Correlation Matrix

A correlation matrix refers to the coefficients entered in tabular form, featuring the values for respective variables. The row-by-column arrangement of the coefficients helps users analyze the relationship between two or more variables and how they depend on each other. The value of the matrix lies between -1 and 1.

The specific inputs in the grid arrangement concerning an event or variable let users predict further related possibilities. As it helps identify the patterns, the correlation matrix is useful in investment management, economics, risk management, and statistics. Moreover, the correlation between the coefficients is the basis of future findings.

• The correlation matrix helps establish the interrelationship or interdependency between two or more variables.
• It is depicted in a tabular form; hence, the datasets are easy to read, understand, and identify patterns for predicting future instances.
• The idea helps summarize the data and reach reliable conclusions, helping investors make wiser investment decisions.
• The matrix can be effectively created simply on Excel or by using advanced technologies, like SPSS and Python-driven Pandas.

A correlation matrix lets analysts summarize a large volume of data in a tabular form, making it more readable and easily understandable. The correlation matrix in Pandas or Python is the most accessible way of creating a data set for further analysis in a tabular form besides Excel. In addition, the SPSS correlation matrix is widely used by market players, given the inbuilt functions it offers.

The clear presentation helps users identify the patterns that the variables follow along with their interdependence to predict future possibilities. However, to ensure the decisions based on the correlation of variables are correct, it is significant to put the correct value for the expected values in the rows and columns.

Thus, a user must be careful while creating such a matrix. The steps involved in the creation are as follows:

• First, users must create the data for which correlation needs to be established. Here, the Nifty price index and certain equity stocks, which are part of the Nifty index, have been used.

• The users can use the Correlation function under the Data Analysis feature of the Data tab in Microsoft Excel.
• The next step is to select the Input range of data as above and click OK.
• The matrix created in Excel looks like this:

Let us consider the following examples to see how a correlation matrix in Excel can help users read and understand the large volume of data:

Example #1

The table below shows a correlation matrix between different bonds issued by the government with different residual maturity stated in the form of years in both horizontal and vertical buckets.

For example, it enables users to interpret that a bond with 0.25 years to maturity and a bond with 0.5 years to maturity has a correlation coefficient of 0.97, indicating price movements similar to other maturity bonds.

Example #2

Xavier Bank has classified its exposure in bonds based on residual maturity as follows:

It has created the matrix across different tenor bonds based on the price movement using the Excel tool (discussed above):

Xavier Bank calculated its exposure-wise matrix across various tenors, as shown below:

To summarize large data, the correlation matrix in R and Python programming is common across different sectors, including finance. When the data set is organized and arranged, users get a clear view of the relationship the variables share at every stage. Therefore, identifying the patterns and trends becomes easier. Thus, investors and traders get a chance to study the pattern and get reliable clues about the expected price movement. This helps them make wiser investment decisions.

When people assess peculiar patterns related to an investment or any regular activities over time, they help people use the conclusions or inferences from studying similar data sets as input in future assessments. In addition, the same analysis can act as a diagnostic for checking other reviews done using the matrix. For example, if linear regression is conducted with the related correlations with a higher value being used as one of the parameters, the result is likely unreliable.

Though people use both terms in statistics to help study patterns, covariance and correlation matrix are two opposite terms. While the former indicates the extent to which two or more variables differ, the latter shows the extent to which they are related.

Some of the differences between correlation and covariance matrix are:

Find the below Excel sheet for detailed calculation:

This is a guide to What is Correlation Matrix. Here, we explain its meaning, applications, examples, & differences from the covariance matrix. You may learn more about financing from the following articles -

• Positive Correlation
• Negative Correlation
• Inverse Correlation
• Covariance vs Correlation