Imagine a hypothetical trader buying EUR/USD and GBP/USD and calling the portfolio diversified because the pair names differ. Both positions share USD exposure and can lose together in a dollar-strengthening scenario. Correlation describes a measured relationship, while currency notionals describe exposure; neither pair count nor a coefficient alone establishes risk reduction.

Correlation before and after a date error

Before interpreting the coefficient’s sign, check that the compared returns cover the same periods.

Scroll sideways to see the full diagram

Correlation before and after a date errorFour fictional same-date pairs have identical A and B, alternating −1% and +1%, so r = +1; each scatter point represents two observations. Pairing A days 1–3 with B days 2–4 incorrectly gives opposite signs, r = −1 and three observations. Both scatterplots use identical scales. The number at a point counts overlapping pairs, not the return value.Date pairing alone can reverse the signSame dateB shifted by 1 day-1%-1%+1%+1%AB22r = +1-1%-1%+1%+1%AB21r = −1Point number: observation-pair countSame data. Different pairs.

Our own counterexample: Four fictional daily percentage returns, matching periods and no transaction costs. Correctly pair A and B from the same date. Incorrectly pair A days 1–3 with B days 2–4. This is a data error, not an arbitrage strategy or market forecast.

Arbitrary dayReturn AReturn B
1−1%−1%
2+1%+1%
3−1%−1%
4+1%+1%

The four correct pairs have B = A, so r = +1. The three incorrect pairs are (−1; +1), (+1; −1), (−1; +1); B = −A, so r = −1. Shifting the pairing alone reverses the sign without changing any return. The NIST formula computes the coefficient from corresponding pairs. Before calculating, compare date, time, time zone and return interval in both series.

A date error reverses the correlation sign without changing either series’ values.

What currency pair correlation actually is

Pearson correlation measures linear association between paired observations and ranges from −1 to +1 when both variances are nonzero. A perfect negative correlation means a negative linear relationship, not equal absolute moves. Zero means no measured linear association and does not prove independence. For returns, use matching dates, times and intervals; a shared price-level trend can produce a different result from return correlation.

Shared currencies can create common exposures, but do not force a particular correlation. Record the currencies, signed notionals and conversion assumptions of each position, then calculate return correlation on aligned observations over a stated window.

Positive and negative correlation in concrete examples

EUR/USD and GBP/USD both quote USD. Two long positions therefore share short-USD exposure, but the measured correlation depends on the sample and return interval. No current coefficient is supplied here. Check the dated data window rather than treating an illustrative positive relationship as a fixed +0.9 property.

USD appears on opposite sides of EUR/USD and USD/CHF. Their returns can be negatively associated, but no current coefficient is established here. The non-USD currencies and policy changes also matter; compute the relationship on a dated and aligned return sample.

No measured coefficients have been supplied for those market pairs. In a separate fictional four-return example, A is −2%, −1%, +1%, +2% and B is −4%, −2%, +2%, +4%. Pearson r = +1 even though B’s amplitude is twice A’s. A perfect negative relationship likewise need not have equal-sized opposite moves. For a constant series Pearson correlation is undefined because its denominator is zero. Four points demonstrate arithmetic, not a stable market relationship.

Currency notionals and total planned risk

In a hypothetical EUR10,000 account, two positions each with EUR100 planned stop risk add to EUR200, or 2%, if both stops execute at their assumed prices. That arithmetic does not depend on correlation. Shared dollar exposure can concentrate scenario risk, but return correlation alone does not determine simultaneous stop hits, loss magnitude or a doubled USD notional.

Calculate signed currency amounts before calling a hedge complete. In a hypothetical spot-equivalent model without spread or financing, buying EUR 10,000 at 1.1000 and GBP 10,000 at 1.2500 gives +EUR 10,000, +GBP 10,000 and −USD 23,500. Instead selling GBP 8,800 at 1.2500 gives +USD 11,000, offsetting the first EUR leg’s −USD 11,000, while +EUR 10,000 and −GBP 8,800 remain. This removes the model’s initial USD notional but does not make the whole portfolio risk-free. Instrument terms, valuation and costs still matter. A long USD/CHF hedge also needs its USD amount matched, not merely equal lot counts.

Why correlation is not constant

A coefficient describes the selected paired sample, not a fixed physical property. Specify dates, interval, price basis and whether you calculate returns or levels. For simple returns use r(t) = P(t)/P(t−1) − 1 and align the same periods. Different windows can produce different estimates, but a changed window does not necessarily change the number. A broker table is interpretable only with its data and calculation definitions.

