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Open Hedging CalculatorHistorical Forex Correlation Matrix
Compare 28 major and cross pairs across 30 to 365 calendar days using Pearson correlation of exact-interval-aligned daily simple returns derived from ECB reference rates. Inspect the actual sample behind every coefficient.
Daily ECB reference observations
Exact return-interval alignment
Model 1.0.0
What this matrix answers
A coefficient describes the direction and strength of a linear relationship between two historical return series in the selected sample. Values run from -1 to +1. They do not mean that the pairs moved together for that percentage of time, and they do not predict that the relationship will persist.
Near +1Moved in similar linear directions
Near 0Little linear association in this sample
Near -1Moved in opposing linear directions
Source and test context
The page requests daily EUR reference-rate legs attributed to the ECB through Frankfurter v2, derives the 28 cross-rate close series, and calculates close-to-close simple returns. The coefficient engine intersects two series by the exact return start and end dates, requires at least 10 aligned intervals, and withholds results when either series has zero variance.
Daily reference data, not live broker pricesThe displayed cross rates are modified analytical data. They are not executable quotes, intraday ticks, dealer spreads or a record of any broker account.
How to use the matrix
- 1Choose a calendar window
Compare the same method across 30, 60, 90, 180 or 365 calendar days.
- 2Scan, then inspect
Use the signed number and text band together. Select any matrix cell—or use the pair lookup on a small screen—to see its exact aligned sample.
- 3Carry context forward
Use the coefficient as one descriptive input. Position weights, volatility, account currency, hedge sizing and execution costs belong in separately governed tools.
Daily-return coefficient explorer
28 pairs, 378 unique pair combinations, one certified formula engine.
ECB reference rates via Frankfurter v2Requesting governed daily observations…
LoadingCoverage28 pairs
Latest observationWaiting for source
Selected window30 calendar days
Methodcorrelation_pearson 1.0.0
Building the matrixAligning daily return intervals and applying the minimum-sample gate.
No governed coefficient is available.The daily ECB reference series could not be loaded or did not pass its display gate. No cached coefficient, zero, hedge or recommendation was substituted.
Inspect a pair combinationAccessible alternative to selecting a matrix cell.
+0.80 to +1.00 Very strong positive
+0.30 to +0.79 Moderate to strong positive
-0.29 to +0.29 Near zero or weak
-0.79 to -0.30 Moderate to strong negative
-1.00 to -0.80 Very strong negative
Bands are descriptive product labels; no significance test is asserted.
Coefficient rankings in this sample
Ranked coefficient values, not trade candidates or hedge recommendations.
Highest positive
Largest positive linear associations.
Lowest negative
Largest negative linear associations.
Closest to zero
Smallest absolute linear associations.
Need a stable comparison view?The summary keeps the model fixed at 90 calendar days.
Open the 90-day summary
Share these display settings
Copies only approved selections. It never includes entered OHLC, prices, rates, balances, risk amounts, account details, source URLs, dates or uploaded content.
Worked example from the verification fixture
This is a synthetic formula test, not current market data or a claim about any forex pair. It exists so the coefficient, alignment rule and sample gate can be independently reproduced.
| Input | Available intervals | Aligned sample | Pearson r |
|---|---|---|---|
| Two synthetic return series | 12 and 10 | 10 exact intervals 2026-01-03 to 2026-01-13 | +1.000 |
The first two intervals of the longer series are omitted because the second series has no matching start-and-end dates. The remaining 10 aligned values form a perfect positive linear relation. This demonstrates why a calendar window or raw series length is not the coefficient’s sample count.
Method and settings
For each pair, the page first derives a daily close series from the available reference-rate legs. It then calculates simple close-to-close returns and intersects two return series only when both share the exact same start and end date interval.
return = (current close - previous close) / previous close
Pearson r = covariance(x, y) / (standard deviation(x) × standard deviation(y))
Pearson r = covariance(x, y) / (standard deviation(x) × standard deviation(y))
- Window: calendar days ending today in UTC; weekends and non-publication dates are not synthesized.
- Missing data: unmatched intervals are omitted pairwise and never replaced with zero.
- Minimum sample: at least 10 exact aligned intervals.
- Undefined result: withheld when either aligned return series has zero variance.
Sources and statistical references
The data adapter requests ECB-attributed daily reference rates through Frankfurter v2. The site then derives cross-rate closes and simple returns before applying the versioned Pearson model.
- European Central Bank euro reference exchange rates — official publication context and reference-rate limitations.
- Frankfurter v2 documentation — API parameters and ECB provider attribution.
- SciPy Pearson correlation documentation — coefficient definition and the -1 to +1 linear-association scale.
Limitations and outputs that require separate models
These limitations prevent a descriptive coefficient from being presented as a hedge, portfolio-risk estimate, significance result or trading recommendation.
Portfolio risk
No risk multiplier is inferred from an average coefficient. Position weights, covariance, volatility and account-currency exposure belong in the governed portfolio model.
Open Portfolio Risk CalculatorCorrelation anomaly
No typical coefficient is hard-coded. A dated, reproducible comparison baseline must be governed before a structural-shift or anomaly label can be displayed.
Frequently asked questions
- Model 1.0.0 calculates simple close-to-close returns from daily ECB reference-rate observations, intersects two series by the exact return start and end dates, and then applies the Pearson product-moment formula.
- The ECB publishes reference rates on business days. Weekends and non-publication days are not filled or interpolated, so the number of aligned return intervals is lower than the number of calendar days.
- A return is included only when both series share the exact same start and end date interval. Unmatched intervals are omitted pairwise and are never replaced with zero.
- Model 1.0.0 is approved for descriptive coefficients only. It does not assert the distribution and independence assumptions required for inferential p-values on these return series.
- No. Correlation alone does not determine hedge direction, size, stability, conversion or basis risk. Hedge-effectiveness outputs require a separate governed model and position inputs.
- No. The matrix uses daily ECB reference rates for information and analysis. The derived cross rates are modified data, not executable broker quotes or intraday prices.
Continue with governed context
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This reference-rate matrix does not include broker spreads, swaps, execution, symbol specifications or account terms. Check the relevant legal entity and platform before trading.
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Disclaimer: The results from this tool are estimates for educational and informational purposes only and may differ from your broker's figures. This is not financial or investment advice. Trading forex and CFDs carries a high level of risk and can result in the loss of all your capital. Always verify calculations with your broker and trade within your risk tolerance.