Correlation and Covariance

Correlation and covariance are key statistical measures used in portfolio design to assess how assets move relative to each other, helping investors optimize diversification and risk management.

Covariance
Covariance measures the directional relationship between two asset returns:
Positive covariance – Assets tend to move in the same direction (e.g., two tech stocks rising together).
Negative covariance – Assets move in opposite directions (e.g., stocks rising while bonds fall).

While covariance indicates whether assets move together, it does not standardize the strength of the relationship.

Correlation
Correlation is a normalized version of covariance, ranging from -1 to +1:
+1 correlation – Assets move perfectly in sync.
  0 correlation – No relationship between asset movements.
-1 correlation – Assets move in completely opposite directions.

Portfolio Design Implications
Diversification – Investors seek assets with low or negative correlation to reduce overall portfolio risk.
Risk Reduction – Combining assets with negative covariance can smooth returns and lower volatility.
Efficient Frontier – Modern Portfolio Theory (MPT) uses correlation to construct portfolios that maximize returns for a given level of risk.

For example, pairing stocks and bonds often works well because they tend to have negative correlation, helping stabilize portfolio performance during market downturns.