Zero correlation is not independence. In a fictional example using percentage-point numbers, A = (−2, −1, 1, 2) and B = (4, 1, 1, 4), so B is A squared. Mean A is 0 and mean B is 2.5. The cross-deviation sum is −3 + 1.5 − 1.5 + 3 = 0, while both variances are nonzero: Pearson r = 0 despite deterministic nonlinear dependence in these four points. This is not a model of actual currency returns or evidence about a fifth observation.

Policy changes can be included in dated scenario analysis. On 15 January 2015 the SNB announced the end of the CHF 1.20-per-euro minimum. The announcement establishes that policy event; it does not provide a measured correlation comparison or prove that all correlations go to one in every crisis. The intermarket analysis guide provides wider context. Assess shared exposures and stress scenarios as well as a linear coefficient.

Triangular exchange cycles versus statistical convergence

A triangular exchange cycle returns to its starting currency using three executable conversions. Selling a base currency uses Bid and buying it uses Ask. A difference between direct and synthetic mid-rates does not establish a positive completed cycle. Assume fictional simultaneous quotes with enough volume for the exercise: EUR/USD 1.1000/1.1002, GBP/USD 1.2500/1.2502 and EUR/GBP 0.8801/0.8803, all Bid/Ask.

Fictional EUR → GBP → USD → EUR cycle
ConversionCorrect sideBalance
Sell EUR 10,000 for GBPEUR/GBP Bid 0.8801GBP 8,801
Sell GBP for USDGBP/USD Bid 1.2500USD 11,001.25
Buy EUR with USDEUR/USD Ask 1.1002EUR 9,999.3183 approximately

The cycle loses about EUR 0.68 before extra fees, even though direct EUR/GBP midpoint 0.8802 differs from the dollar-pair midpoint ratio, about 0.88001. Spread is already in the Bid/Ask prices. For this direction, EUR/GBP Bid must exceed 1.1002/1.2500 = 0.88016 just to produce a positive gross result. Commissions and execution risk add further conditions.

Fenn and co-authors’ 2008 paper distinguishes indicative prices from executable quotes and a displayed discrepancy from successfully completing all legs. Its historical data and simulations have stated periods, fill and cost assumptions; they are not a universal current latency measurement. Check available size, timestamp consistency, fees and the residual exposure if only part of the cycle fills. Three retail CFDs do not automatically replicate three delivered-currency exchanges. ECB reference rates are information-only and the ECB discourages their use for transactions; they are not executable arbitrage quotes.

Pairs trading seeks a change in relative valuation; it does not guarantee convergence. Define the spread, position weights, entry/exit conditions and evaluation horizon. High return correlation does not prove a chosen price combination is stationary or will revert. Cointegration concerns a suitable stationary combination of otherwise nonstationary series, rather than merely correlated short-term returns. Gatev, Goetzmann and Rouwenhorst’s cited study forms stock pairs in a twelve-month period and trades them in the next six months, with stated exit and cost assumptions. It is not evidence that any two Forex pairs will be profitable. Statistical arbitrage is a broader family; pairs trading is one example and still has divergence and execution risk.

Keep three questions separate: what a linear coefficient says about the sample, what signed notionals say about the positions, and whether a specified strategy or exchange cycle produces a net result under executable prices. Neither a correlation threshold nor an apparent midpoint gap supplies a position size, a complete hedge or a free-money trade.

What to do tomorrow

  1. Write each position’s signed currency notionals, conversion prices and instrument settlement assumptions. Add shared components before assessing risk.
  2. Align each return by date, time zone and period, then state the window and calculation. Check missing observations and constant-series cases.
  3. Assess total planned stop risk and residual exposure. A chosen correlation of +0.7 does not imply that halving both positions restores a specific account risk.
  4. Compare dated windows and stress scenarios under a prewritten update rule. No universal weekly schedule or macro event guarantees that a relationship changes.
  5. For a proposed cycle, use executable Bid/Ask, volume and all fees. Record incomplete fills and the remaining currencies as well as successful complete cycles.

A repeatable comparison retains failed convergence, incomplete cycles and all costs as well as successful cases. Choose rules on one segment and assess unchanged rules on later data. The fictional examples here explain arithmetic and data alignment; they do not estimate current correlations, broker execution quality or future profits.