Correlation

IntermediateRisk Management2 min read

Quick Definition

A statistical measure ranging from -1 to +1 that describes how two investments move in relation to each other.

What Is Correlation?

Correlation measures the degree to which two assets move together. It's fundamental to portfolio construction and diversification.

Correlation Scale:

ValueMeaningExample
+1.0Perfect positive — move togetherS&P 500 and large-cap ETF
+0.5Moderate positiveUS stocks and developed market stocks
0.0No relationshipGold and tech stocks (historically)
-0.5Moderate negativeStocks and long-term Treasuries
-1.0Perfect negative — move oppositeLong stock vs short stock

Key Correlation Pairs:

Asset PairTypical CorrelationDiversification Benefit
US Stocks / Int'l Stocks+0.7 to +0.85Low
Stocks / Bonds-0.2 to +0.3Moderate to High
Stocks / Gold-0.1 to +0.2Moderate
Stocks / Real Estate+0.5 to +0.7Low to Moderate
Stocks / Commodities+0.1 to +0.4Moderate

Why Correlation Matters:

  • Low/negative correlation between assets = better diversification
  • During crises, correlations often increase (everything falls together)
  • The optimal portfolio combines assets with the lowest correlations

Correlation vs. Causation: Correlation does not imply causation. Two assets may move together without one causing the other's movement.

Rolling Correlation: Correlations change over time. The stock-bond correlation was positive in the 1970s-1990s but turned negative after 2000. Always use rolling windows rather than long-term averages.

Formula

Formula

ρ(X,Y) = Cov(X,Y) / (σX × σY)

Correlation Example

  • 1Stocks and bonds had a correlation of about -0.3 from 2000-2021, making them excellent diversifiers
  • 2During the 2008 crisis, correlations spiked to +0.9 across most asset classes — diversification failed temporarily