What is a Correlation?
A correlation is a statistical measure of the relationship between two variables. The measure is best used in variables that demonstrate a linear relationship between each other. The fit of the data can be visually represented in a scatterplot. Using a scatterplot, we can generally assess the relationship between the variables and determine whether they are correlated or not.
The correlation coefficient is a value that indicates the strength of the relationship. The coefficient can take any values from -1 to 1. The interpretations of the values are:
- -1: Perfect negative correlation. The variables tend to move in opposite directions (i.e., when one variable increases, the other variable decreases).
- 0: No correlation. The variables do not have a relationship between each other.
- 1: Perfect positive correlation. The variables tend to move in the same direction (i.e., when one variable increases, the other variable also increases).
One of the primary applications of the concept in finance is portfolio managementPortfolio Management Career ProfilePortfolio management is managing investments and assets for clients, which include pension funds, banks, hedge funds, family offices. Salary, skills,. A thorough understanding of the statistical concept among various securitiesMarketable SecuritiesMarketable securities are unrestricted short-term financial instruments that are issued either for equity securities or for debt securities of a publicly listed company. The issuing company creates these instruments for the express purpose of raising funds to further finance business activities and expansion. is essential to a successful portfolio optimization.
Correlation and Causation
Correlation must not be confused with causality. The famous expression “correlation does not mean causation” is crucial to the understanding of the two statistical concepts.
If two variables are correlated, it does not imply that one variable causes the changes in another variable. Correlation only assesses relationships between variables, and there may be different factors that can lead to the relationships. Causation may be a reason for the correlation, but it is not the only one.
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How to Find the Correlation?
The correlation coefficient that indicates the strength of the relationship between two variables can be found using the following formula:
Where:
- r_{xy} – the correlation coefficient of the linear relationship between the variables x and y
- x_{i }– the values of the x-variable in a sample
- x̅ – the mean of the values of the x-variable
- y_{i }– the values of the y-variable in a sample
- ȳ – the mean of the values of the y-variable
In order to calculate the correlation coefficient using the formula above, you must undertake the following steps:
- Obtain data sample with the values of x-variable and y-variable.
- Calculate the means (averages) x̅ for the x-variable and ȳ for the y-variable.
- For the x-variable, subtract the mean from each value of the x-variable (let’s call this new variable “a”). Do the same for the y-variable (let’s call this variable “b”).
- Multiply each a-value by the corresponding b-value and find the sum of these multiplications (the final value is the numerator in the formula).
- Square each a-value and calculate the sum of the resulted values. Do the same for the b-values.
- Multiply the sums from the previous step.
- Find the square root of the value obtained in the previous step (this is the denominator in the formula).
- Divide the value obtained in step 4 by the value obtained in step 7.
You can see that the manual calculation of the coefficient is an extremely tedious process, especially if the data sample is large. However, there are many software tools that can help you to save time when calculating the coefficient. The CORREL function CORREL FunctionThe CORREL function is categorized under Statistical functions. It will calculate the correlation coefficient between two variables. As a financial analyst, the CORREL function is very useful when we want to find the correlation between two variables, i.e., the correlation between ain Excel is one of the easiest ways to quickly calculate the correlation between two variables for a large data set.
Example of Correlation
John is an investor. His portfolio primarily tracks the performance of the S&P 500 and John wants to add the stock of Apple Inc. Before adding Apple to his portfolio, he wants to assess the correlation between the stock and S&P 500S&P - Standard and Poor'sStandard and Poor's (S&P) is a market leader in the provision of benchmarks and investible indices, as well as credit ratings for companies and countries, and other financial information services. to ensure that in the case of a market decline, the stock will not also go down. To find the coefficient, John gathers the following prices for the last five years (Step 1):
Using the formula above, John can determine the correlation between the prices of S&P 500 and Apple Inc.
Firstly, John calculates the average prices of each security for the given periods (Step 2):
After the calculation of the average prices, we can find the other values. A summary of the calculations is given in the table below:
Using the obtained numbers, John can calculate the coefficient:
The coefficient indicates that the prices of S&P 500 and Apple Inc. are highly positively correlated. It means that the prices of the securities tend to move in the same direction.
Related Readings
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To keep learning and developing your knowledge of financial analysis, we highly recommend the additional resources below:
- Anchoring BiasAnchoring BiasAnother bias is the behavioral finance theory that we need to label and acknowledge in order to mitigate against is something called the anchoring bias.
- Dynamic Financial AnalysisDynamic Financial AnalysisThis guide will teach you how to perform dynamic financial analysis in Excel using advanced formulas and functions. INDEX, MATCH, and INDEX MATCH MATCH Functions, Combining CELL, COUNTA, MID and OFFSET in a Formula. When used, these Excel functions make your financial statement analysis more dynamic
- Hypothesis TestingHypothesis TestingHypothesis Testing is a method of statistical inference. It is used to test if a statement regarding a population parameter is correct. Hypothesis testing is a powerful tool for testing the power of predictions. A business owner for example might want to make a prediction of that the mean value a customer would greater
- Poisson DistributionPoisson DistributionThe Poisson Distribution is a tool used in probability theory statistics to predict the amount of variation from a known average rate of occurrence, within