Finocturne
Statistics & Data Analysis

Correlation & Co-movement

Do two assets move together, in opposite directions, or without a straight-line pattern? Read paired returns before reading r.

Question, try, then observe

Moving together, or a different kind of relationship?

Each point pairs assets A and B in the same month. Switch the paired pattern, then append one complete outlier pair. Observe r and the scatter plot.

Illustrative data, not live market data. A monthly return of 2 = 2%; dispersion and return differences use percentage points, with no annualization.

01 · Make a predictionDoes r near zero prove there is no relationship?

Same-month paired returns

Asset B monthly return (%)
Same-month paired returns7 observations. Horizontal axis: Asset A monthly return (%). Vertical axis: Asset B monthly return (%). Read values with the observation selector or data table below.-214-303
Asset A monthly return (%)
Observed pairs (circles)
Observation 1 · Asset A monthly return (%): -3Asset B monthly return (%): -2
Read the data table
7 observations; units are shown in the headings.
No.Asset A monthly return (%)Asset B monthly return (%)
1-3-2
2-2-1
3-10
401
512
623
734

Centered sums of squares and cross-products for current pairs

Sxx≈28;Syy≈28;Sxy≈28

Cross-product sum divided by the root of the two square-sum product

r=2828×28≈1
  1. If either series has no variation, the denominator is zero and correlation is undefined, not zero.
Current Pearson r1.000
r without the outlier1.000
Paired sample size7

Current r=1.000. A positive sign means same-direction association; a negative sign means opposite-direction association. Its magnitude describes linear strength.

Correlation does not imply causation, and historical correlation need not persist. r is undefined if either series has no variation. Keep months correctly paired; never delete an observation from just one side.

Pair the deviations from each series' mean, sum their products, and divide by the square root of the two sums of squared deviations. r has no units and ranges from −1 to +1.

What did you just see?

Points rising to the right often have positive ; points falling to the right often have negative correlation. A clear curve may still have r near zero. One outlier can alter the overall reading.

Check pairing and shape first

Use matching periods and frequency across both series. Keep complete X/Y pairs. Missing values and mismatched counts are reported rather than silently deleting one side. Interpret r alongside outliers and nonlinear shapes.

Another example

  1. Place X and Y returns from the same period on the same row; 2 means 2%.
  2. Preserve one-to-one period pairing and check equal counts with no missing values.
  3. Calculate r and inspect the scatter plot for shape, outliers and nonlinear patterns.
Show formal definition and formula

Pearson correlation standardizes the co-movement of paired observations to describe linear association, not causation.

Pearson linear correlation

Divide paired deviation products by the square root of the product of squared-deviation sums. The result is undefined if either sum is zero.

xᵢ / yᵢ
Observations from the same period. A return input of 2 means 2%, calculated directly in percentage units.
n / x̄ / s
n is sample size, x̄ the sample mean, and s the sample SD using n−1 in the variance denominator.
r
Pearson r measures linear association from −1 to +1, without units. It is undefined if either series has no variation.

Common mistakes

Correlation is not causation. r≈0 does not rule out a nonlinear relationship, and history does not guarantee future stability. Two observations may give ±1 but provide very limited evidence.

Frequently asked questions

Can I sort the two series separately?

No. Each row represents the same period. Separate sorting or deleting a missing value on only one side breaks pairing and changes the question the correlation answers.

Does r near zero mean no relationship?

No. It indicates weak linear association, while a strong curved relationship may remain. Inspect the scatter plot too.

Does correlation establish causation or a future relationship?

No. Shared factors may drive both series, and historical correlation can change as market conditions change.

You can now explore…

  • Linear direction and outlier sensitivity
  • Correlation is not causation; zero r can hide a curve
Term reference2 terms

Open a term when you need a reminder. Underlined words in the article work too.