Worked example of Negative Correlation (with assumptions)

Direct answer

Negative correlation describes a relationship where two quantities tend to move in opposite directions. In the context of currency prices, traders often discuss correlation between returns (how much prices change), not the price levels themselves. A worked example can clarify the idea by using simple numbers and stating assumptions.

Mechanism and definition

Assume you observe two time series, A and B, and you compute returns for each period (for example, percentage changes). A common statistical summary is correlation, which measures whether movements go together:

• Positive correlation: when A goes up, B tends to go up.
• Negative correlation: when A goes up, B tends to go down, and vice versa.

A more direct building block is covariance. If the product of deviations from their averages is mostly negative, covariance and correlation tend to be negative. This is about joint movement patterns in the chosen time window.

Evidence via a worked numerical scenario (all assumptions stated)

We will create a small, fictional dataset with clear assumptions:

Assumptions

1. We use returns, not raw prices.
2. Returns are computed from close-to-close prices (how exactly is not important for the correlation logic).
3. We use five periods with equal spacing.
4. The numbers below are hypothetical and chosen to show the mechanism.

Data (returns per period, in percent)

• Series A returns: +1, +2, +1, 0, −1
• Series B returns: −1, −2, −1, 0, +1

Step 1: Compute averages

• Average(A) = (1 + 2 + 1 + 0 − 1) / 5 = 3/5 = 0.6
• Average(B) = (−1 − 2 − 1 + 0 + 1) / 5 = −3/5 = −0.6

Step 2: Compute deviations and products For each period, compute (A−avgA) and (B−avgB), then multiply:

• Period 1: (1−0.6)=0.4, (−1−(−0.6))=−0.4 → product = −0.16
• Period 2: (2−0.6)=1.4, (−2−(−0.6))=−1.4 → product = −1.96
• Period 3: (1−0.6)=0.4, (−1−(−0.6))=−0.4 → product = −0.16
• Period 4: (0−0.6)=−0.6, (0−(−0.6))=+0.6 → product = −0.36
• Period 5: (−1−0.6)=−1.6, (1−(−0.6))=+1.6 → product = −2.56

All products are negative, so covariance is negative.

Step 3: Interpret correlation Because A’s deviations are mostly opposite to B’s deviations in sign and the products are consistently negative, the correlation is negative in this constructed dataset.

Material limitation for this example This dataset is symmetric by design (Series B mirrors Series A with opposite sign). Real-world relationships rarely stay this exact: correlation can weaken, change sign, or become unstable when the market regime changes.

Limitations and risks (what can break negative correlation)

1. Window and sampling dependence: Correlation depends on the chosen time period and how you compute returns. Using different windows can yield different results.
2. Regime shifts: Relationships that look negatively correlated in one environment can move toward zero or even positive correlation in another.
3. Execution and costs: If applying the concept to trading or hedging, costs and timing differences can change realized co-movements versus what the statistical calculation suggests.
4. Non-stationarity: Currency dynamics can be affected by shifting expectations, liquidity conditions, and macro events; these can alter the joint behavior.
5. Small samples: With few periods, correlation estimates can be misleadingly strong. More data can reduce the chance of over-interpreting noise.

Verification and next question

To verify negative correlation independently, define clearly:

• what you treat as the two variables (e.g., returns of two instruments),
• the return calculation method,
• the time window and frequency,
• and the statistic (correlation, covariance, or scatter pattern).

Then check whether the joint movements show opposite-direction behavior consistently across multiple windows. If you want, tell me the exact two return series you’re comparing (in abstract terms) and the number of periods, and I can help you set up the calculations using your own data.