Correlation Calculator Pro
Calculate the Pearson correlation coefficient between two return series, measure how relationships change over time with rolling correlation, build a full correlation matrix heatmap for up to 6 assets, and run linear regression to find Beta and R² — all from pasted return data, with no sign-up required.
Paste return values (one per line, or comma/space separated). Use decimal or percentage format — e.g. 0.05 or 5.0
Enter two return series and a window size to see how correlation changes over time.
Enter return data for up to 6 assets. Each column = one asset's return series. Paste each series separately.
Runs OLS linear regression: Y = α + β·X + ε. X = market / benchmark. Y = asset / portfolio.
Pearson r — Strength & Direction
| r Range | Interpretation | Portfolio Use |
|---|---|---|
| −1.00 to −0.70 | Strong negative | Excellent hedge |
| −0.70 to −0.30 | Moderate negative | Good diversifier |
| −0.30 to +0.30 | Weak / no correlation | True diversification |
| +0.30 to +0.70 | Moderate positive | Some diversification |
| +0.70 to +0.90 | Strong positive | Limited diversification |
| +0.90 to +1.00 | Very strong positive | No diversification benefit |
R² — Coefficient of Determination
R² = r² tells you what percentage of the variance in Y is explained by X.
| R² | Meaning |
|---|---|
| 0.90+ | X explains 90%+ of Y's moves |
| 0.50–0.90 | X is a major driver of Y |
| 0.20–0.50 | X is a moderate driver of Y |
| 0–0.20 | X explains little about Y |
Beta (β) — Market Sensitivity
Beta measures how much Y moves for every 1% move in X (the market benchmark).
| Beta | Meaning |
|---|---|
| β > 1.0 | More volatile than market (aggressive) |
| β = 1.0 | Moves with the market |
| 0 < β < 1.0 | Less volatile than market (defensive) |
| β = 0 | No relationship with market |
| β < 0 | Moves opposite to market (true hedge) |
p-value — Statistical Significance
The p-value tests whether the correlation is statistically different from zero.
| p-value | Interpretation |
|---|---|
| p < 0.01 | Highly significant (99% confidence) |
| 0.01 ≤ p < 0.05 | Significant (95% confidence) |
| 0.05 ≤ p < 0.10 | Marginally significant (90% confidence) |
| p ≥ 0.10 | Not significant — correlation may be random |
Rolling Correlation — Stability
Rolling correlation reveals how the relationship between two assets changes over time. Key questions:
- Is the correlation stable? — Low std dev of rolling r means a reliable, predictable relationship.
- Does r rise during downturns? — Correlation often spikes toward +1 during market stress, reducing diversification exactly when you need it most.
- % of periods with r < 0 — High percentage indicates a genuine long-term diversifier.
- Regime changes — Sudden sustained shifts in rolling r may indicate structural changes in the relationship (e.g., a policy change affecting one asset).
Using Correlation in Portfolio Construction
- True diversification requires r < 0.3 — adding an asset with r > 0.7 to an existing portfolio provides very limited risk reduction.
- Negative correlation ≠ always good — an asset with r = −0.8 to equities (like long bonds) also tends to have lower expected returns, reducing portfolio return as well as risk.
- Correlation is not causation — two assets may move together due to a shared factor (e.g., both are sensitive to USD strength), not because one drives the other.
- Short-period correlations are unreliable — with fewer than 30 data points, even a correlation of 0.4 may not be statistically significant. Always check the p-value.
- Correlation matrices change over time — always use rolling correlation alongside static correlation to understand the stability of relationships.
What each tab calculates
Pearson
Calculates the Pearson correlation coefficient r = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n·σx·σy), plus R² (coefficient of determination), t-statistic, p-value for significance testing, sample size, mean, and standard deviation for both series. Scatter plot visualizes the relationship.
Rolling
Computes Pearson correlation within a sliding window over the full return series, showing how the relationship between two assets changes over time. Reports latest, min, max, average, and std dev of rolling r, plus the percentage of periods where correlation was negative.
Matrix
Calculates all pairwise Pearson correlations between up to 6 assets simultaneously and displays results as a color-coded heatmap matrix. Darker green = lower correlation (better diversification); darker red = higher correlation. Reports average, min, and max pairwise r.
Regression
Runs OLS linear regression Y = α + β·X, calculating Beta (market sensitivity), Alpha (intercept), Jensen's Alpha (annualized), R², standard error of regression, tracking error, information ratio, and Beta p-value. Scatter plot with regression line and 95% confidence band.
Interpret
A comprehensive reference guide explaining how to interpret Pearson r, R², Beta, p-values, and rolling correlation — including practical tables for portfolio construction, diversification decisions, and statistical significance assessment.