Currency Pair Correlation Calculator
Calculate currency pair correlation with our free Currency pair correlation Calculator. Compare rates, see projections, and make informed financial
Currency Pair Correlation Calculator
Calculator
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Formula: r = Cov(X,Y) / (StdDev(X) × StdDev(Y))
Worked example — Correlation = 0.9623 (Very Strong Positive) | R² = 92.60%
Formula
r = Cov(X,Y) / (StdDev(X) × StdDev(Y))
The Pearson correlation coefficient divides the covariance of two return series by the product of their standard deviations. It produces a value between -1 (perfectly inverse) and +1 (perfectly aligned). R-squared (r²) gives the proportion of variance explained.
Worked Examples
Example 1: EUR/USD vs GBP/USD Positive Correlation
Problem:Given 10 daily returns for EUR/USD (0.5, -0.3, 0.8, -0.1, 0.4, -0.6, 0.2, 0.7, -0.4, 0.3) and GBP/USD (0.4, -0.2, 0.6, -0.3, 0.5, -0.5, 0.1, 0.8, -0.3, 0.2), calculate correlation.
Solution:Mean EUR/USD = 0.15, Mean GBP/USD = 0.13 Sample covariance = 0.2039 Std EUR/USD = 0.4790, Std GBP/USD = 0.4423 Correlation = 0.2039 / (0.4790 × 0.4423) = 0.9623 R-squared = 0.9623² = 92.60%
Result:Correlation = 0.9623 (Very Strong Positive) | R² = 92.60%
Example 2: Hedge Ratio Calculation
Problem:EUR/USD and USD/CHF have correlation -0.92, StdDev 0.45% and 0.40% respectively. Calculate hedge ratio for a $100,000 EUR/USD position.
Solution:Hedge Ratio = -(corr × StdDev1 / StdDev2) = -(-0.92 × 0.45 / 0.40) = 1.035 Hedge Size = 1.035 × $100,000 = $103,500 Note: the diversification benefit the tool reports needs the two return series, not just the summary statistics above, so it is not derivable from this example alone — paste both series in to see it.
Result:Hedge Ratio = 1.035 | Hedge Size = $103,500 USD/CHF long
Frequently Asked Questions
What is currency pair correlation in forex trading?
Currency pair correlation measures how two currency pairs move in relation to each other over a given time period. The correlation coefficient ranges from +1.0 (perfectly positively correlated, moving in the same direction) to -1.0 (perfectly negatively correlated, moving in opposite directions), with 0 indicating no relationship. For example, EUR/USD and GBP/USD often show positive correlation because both are quoted against the US dollar. Understanding correlations helps traders avoid doubling risk by taking similar positions in correlated pairs, identify hedging opportunities using negatively correlated pairs, and build diversified portfolios that reduce overall risk exposure in the forex market.
How do you calculate the Pearson correlation coefficient?
The Pearson correlation coefficient (r) is calculated by dividing the covariance of two data sets by the product of their standard deviations. The formula is: r = sum((xi - mean_x)(yi - mean_y)) / sqrt(sum((xi - mean_x)^2) * sum((yi - mean_y)^2)). First, compute the mean of each data set. Then, for each observation, calculate the deviation from the mean for both series. Multiply corresponding deviations, sum them for the covariance numerator. Separately, square each deviation and sum them for the denominator components. The resulting coefficient is bounded between -1 and +1 and is dimensionless, making it easy to compare correlations across different pairs regardless of their pip values or volatilities.
Why do currency correlations change over time?
Currency correlations are dynamic and shift due to evolving macroeconomic conditions, central bank policies, geopolitical events, and market sentiment changes. For instance, during risk-off events, traditionally uncorrelated pairs may become highly correlated as investors flee to safe-haven currencies simultaneously. Changes in interest rate differentials between countries alter carry trade dynamics, shifting correlations. Commodity price swings affect commodity-linked currencies (AUD, CAD, NZD) differently depending on which commodities are moving. Trade policy changes, economic divergence between regions, and shifts in capital flows all contribute. Traders should regularly recalculate correlations using rolling windows rather than relying on static historical values.
How can traders use correlation for hedging?
Traders use negative correlations to hedge existing positions and reduce portfolio risk. If you hold a long EUR/USD position, you could hedge by going long on USD/CHF, which historically has a strong negative correlation with EUR/USD. The hedge ratio determines the position size: Hedge Size = -(correlation * StdDev_pair1 / StdDev_pair2) * Position_pair1. A perfect hedge (correlation of -1.0) eliminates directional risk but also eliminates profit potential. Partial hedges using moderately negatively correlated pairs (-0.5 to -0.8) reduce risk while retaining some profit potential. Traders should monitor correlation stability, as correlations can break down during high-volatility events precisely when hedging is most needed.
What is R-squared and how does it relate to correlation?
R-squared (coefficient of determination) is the square of the correlation coefficient and represents the percentage of one variable's variance that is explained by the other variable. For example, if EUR/USD and GBP/USD have a correlation of 0.85, the R-squared is 0.7225 or 72.25%, meaning approximately 72% of GBP/USD's price movements can be explained by EUR/USD's movements. The remaining 28% is driven by independent factors. R-squared ranges from 0 to 1 (0% to 100%) and does not indicate direction — both +0.8 and -0.8 correlations yield the same R-squared of 0.64. R-squared is particularly useful for assessing the reliability of using one pair as a proxy or hedge for another.
Why do two pairs that share the US dollar sometimes correlate negatively?
What matters is which side of the quote the shared currency sits on. In EUR/USD and GBP/USD the dollar is the quote currency in both, so broad dollar strength pushes both lower and the coefficient is usually positive. In USD/CHF the dollar is the base currency, so that same strength lifts it while EUR/USD falls, giving a negative reading. Simply inverting how a pair is quoted flips the sign of every correlation it appears in.
How does the portfolio risk figure combine two correlated positions?
It applies the two-asset variance formula: the squared risk of each leg, plus twice the product of the two risks and the correlation, then takes the square root. That is why combined risk is not the simple sum of the parts. Two equally sized legs of equal volatility add to the full arithmetic sum at a correlation of +1, come to about 71 percent of it at zero correlation, and cancel entirely at -1.
What is the difference between the correlation coefficient and the beta reported here?
Correlation is symmetric, unitless and bounded between -1 and +1, describing how tightly two series move together. Beta is the slope of a regression of the second pair on the first and equals the correlation multiplied by the ratio of the two standard deviations, so it describes how far pair two typically travels per unit move in pair one. Swap which pair you treat as the driver and beta changes, while correlation does not.
Why should correlation be measured on returns rather than raw exchange rates?
Exchange rate levels trend, and two trending series can produce a high coefficient simply because both drifted across the sample rather than because they share a driver. Percentage returns remove the level and leave the co-movement you actually trade. Sampling times matter as well: comparing a series taken at the New York close with one taken at a broker using a different rollover time blurs the day-to-day pairing and weakens the measured relationship.
How many observations should I paste in for a stable reading?
The calculator will run on as few as three pairs of returns and truncates both series to the length of the shorter one, but with a handful of observations a single outlier session dictates the answer. Rolling windows of roughly 20 to 30 daily returns are common for tactical decisions, with a hundred or more used for structural relationships. Recompute the window as it rolls forward instead of relying on one static figure.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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