Negative Correlation
Negative correlation means that as one variable increases, the other variable tends to decrease.
Definition
Negative correlation means two things tend to move in opposite directions: when one goes up, the other tends to go down. It exists when the correlation coefficient r is between -1 and 0, with a value near -1 indicating a strong negative linear relationship and near 0 a weak one, and the line of best fit for negatively correlated data has a negative slope. Formally, negative correlation corresponds to negative covariance: $\text{Cov}(X,Y) < 0$; in portfolio theory, assets with negative correlation reduce overall portfolio variance, since $\text{Var}(aX+bY) = a^2\text{Var}(X) + b^2\text{Var}(Y) + 2ab\,\text{Cov}(X,Y)$, and when $\text{Cov}(X,Y) < 0$, combining assets reduces total variance below the weighted average of individual variances.
Example
As the number of absences increases, test grades tend to decrease, a negative correlation that on a scatter plot looks like dots drifting downward from left to right, like a slope going downhill. Price and quantity demanded for most goods are negatively correlated ($r \approx -0.6$ to $-0.9$): as price increases, consumers tend to buy less, the economic law of demand. Gold prices and equity returns have historically had a weak negative correlation, and including gold in an equity portfolio reduces variance, improving the risk-return tradeoff (Sharpe ratio), the mathematical basis of diversification.
Key Insight
A perfect negative correlation ($r = -1$) means that knowing one variable tells you exactly the other via a linear equation with a negative slope, though few real-world relationships are this precise. The Cauchy-Schwarz inequality guarantees $-1 \le \rho \le 1$: $|\text{Cov}(X,Y)| \le \sigma_X \sigma_Y$, with equality only when $X$ and $Y$ are perfectly linearly related ($Y = aX+b$ with $a < 0$ for $\rho = -1$).