Correlation - Parallax API

Correlation measures whether two investments tend to move together, move in opposite directions, or move independently. It’s the foundation of diversification and portfolio construction.

Beginner

What It Means

Correlation tells you the relationship between how two investments move:

Positive correlation (+1): They move together
Negative correlation (-1): They move in opposite directions
Zero correlation (0): Their movements are unrelated

Portfolio Examples

Stock Pair	Correlation	What It Means
Stock A & B	+0.9	When A goes up, B strongly tends to go up too
Stock A & C	-0.7	When A goes up, C strongly tends to go down
Stock A & D	0.0	A’s movements tell you nothing about D

Correlation doesn’t tell you the magnitude of movements, only the direction and strength of the relationship. The actual percentage moves depend on each investment’s volatility.

Why It Matters

Lower correlation between your holdings means better diversification. When one investment falls, others may hold steady or rise, reducing overall portfolio risk. This is the only “free lunch” in investing.

Advanced

Mathematical Definition

Correlation (ρ) = Cov(Ra, Rb) / (σa × σb)

Where:
- Cov(Ra, Rb) = Covariance of returns between assets A and B
- σa, σb = Standard deviations of assets A and B
- Range: -1.0 to +1.0

Interpretation Scale

Correlation	Interpretation
+1.0	Perfect positive (move in lockstep)
+0.7 to +0.9	Strong positive
+0.4 to +0.6	Moderate positive
-0.1 to +0.3	Weak/no correlation
-0.4 to -0.6	Moderate negative
-0.7 to -0.9	Strong negative
-1.0	Perfect negative (perfect hedges)

Historical Context

Correlation’s importance in portfolio theory stems from Markowitz’s Modern Portfolio Theory (1952). He showed mathematically that portfolio risk depends not just on individual asset risks, but critically on how assets correlate with each other. This insight revolutionized portfolio construction.

What Makes It Useful

Diversification Quantification: Lower correlation = greater diversification benefits
Portfolio Risk Reduction: Portfolio with N uncorrelated assets has risk reduced by factor of √N
Risk Decomposition: Identify which holdings contribute most to portfolio risk
Hedging Strategy: Find negative correlation assets for portfolio protection
Multi-Asset Allocation: Construct portfolios spanning stocks, bonds, commodities based on correlation matrix

Diversification Math

Two-asset portfolio variance:
σp² = wa²σa² + wb²σb² + 2wawbσaσbρab

Where ρab is correlation between assets A and B

If ρab = 1.0:  No diversification benefit (risk is weighted average)
If ρab = 0.0:  Significant diversification (portfolio risk < weighted average)
If ρab = -1.0: Maximum diversification (can create zero-risk portfolio)

Data Requirements

Requirement	Duration	Notes
Minimum	36 months (3 years)	Basic correlation estimate
Preferred	60+ months (5 years)	Portfolio construction decisions
Updates	Quarterly or semi-annually	Correlations change across regimes

“Correlation goes to 1 in a crisis” - diversification fails when you need it most. Update correlations frequently.

Limitations

Instability Over Time: Correlations increase during market stress
Linear Relationship Only: Doesn’t capture non-linear dependencies
Outlier Sensitivity: Extreme events disproportionately influence correlation
Assumes Stationarity: Historical correlation may not persist

Alternatives

Alternative	Description
Rank Correlation (Spearman)	More robust to outliers, captures monotonic relationships
Tail Dependence	Measures correlation specifically during extreme events
Copulas	Capture full dependency structure beyond linear correlation
Rolling Correlation	Time-varying correlation that adapts to changing relationships

Correlation Breakdown in Crises

Empirical Reality:

Market Condition	Average Stock Correlation
Calm (VIX < 15)	~0.25
Normal (VIX 15-25)	~0.35
Stress (VIX > 30)	0.65-0.80
2008 Crisis	~0.85

Key Insight: Longin and Solnik (2001) documented extreme correlation asymmetry - correlations spike during crashes but not rallies.

Practical Guidance: Stress test portfolios using correlation = 0.8, not historical average. Diversification works in calm markets but fails in crises.

Beta

Correlation with market specifically

Standard Deviation

Individual asset volatility

Drawdown

What happens when correlations spike

​Beginner

​What It Means

​Portfolio Examples

​Why It Matters

​Advanced

​Mathematical Definition

​Interpretation Scale

​Historical Context

​What Makes It Useful

​Diversification Math

​Data Requirements

​Limitations

​Alternatives

​Correlation Breakdown in Crises

​Related Terms

Beta

Standard Deviation

Drawdown

Beginner

What It Means

Portfolio Examples

Why It Matters

Advanced

Mathematical Definition

Interpretation Scale

Historical Context

What Makes It Useful

Diversification Math

Data Requirements

Limitations

Alternatives

Correlation Breakdown in Crises

Related Terms