Correlation Calculator
Calculate the Pearson correlation coefficient between two asset price or return series.
10 values parsed
10 values parsed
Formula
Ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). 0 means no linear relationship.
The proportion of variance in one series explained by the other. An R² of 0.80 means 80% of one asset's variance is explained by the other.
Examples
- Series X (BTC): 0.02, -0.01, 0.03, -0.02, 0.01, 0.015, -0.005
- Series Y (ETH): 0.025, -0.015, 0.035, -0.025, 0.012, 0.02, -0.008
- Mean X = 0.00643, Mean Y = 0.00629
- Compute Σ(x−x̄)(y−ȳ), Σ(x−x̄)², Σ(y−ȳ)²
- r = 0.998
- Series X (BTC returns): 0.05, -0.03, 0.02, -0.04, 0.01
- Series Y (yield): 0.001, 0.0012, 0.001, 0.0011, 0.001
- Mean X = 0.002, Mean Y = 0.00106
- Very small covariance relative to X's variance
- r ≈ 0.12
- Series X (market): 0.03, -0.02, 0.01, 0.04, -0.03
- Series Y (strategy): -0.02, 0.015, -0.005, -0.03, 0.025
- The strategy tends to profit when the market drops
- Covariance is negative
- r ≈ −0.95
Key Concepts
What is Correlation?
Correlation measures the degree to which two variables move together. A correlation of +1 means they move perfectly in sync, −1 means they move in perfect opposition, and 0 means no linear relationship. In portfolio management, understanding correlations between assets is key to effective diversification.
Correlation in Crypto Markets
Most major cryptocurrencies are highly correlated with Bitcoin, often showing r values of 0.7–0.95. During market stress, correlations tend to spike toward 1.0 (everything drops together). True diversification in crypto often requires exposure to non-crypto assets or market-neutral strategies.
Correlation is Not Causation
Two assets can be highly correlated without one causing the other to move. Both might be driven by a common factor (like overall market sentiment or risk appetite). Always investigate the fundamental reasons behind observed correlations rather than assuming a causal link.
Diversification Benefit
Combining assets with low or negative correlations reduces overall portfolio volatility. If two assets have 20% individual volatility but a correlation of 0, the 50/50 portfolio has ~14% volatility (lower than either alone). At correlation −1, portfolio volatility can theoretically reach 0%.
Rolling vs Static Correlation
A single correlation number can be misleading. Correlations change over time — crypto assets that are uncorrelated in bull markets often become highly correlated during crashes. Rolling correlation (e.g., 30-day windows) reveals how the relationship evolves and helps with dynamic portfolio rebalancing.
Limitations of Pearson Correlation
Pearson correlation only captures linear relationships. Two assets could have a strong nonlinear relationship (like options and their underlying) but show a low Pearson r. It's also sensitive to outliers — a single extreme data point can significantly distort the result.
How to Calculate and Use Correlation for Portfolio Construction
The Pearson correlation coefficient is the standard measure for linear association between two series. For portfolio construction, it tells you how much diversification benefit you get from combining two assets. The lower the correlation, the greater the risk reduction when held together.
To use this calculator, paste two series of equal length — these can be daily returns, prices, or any paired numeric data. The calculator computes the Pearson r, its interpretation, and R² (the proportion of variance explained). For prices, consider using returns instead, as raw prices can show spurious correlation due to shared upward trends.
In crypto portfolio management, correlation analysis helps identify which tokens provide genuine diversification and which are effectively just leveraged bets on the same direction. Adding a token with r = 0.95 to BTC provides almost no diversification benefit, while adding one with r = 0.3 meaningfully reduces portfolio risk.
Frequently Asked Questions
Should I use prices or returns for correlation?
Returns (percentage changes) are strongly preferred. Raw prices of two assets that both trend upward will show high positive correlation even if their movements are unrelated. Returns remove the trend component and capture the actual co-movement of price changes.
How many data points do I need?
At minimum 20–30 pairs for a meaningful estimate. For reliable results, 60+ data points are recommended. With fewer than 15 pairs, the correlation estimate has very high uncertainty and may not reflect the true relationship.
Why does crypto correlation increase during crashes?
During market stress, most assets are sold simultaneously as traders reduce risk. This 'correlation breakdown' or 'risk-off' behavior means diversification benefits disappear precisely when you need them most. It's a well-known phenomenon in both traditional and crypto markets.