What Is a Correlation?
Correlation is a statistical term. It describes how much two variables change their values in coordination with each other. If the values of two variables move in the same direction, that means those variables have a positive correlation. If the values move in opposite directions, that means they have a negative correlation. Otherwise, if the values change without any coordination, then there is no correlation between those two variables.
What we can understand by looking at the Correlation Coefficient?
The correlation coefficient numerically expresses the degree of coordination between two variables. The correlation coefficient’s values range between -1.0 and +1.0.
When the correlation coefficient is exactly 1, it is called “perfect positive correlation”. You can read more about it from this link. Basically, this means, when one value of a variable moves, up or down, the other variable’s value also moves in lockstep, in the same direction.
When the correlation coefficient is exactly -1, it means “perfect negative correlation”. Follow this link to read more about it. This means two assets move in opposite directions.
When the correlation coefficient is 0, that means no linear relationship between the variables at all.
How Correlations can be used in Finance?
We can use Correlations to forecast future trends. That means we can acquire the maximum advantage of investment while managing the risks. Correlations between assets can be easily calculated using various software programs and services. Correlations play an important role in the creation and pricing of complex financial instruments such as derivatives. Read more about derivatives from this link.
Apart from that, a portfolio manager of a company can reduce their risk by ensuring that the individual assets within the company are not overly correlated with one another. So that sudden drop in the value of an asset may not affect other assets or portfolios of the company.
How to Calculate Correlation Coefficient?
Here is a simple example to understand how it is calculated.
X: (20, 30, 50, 40, 10, 70, 90)
Y: (90, 60, 50, 30, 80, 20, 60)
Use the following steps to calculate the correlation coefficient:
SUM(X) = (20 + 30 + 50 + 40 + 10 + 70 + 90) = 310
SUM(Y) = (90 + 60 + 50 + 30 + 80 + 20 + 60) = 390
SUM(X,Y) = (20 x 90) + (30 x 60) + (50 x 50) + … (90 x 60) = 14900
Then take each X and Y value, square it, and sum up all these values:
SUM(X^2) = (20^2) + (30^2) + (50^2) + … (90^2) = 18500
SUM(Y^2) = (90^2) + (60^2) + (50^2) + … (60^2) = 25500
The following equation can be used to find the correlation coefficient, r:
r = Correlation coefficient
n = Number of observations
In this example, the correlation would be:
r = 7 x (14900 – (310 x 390)) / SquareRoot((7 x 18500 – 310^2) x (7 x 25500 – 390^2)) = -0.5590
This means X and Y variables are correlated slightly negatively. But it is not good enough to take any decision about the relationship between these two variables. If we get a value between 0.8 and 1 or -0.8 and -1 then it can be considered as a good correlation between the two variables
As mentioned above, correlation plays an important role in finance. It can be used to understand future trends in investment opportunities and risk management. There are various software products and services available to calculate the correlation coefficient. Along with other statistical concepts, you can use this strategy to analyse your future investment opportunities and to handle the risk factors.