What is Correlation?

What is correlation?

Correlation, signified by the Greek letter rho, scales or standardises the covariance number, neutralising the magnitude. As we can see from the formula, it is calculated by dividing the covariance by the product of the respective standard deviations of the two assets being considered. The result is a correlation number between minus one and plus one. That does two things. Firstly, the sign defines the directional relationship and secondly it gives you an idea of the strength of that relationship.

Pearson's ρ = Cov(xy)/σ_xσ_y

How do you interpret the correlation number?

A number close to zero suggests that the movements of the two assets are unrelated, uncorrelated. The closer you get to the limits of minus and plus one, the greater the connection. If it’s plus one, movements in one are exactly mirrored by movements in the other. Let’s just introduce one more bit of terminology and that’s r squared, or the coefficient of determination. Squaring the correlation number tells us what proportion of the change in one can be explained by a change in the other.