Financial modelling terms explained

# Covariance

Covariance is a statistical measure that describes how two variables change together. Covariance can be positive, zero or negative. The value of the covariance indicates the degree to which two variables are related.

## What Is Covariance?

Covariance is a statistic that is used to measure the degree to which two random variables are related. It is calculated by taking the product of the standard deviations of the two variables and dividing by the square root of the product of the two standard deviations. Covariance is usually expressed in terms of a unitless measure, such as correlation coefficient.

## What Is the Covariance Between X and Y?

The covariance between two random variables X and Y is a measure of their mutual dependence. It is calculated as the sum of the products of the deviations of each variable from its mean, divided by the product of their standard deviations:

Cov(X,Y) =

E(X-Î¼X)Â·E(Y-Î¼Y) / ÏƒXÏƒY

## What Is the Covariance of Two Vectors?

The covariance of two vectors is a measure of how correlated the two vectors are. The covariance is calculated by taking the product of the two vectors and then dividing it by the product of the two vectors' standard deviations. The covariance can be positive or negative, depending on how correlated the two vectors are. A positive covariance means that the two vectors are positively correlated, while a negative covariance means that the two vectors are negatively correlated.

## What Is the Covariance Between Two Sets?

The covariance between two sets of numbers is a measure of how much they vary together. It is calculated by taking the product of the deviations of each number in one set from the mean of that set, and then dividing by the square root of the number of data points in the set. This gives you a number between -1 and 1, which indicates how correlated the two sets of numbers are. A covariance of 1 means that the two sets vary together perfectly, while a covariance of 0 means that they vary completely independently.

## What Is the Covariance Matrix?

The covariance matrix is a measure of the relationships between pairs of random variables. It is a square matrix, with the number of rows equal to the number of random variables, and the number of columns equal to the number of pairs of random variables. The covariance matrix is filled with the covariance values between each pair of random variables.

## What Is the Covariance of a Random Vector?

The covariance of a random vector is a measure of the degree of linear association between its components. It is computed as the average of the product of the deviations of each component from its mean, divided by the product of the standard deviations of the components.

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