A statistical measure of the degree to which two variables (e.g., securities' returns) move together is:
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The statistical measure of the degree to which two variables move together is called the co-variance. The co-variance measures the joint variability of two variables and indicates the direction of the relationship between them.
For example, in finance, co-variance is used to measure the degree to which the returns of two securities move together. If the returns of two securities tend to move in the same direction, then their co-variance is positive. Conversely, if the returns of two securities tend to move in opposite directions, then their co-variance is negative.
The formula for co-variance is:
co-variance = (sum of (x - x̄) * (y - ȳ)) / (n - 1)
where x is the value of the first variable, y is the value of the second variable, x̄ is the mean of the first variable, ȳ is the mean of the second variable, and n is the sample size.
A limitation of co-variance is that it does not provide a standardized measure of the relationship between two variables. To overcome this limitation, the co-variance can be divided by the standard deviation of each variable to obtain the correlation coefficient. The correlation coefficient is a standardized measure of the relationship between two variables and takes values between -1 and 1, where a value of -1 indicates a perfectly negative relationship, a value of 0 indicates no relationship, and a value of 1 indicates a perfectly positive relationship.