Covariance

Covariance measures how two variables vary together by averaging the products of their deviations from their means. Its sign indicates whether they tend to move in the same or opposite directions.

Expected value: The probability-weighted average of a random variable’s possible values. Covariance is defined using an expectation of paired deviations.
Arithmetic mean: The sum of a set of values divided by the number of values. Each variable’s deviations are measured from its arithmetic mean in a data sample.
Portfolio variance: The variance of a portfolio’s returns, accounting for asset weights and pairwise covariances. Covariances between asset returns determine how diversification changes total risk.
Uncorrelatedness: A condition in which two variables have zero covariance, when their covariance exists. Zero covariance states a specific absence of linear co-variation, not independence in general.
Variance: The expected squared deviation of a variable from its mean. Variance is covariance of a variable with itself.
Deviation (statistics): The difference between an observed value and a chosen reference value, often the mean. Covariance multiplies the two variables’ deviations from their means.
Ordinary least squares: A method that estimates a linear model by minimizing the sum of squared residuals. In simple regression, the fitted slope depends on the covariance of predictor and outcome.
Nonlinear correlation: Statistical dependence expressed through a nonlinear relationship between variables. A strong nonlinear relationship can exist even when covariance is zero.
Correlation: A standardized measure of the direction and strength of linear association between variables. Unlike covariance, correlation is unitless and bounded between −1 and 1.
Joint probability distribution: A probability distribution describing the values of two or more random variables together. It determines the probabilities used to calculate covariance for random variables.

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