Correlation

Correlation is measured using the Pearson correlation coefficient, which ranges from -1.0 to +1.0:

Formula: Correlation(A,B) = Covariance(A,B) / (Std Dev A x Std Dev B)

The calculation uses daily returns (not prices) over a lookback period (typically 30, 60, or 252 trading days).

Interpretation scale:

• +0.7 to +1.0: Strong positive correlation. Assets move together. Most stocks within the same sector fall here (AAPL and MSFT: ~0.75). Holding both provides little diversification.
• +0.3 to +0.7: Moderate positive correlation. Assets move somewhat together. Stocks in different sectors (AAPL and JPM: ~0.45). Some diversification benefit.
• -0.3 to +0.3: Low or no correlation. Asset movements are largely independent. Stocks vs gold: ~0.05. Strong diversification benefit.
• -0.3 to -0.7: Moderate negative correlation. Assets tend to move in opposite directions. Stocks vs Treasury bonds: ~-0.30 to -0.50. Excellent for hedging.
• -0.7 to -1.0: Strong negative correlation. Assets move in opposite directions. Long SPY vs short SPY: -1.0 by definition.

Critical caveat — correlation is not constant. It changes over time and, most dangerously, spikes toward +1.0 during market crises. In the 2008 financial crisis and 2020 COVID crash, almost everything fell together. The diversification you planned for may disappear precisely when you need it most.

The diversification math: Portfolio volatility is not just the weighted average of individual position volatilities — correlation reduces it. Two assets with 20% individual volatility and 0.0 correlation, held equally, produce a portfolio volatility of only 14.1% (not 20%). The lower the correlation between holdings, the more free risk reduction you get.

Practical application: When adding a new position to your portfolio, check its correlation with existing holdings. If you already hold AAPL, MSFT, GOOGL, and NVDA (all 0.6-0.8 correlated with each other), adding AMZN provides minimal diversification. Adding gold (GLD, correlation ~0.05) or a utility stock (NEE, correlation ~0.3) reduces portfolio risk more effectively.

Correlation matrix: Professional portfolio managers use correlation matrices showing the correlation of every asset pair in the portfolio. Visualize it as a heat map — clusters of high correlation identify concentrated risk. If your matrix shows many cells above 0.7, you have a concentrated portfolio that will suffer large drawdowns when the correlated sector declines.

Position sizing adjustment: Some traders adjust position sizes based on correlation. If adding a position that correlates 0.8 with an existing position, reduce both sizes by 20-30% because they effectively behave as a single larger bet. This prevents stealth concentration where nominally different positions create the same risk exposure.

Rolling correlation: Check 30-day rolling correlation to see if relationships are stable or shifting. If two assets that were historically uncorrelated suddenly show rising correlation, your portfolio may be more concentrated than you think.

Correlation measures direction of movement. Two stocks that both go up on most days have high positive correlation. But correlation says nothing about the magnitude or long-term relationship — highly correlated stocks can drift apart permanently.

Cointegration measures a long-term equilibrium. Two cointegrated stocks maintain a stable price relationship over time. They may diverge temporarily but always revert to their historical spread. This is a stronger and more useful relationship for trading.

Example: Coca-Cola (KO) and PepsiCo (PEP) are both correlated and cointegrated — they move together and maintain a stable price ratio. Tesla (TSLA) and NVIDIA (NVDA) may be highly correlated (both move with tech sentiment) but are NOT cointegrated — their price ratio drifts unpredictably over time.

For pairs trading: Use cointegration, not just correlation. A pairs trade based only on high correlation may suffer unlimited loss if the spread keeps widening. A cointegrated pair has a statistical tendency to revert, giving the trade a mathematical edge.

For portfolio diversification: Use correlation. You want to hold assets that tend to move independently. Cointegration is not relevant for diversification — two cointegrated assets provide poor diversification because they move together in the long run.