Correlation Formula (Table of Contents)
 Correlation Formula
 Examples of Correlation Formula (With Excel Template)
 Correlation Formula Calculator
Correlation Formula
Correlation is widely used in portfolio measurement and the measurement of risk. Correlation measures the relationship between two independent variables and it can be defined as the degree of relationship between two stocks in the portfolio through correlation analysis. The measure of correlation is known as the coefficient of correlation and it is a major measure of the risk. The correlation analysis enables us to have an idea about the degree & direction of the relationship between the two variables under study.
The formula for correlation is equal to Covariance of return of asset 1 and Covariance of return of asset 2 / Standard
Deviation of asset 1 and a Standard Deviation of asset 2.
 ρ_{xy} = Correlation between two variables
 Cov(r_{x}, r_{y}) = Covariance of return X and Covariance of return of Y
 σ_{x = }Standard deviation of X
 σ_{y} = Standard deviation of Y
Correlation is based on the cause of effect relationship and there are three kinds of correlation in the study which is widely used and practiced.
 Positive Correlation – There exists a positive correlation between two variables when they are said to move in the same direction. Example height and weight.
 Negative Correlation – There said to exist a negative correlation between two variables when the variable change with opposite direction. Example the law of demand, quantity, and supply.
 No Correlation – There exists no correlation between two variables when there is no movement of a direct relationship between the two variables. That is they do not have any relationship in the movement of each other.
Examples of Correlation Formula (With Excel Template)
Let’s take an example to understand the calculation of Correlation formula in a better manner.
Correlation Formula – Example #1
A fund manager wants to calculate the coefficient of correlation between two stocks in the portfolio of debt real estate assets.
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Solution:
Correlation is calculated using the formula given below
ρ_{xy} = Cov(r_{x}, r_{y}) / (σ_{x} * σ_{y)}
 Correlation = 0.2 / (1.4 * 1.2)
 Correlation = 0.12
Correlation Formula – Example #2
A student wants to calculate the coefficient of correlation between two stocks in the portfolio.
Solution:
Correlation is calculated using the formula given below
ρ_{xy} = Cov(r_{x}, r_{y}) / (σ_{x} * σ_{y)}
 Correlation = 1 / (4 * 2)
 Correlation = 0.13
Correlation Formula – Example #3
A VC fund is evaluating its portfolio and he wants to calculate the coefficient of correlation between two stocks in the portfolio.
Solution:
Correlation is calculated using the formula given below
ρ_{xy} = Cov(r_{x}, r_{y}) / (σ_{x} * σ_{y)}
 Correlation = 4 / (0.98 * 0.12)
 Correlation = 34.01
Explanation
Correlation is used in the measure of the standard deviation.
 A coefficient of 1 means a perfect positive relationship – as one variable increases, the other increases proportionally.
 A coefficient of 1 means a perfect negative relationship – as one variable increases, the other decreases proportionally.
 A coefficient of 0 means no relationship between two variables – the data points is scattered all over the graph.
Relevance and Uses of Correlation
 Correlation empowers the researcher to detect the unethically occurring variables to test experimentally
 Correlation is very important in the field of Psychology and Education as a measure of the relationship between test scores and other measures of performance.
 Correlation formula is an important formula which tells the user the strength and the direction of a linear relationship between variable x and variable y. The greater is the absolute value the stronger the relationship tends to be.
 Researchers should avoid inferring causation from correlation, and correlation is unsuited for analyses of agreement. Correlational research has had and will continue to have an important role in quantitative research in terms of exploring the nature of the relations among a collection of variables.
Correlation Formula Calculator
You can use the following Correlation Calculator
Con(r_{x},r_{y})  
σ_{x}  
σ_{y}  
ρ_{xy}  
ρ_{xy} = 



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