A plain-English guide to currency correlations.
What the correlation between two markets measures, how to compute it in five lines of arithmetic, and the one cell of today’s dollar matrix that’s gone the wrong way.
A correlation is one number that summarises how two markets moved together. It is also the most over-used number on a trading desk. What follows is the math, the worked example, and the live correlation matrix between the dollar, four FX pairs, gold, Brent, bitcoin, the S&P 500 ETF, and the US 10-year yield. We will point at the one cell that has gone the wrong way and explain why that is the most interesting number on the page.
What correlation actually measures
The Pearson correlation coefficient between two series, written r, takes values in [-1, +1]. It is defined as the covariance of the two series divided by the product of their standard deviations:
r(x, y) = Σ(xi - x̄)(yi - ȳ) / √(Σ(xi - x̄)² · Σ(yi - ȳ)²)
Two intuitions that matter. First, r is invariant to scale. Multiplying one series by ten does not change it; adding a constant does not change it. That is why it can compare a US Treasury yield in percentage points against bitcoin in dollars without converting units. Second, r measures the strength of the linear relationship only. A series that moves with its partner most of the time but reacts non-linearly on tail days will have a softer r than the eye expects.
Why we use returns, not prices
The cardinal mistake in retail correlation analysis is computing the correlation between two price levels. Two unrelated series with persistent trends will print high correlations purely because both are drifting; that is a property of the trend, not of the relationship between the assets. The right input is daily returns, ideally log returns, which are stationary in a way prices are not.
A log return between two consecutive closes is ln(Pt / Pt-1). Across a small daily move it is almost identical to the simple percentage return. Across a 10 percent move it differs by about half a percent. We use log returns because they aggregate cleanly across time (sum of daily log returns equals the log return over the full window).
A five-day worked example
Suppose we observe five daily closes for two assets, called x and y:
| Day | x | y | rx | ry |
|---|---|---|---|---|
| 0 | 100.0 | 50.0 | ||
| 1 | 101.0 | 49.6 | +0.99% | -0.80% |
| 2 | 100.7 | 49.9 | -0.30% | +0.60% |
| 3 | 102.0 | 49.2 | +1.28% | -1.41% |
| 4 | 101.5 | 49.5 | -0.49% | +0.61% |
Compute the means of the daily returns: r̄x = 0.37%, r̄y = -0.25%. Take deviations, multiply, sum. Take sums-of-squared deviations for each leg. Divide. The result for this toy series is r ≈ -0.99: a near perfect inverse relationship. Five days is not enough data to trust that number; a real correlation wants at least 60 trading days, which is the convention used by most desks for a rolling three-month measure.
The live matrix
Below is the daily-log-return correlation matrix across the dollar index, three USD-cross majors, gold, Brent, bitcoin, the S&P 500 ETF as an equity proxy, and the US 10-year yield. The window is the 47 trading days from 23 Mar 2026 to 28 May 2026 where every series had a close. Cells shade green for positive, oxblood for negative; intensity scales with the absolute reading.
| DXY | EUR/USD | USD/JPY | GBP/USD | Gold | Brent | BTC | SPY | US10Y | |
|---|---|---|---|---|---|---|---|---|---|
| DXY | -0.97 | +0.70 | -0.93 | -0.73 | +0.53 | -0.35 | -0.48 | +0.32 | |
| EUR/USD | -0.97 | -0.56 | +0.88 | +0.74 | -0.50 | +0.34 | +0.42 | -0.28 | |
| USD/JPY | +0.70 | -0.56 | -0.59 | -0.49 | +0.48 | -0.27 | -0.45 | +0.38 | |
| GBP/USD | -0.93 | +0.88 | -0.59 | +0.61 | -0.48 | +0.25 | +0.41 | -0.27 | |
| Gold | -0.73 | +0.74 | -0.49 | +0.61 | -0.44 | +0.34 | +0.37 | -0.40 | |
| Brent | +0.53 | -0.50 | +0.48 | -0.48 | -0.44 | -0.26 | -0.65 | +0.52 | |
| BTC | -0.35 | +0.34 | -0.27 | +0.25 | +0.34 | -0.26 | +0.45 | -0.31 | |
| SPY | -0.48 | +0.42 | -0.45 | +0.41 | +0.37 | -0.65 | +0.45 | -0.60 | |
| US10Y | +0.32 | -0.28 | +0.38 | -0.27 | -0.40 | +0.52 | -0.31 | -0.60 |
What stands out today
Three rows are doing what they should and one is not.
- DXY vs EUR/USD: -0.97. This is mechanical. The euro is the largest weight in the dollar index basket, at roughly 57 percent. The index has to move strongly inverse to EUR/USD. If you ever see this number far from the high 0.9s, the cause is a numerical glitch, not a market signal.
- DXY vs Gold: -0.73. The classic inverse: a stronger dollar lowers the price of gold measured in dollars, and vice versa. The number being this far below zero is the regime working as the textbook says.
- DXY vs Brent: +0.53. This is the surprise. The conventional sign is negative, on the same logic as gold. In the current window the two have moved together: the early-2026 geopolitical episode bid both the dollar and oil at the same time on safe-haven and supply premia. As the premium has unwound, both have come back together. A correlation can be a regime indicator before it is a hedging ratio. This number is telling you the dollar's behaviour is currently being driven by the same flow that drives oil, not by its usual rate-differential anchor.
Rolling windows beat single numbers
A single correlation collapses a regime into a number, which is fine for a glance and misleading for analysis. The standard response is to recompute the correlation on a rolling window: typically 30, 60, or 120 days. The DXY-Brent series we just discussed has spent most of the last decade slightly negative. Episodes of positive correlation tell you the dollar is being moved by something it usually isn't.
From correlation to beta
Correlation is unit-free. Beta is the slope of a linear regression of one series on the other, and it carries units. If you regress EUR/USD daily returns on DXY daily returns, the slope tells you how many percent EUR/USD moves per one percent move in DXY. With correlation near -0.97 and the basket weight on EUR at ~0.576, the regression slope you'd expect is close to -1/0.576 ≈ -1.74. The math falls out of the basket construction, not the market.
Practically: correlation tells you whether to use a pair as a hedge. Beta tells you how much of it. Confusing the two is the source of a lot of over-hedged and under-hedged books.
Things a correlation does not tell you
- Causation. A high r says the two series moved together. It does not say one moved the other, nor that a third factor isn't moving both.
- Tail behaviour. Pearson is dominated by typical days. Two assets can have r = 0.4 in calm weather and r = 0.95 in crisis weather. Rank correlation (Spearman, Kendall) and copula models exist for exactly this reason.
- Lead-lag. If one series moves first and the other follows by a day, the contemporaneous correlation understates the relationship. Cross-correlation at one or two lags is the cheap diagnostic.
- Stationarity of the regime. Correlations decay and re-form. The DXY-Brent number above is informative because it is unusual for this pair, not because the number itself is high.
What to read alongside this
- The dollar context that drives the matrix above: The dollar is weaker on the data, not the dots
- EUR positioning, the other side of the EUR/USD trade: EUR positioning has caught up
- How OIS prices fit into the rate side of the matrix: A plain-English guide to OIS