Correlation coefficient is a statistical index measuring the strength and weakness of the relationship between two variables.

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## What is the correlation coefficient

Correlation coefficient is a statistical indicator that measures the strength and weakness of the relationship between two variables. Inside:

The correlation coefficient is valid from -1.0 to 1.0. A result greater than 1.0 or less than -1 indicates an error in the correlation measurement.

– Correlation coefficient with negative value shows that two variables have an inverse relationship or negative correlation (absolute inverse when the value is -1)

Correlation coefficient of positive value indicates a positive relationship or correlation (absolute positive when the value is 1)

– Correlation is 0 for two independent variables.

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## How to calculate Pearson’s correlation coefficient

There are many types of correlation coefficients, but the most common is the Pearson correlation. This index measures the strength and linear relationship between two variables. It cannot measure nonlinear relationships between two variables and cannot distinguish between dependent and independent variables.

Formula for calculating Pearson’s correlation coefficient

**Inside:**

ρxy: Pearson correlation coefficient

Cov (x, y): Covariance of variables x and y

σx: Standard deviation of x

σy: Standard deviation of y

Standard deviation represents the dispersion of word data compared to the average. Covariance shows a linear relationship between two variables.

## Application of correlation coefficients in finance

The strength of the relationship is based on the value of the correlation coefficient. Example: A value of 0.2 indicates a positive correlation, but it is weak and insignificant. Experts say that the correlation is significant at least 0.8. However, a correlation coefficient with an absolute value of 0.9 or greater indicates a very strong relationship.

**Example 1:**

A correlation coefficient can be calculated to determine the degree of correlation between the price of crude oil and the stock price of an oil producer, such as Exxon Mobil Corporation. Since the oil companies make larger profits when oil prices rise, these two variables are positively correlated.

**Example 2:**

The correlation coefficient is used to determine the effectiveness of a fund relative to its benchmark index, or other assets or funds. By adding a low or negatively correlated mutual fund to an existing portfolio, the investor gains diversification benefits.

In other words, investors can use assets or securities with negative correlations to hedge their portfolios and reduce the risk of market volatility.

Correlation statistics also allow investors to determine when the correlation between two variables changes. For example, bank shares often have a positive correlation with interest rates because lending rates are usually calculated based on market rates:

If the share price of a bank is falling while interest rates are rising, investors may question something.

– If the share prices of similar banks in the industry also rise, the investor may conclude that the bank’s share falls not due to interest rates, possibly due to poor bank performance or internal problems…

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