Correlation Formula

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 in the opposite direction. For 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 the 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.

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.
• It is an important formula that 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

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