Who this is for — Anyone comparing assets or strategies who wants to measure one precise form of co-movement without turning it into a promise of diversification.
Pearson correlation standardises covariance between two series
X and Y:
ρ(X,Y) = Cov(X,Y) / (σₓ × σᵧ)The coefficient lies between −1 and +1 when both standard deviations are positive. Its sign gives the direction of the linear relation; its absolute value describes strength in the selected sample. The estimate does not prove causality and does not by itself describe nonlinear or tail dependence.
The sample comes before the number
A correlation is interpretable only when the following are stated:
- variables used, normally returns or P&L changes rather than cumulative levels;
- frequency, interval, time zone and synchronisation rule;
- currency and treatment of missing prices, holidays and outliers;
- window or regime and estimation method;
- gross or net-of-cost data when strategies are compared.
Correlating equity-curve levels can produce a spurious result because both series embed their cumulative paths. For strategies with asynchronous trades, build returns or P&L over common calendar intervals; matching trades by sequence number does not create economic simultaneity.
What the coefficient does not establish
| Reading | Limitation |
|---|---|
| ρ near zero | no linear relation in the sample, not independence |
| negative ρ | opposite linear co-movement, not a perfect hedge or zero P&L |
| high ρ | strong observed linear relation, not “the same trade” by definition |
| rolling ρ | window-dependent diagnostic, not a stable forecast |
| historical matrix | estimate subject to sampling error, regime and data quality |
No universal bands divide “good” from “bad” correlation. A control threshold must reflect the mandate, the decision's risk, statistical uncertainty and the scenarios that matter.
Stress, volatility and tails
Dependencies can change in sell-offs, but “everything goes to +1 in a crisis” is an invalid generalisation. Longin and Solnik document higher international equity correlation in extreme bear markets, not a universal law; flight-to- quality relationships can also become more negative. Forbes and Rigobon show that rising volatility can bias comparisons of conditional correlation across periods.
Portfolio decisions should therefore pair correlation with scatter plots, regime analysis, common scenarios, downside co-movement and factor concentration. Diversification is an outcome of the full portfolio, not of a single pairwise coefficient.
Common mistake — Selecting a window until it gives the desired value, then treating that value as structural. Window and method are part of the result and must remain visible.
Sources
- National Institute of Standards and Technology, CORRELATION — Dataplot Reference Manual — definition, formula, range and interpretation of the linear correlation coefficient.
- Harry Markowitz, Portfolio Selection, The Journal of Finance (1952) — the role of variances and covariances in portfolio construction.
- François Longin and Bruno Solnik, Extreme Correlation of International Equity Markets, The Journal of Finance (2001) — asymmetric dependence in extreme international equity returns.
- Kristin Forbes and Roberto Rigobon, No Contagion, Only Interdependence: Measuring Stock Market Comovements, The Journal of Finance (2002) — heteroskedasticity bias when comparing correlations across turbulent periods.