the right read for "do these two strategies move together," independent of when money was deposited or withdrawn.
What it tells you
| Value | Reading | Notes |
|---|---|---|
| +0.7 to +1.0 | Redundant | The two move as one — little diversification benefit. |
| +0.3 to +0.7 | Related | Some shared drivers; partial diversification. |
| −0.3 to +0.3 | Independent | Largely uncorrelated — genuine diversification. |
| −1.0 to −0.3 | Hedging | One tends to rise when the other falls. |
Worked example
Two trend-following EAs both long EURUSD show ρ ≈ +0.85 — stacking them barely reduces risk, you've just doubled the same bet. Swap one for a mean-reversion system on a different pair and the pair might read ρ ≈ +0.1: now the combined curve is meaningfully smoother for the same return.
Pitfalls
- Correlation is regime-dependent. Pairs that look independent in calm markets often snap to +1 in a crisis — exactly when you needed diversification. Check the downside correlation, which measures co-movement on losing days only.
- One number hides a moving target. The ρ you see is an average over the whole overlap, but rolling correlation drifts as strategies, instruments, and market structure change — two reports can average ρ≈0.3 while swinging between −0.2 and +0.7. Treat a single coefficient as a summary, not a constant; a low average built from wild swings isn't the same diversification as a steadily-low pair.
- The payoff isn't linear. Cutting correlation from 0.9 to 0.7 barely improves real diversification; cutting it from 0.3 to 0.0 helps a lot. Independence is worth chasing hardest once a pair is already loosely coupled — which is why a whole book is summarized as Effective Strategies, not an average ρ.
- Needs enough overlap, and N varies per pair. Two reports sharing only a few weeks produce an unstable coefficient (SE ≈ 1/√N — about ±0.18 at 30 days); EquityTruth withholds a value below the minimum overlap. Always read ρ next to how many overlapping periods it's based on.
- Daily ρ is biased low (the Epps effect). Strategies that trade at different times of day look less correlated on daily returns than they really are; the weekly view heals most of it. A daily-vs-weekly gap is a sampling artifact, not a data error.
- It only sees the equity curve. Two strategies can show modest return correlation yet both be long the same symbol at the same moment — hidden concentration this number can't see. That's what the trade-overlap (exposure) view is for.
- Linear only. Pearson misses non-linear relationships. The rank-based Spearman variant catches some of what Pearson can't.
From pairs to a portfolio
A whole matrix of pairwise correlations is hard to read at a glance. EquityTruth distills it into Effective Strategies (N-eff) — the number of truly independent bets in a collection. Ten reports that all move together have an N-eff near 1; ten uncorrelated ones approach 10.