Correlation

Correlation measures the statistical relationship between two variables (investments), expressed as a coefficient between -1 and +1. It's fundamental to understanding diversification and portfolio construction.

Correlation Coefficient (r):

• +1.0: Perfect positive correlation (move together)
• 0: No correlation (independent movements)
• -1.0: Perfect negative correlation (move opposite)

Interpretation:

Range	Meaning
+0.7 to +1.0	Strong positive
+0.3 to +0.7	Moderate positive
-0.3 to +0.3	Weak/No correlation
-0.7 to -0.3	Moderate negative
-1.0 to -0.7	Strong negative

Examples:

• S&P 500 vs Total Stock Market: ~0.99 (nearly identical)
• US Stocks vs Int'l Stocks: ~0.70-0.85 (moderate-high)
• Stocks vs Bonds: ~0.0-0.3 (low)
• Stocks vs Gold: ~0.0-0.1 (very low)
• Stocks vs Inverse ETFs: ~-0.99 (nearly perfect negative)

Why Correlation Matters:

1. Diversification:

• Lower correlation = Better diversification
• Combining uncorrelated assets reduces portfolio risk
• "Don't put all eggs in one basket"

2. Portfolio Optimization:

• Modern Portfolio Theory uses correlations
• Efficient frontier depends on correlations
• Can achieve better risk-adjusted returns

3. Risk Management:

• Correlations can spike during crises
• "Correlations go to 1 in a crash"
• Tail correlations often higher than average

Limitations:

• Changes over time (not stable)
• Doesn't imply causation
• Historical correlation ≠ future correlation
• Non-linear relationships not captured