Negative Correlation

Negative correlation (also called inverse correlation) describes a relationship between two variables in which one tends to rise when the other falls. In statistics it is measured by the correlation coefficient, which ranges from -1.0 (perfect negative correlation) to +1.0 (perfect positive correlation); 0 indicates no linear relationship.

How negative correlation works

• If two variables are negatively correlated, increases in one typically coincide with decreases in the other, and vice versa.
• Perfect negative correlation (-1.0) is rare in real-world data; most negative correlations are imperfect and include exceptions and outliers.
• Correlation measures linear association only and does not imply causation.

The correlation coefficient

• Definition: correlation coefficient = covariance(x, y) / (σx × σy).
• Interpretation:
• +1.0 — move exactly together.
• 0 — no linear relationship.
• -1.0 — move exactly opposite.
• Limitations:
• Sensitive to outliers and non‑linear relationships.
• Based on historical data; relationships can change over time.

Negative correlation in investing

Negative correlations are used to reduce portfolio volatility and to hedge risk:
* Diversification: Combining assets that move differently can smooth returns—losses in one asset may be offset by gains in another.
* Hedging: Investors may hold negatively correlated assets to protect core positions.

Common examples (historical tendencies, not guarantees):
* Stocks vs. bonds — often (but not always) negatively correlated, especially during market stress.
* Gold vs. U.S. dollar — gold often rises when the dollar weakens.
* Defensive stocks vs. cyclical stocks — utilities and consumer staples may hold up when cyclicals lag.

Practical example: portfolio correlation (summary)

A sample diversified portfolio might include equities, bonds, gold, and commodities. To gauge how assets move together, you can compute a portfolio’s weighted average correlation:

Steps (high level)
1. Obtain pairwise correlations among all assets.
2. For each asset, compute its average correlation with the others.
3. Multiply each asset’s average correlation by its portfolio weight.
4. Sum those weighted values to get a weighted average correlation.

Interpretation
* A weighted average correlation near 0 indicates low co-movement (better diversification).
* Positive values indicate a tendency for assets to move together; negative values suggest offsetting movements.
* Example outcome: a hypothetical mix produced a weighted average correlation of about 0.34, implying moderate co-movement across holdings—some diversification but exposure to common market moves.

Limits and pitfalls

Relying on correlation alone is risky:
* Correlations change: market regimes, economic cycles, and crises can shift relationships (assets once negatively correlated can move together).
* Only linear relationships: correlation misses nonlinear dynamics.
* No volatility information: correlation says nothing about magnitude of moves—pair it with volatility measures (standard deviation, value at risk).
* Outliers distort results: extreme events can bias correlation estimates.
* Historical bias: past correlations aren’t a guaranteed guide to the future.

Types of correlation measures

• Pearson correlation — measures linear association of continuous variables.
• Spearman and Kendall rank correlations — assess monotonic relationships and are less sensitive to outliers or nonlinearity.
• Point-biserial — for one continuous and one binary variable.

Practical guidance

• Use recent data and multiple time windows to check stability of correlations.
• Combine correlation analysis with volatility, liquidity, and fundamental considerations.
• Stress-test portfolios (simulations, historical scenario analysis) to see how correlations behave in crises.
• Rebalance and update allocations as relationships and market conditions evolve.

Takeaway

Negative correlation is a fundamental concept for risk management and portfolio construction. When used carefully—alongside volatility measures, robust data, and ongoing monitoring—it helps create portfolios that can better withstand market swings. However, correlations are dynamic and imperfect, so diversification strategies must be adaptive rather than static.