Covariance

Covariance measures how two variables move together, whether they tend to rise and fall at the same time.

• Positive covariance: variables move in the same direction.
• Negative covariance: variables move in opposite directions.

Formula:

$$\text{Cov}(X,Y)=\frac{\sum (X_i-\bar{X})(Y_i-\bar{Y})}{n-1}$$

Where:

• $X$ and $Y$ are the two variables.
• $X_i$ and $Y_i$ are individual data points.
• $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$.
• $n$ is the number of data points.

In finance, used to see how a stock’s returns move with the market, key to calculating Beta.