Correlation

Correlation tells you how much two assets move together. It runs from -1 to +1:

• +1 means they move in lockstep.
• 0 means no consistent relationship.
• -1 means they move in opposite directions.

Why it matters: correlation drives diversification. Two volatile assets can still make a steadier portfolio if their moves don't line up.

The formula (Pearson)

We use the standard Pearson correlation of daily returns:

$$\rho = \frac{\text{Cov}(r_a, r_b)}{\sigma_a \sigma_b}$$

Where $r_a$ and $r_b$ are daily returns for the two assets.

Example (what the number means)

• A correlation of 0.80 usually means the assets rise and fall together.
• A correlation of 0.10 means they're mostly independent.
• A correlation of -0.20 means they often move in opposite directions (good for hedging).

How we calculate it at Gale Finance

• Daily returns on shared dates. We only compare days where both assets have a price.
• Rolling Pearson correlation. We use a 30-day rolling window and report the current, average, min, and max correlation from that series.
• Same window as the article. Rolling comparisons use the same 1-year window shown on the page.
• Context matters. Correlation tends to rise during stress, so a "low" correlation today can become "high" in a selloff.

Common misconceptions

• Correlation is not causation. Two assets can be highly correlated without any direct link.
• Correlation isn't stable. It changes by regime.
• Low correlation doesn't guarantee safety. In a crisis, correlations often spike.

For a fuller risk picture, pair correlation with volatility and tail dependency.