# What is a correlation coefficient?

The correlation coefficient is one of the most important concepts in statistical analysis, and can be highly useful to investors. Here's why.

You've probably noticed certain things that have a clear relationship with one another. For example, the amount of petrol your car uses increases along with the number of kilometres you drive. Or, if a restaurant increases its prices, people will eat there less often.

These are simplified examples of a core statistical concept known as correlation. In simple terms, correlation describes the strength of a relationship between two variables. We can express correlation using a number known as the correlation coefficient, which can have several different applications in investing.

## Understanding a correlation coefficient

A correlation coefficient is a number used to describe the strength of a relationship between two variables. These numbers range from -1 to +1, with zero describing no correlation at all. If two variables have a correlation coefficient of 1, they have a perfectly linear correlation. That means when one goes up, the other will go up in the same proportion, and when one goes down, so will the other.

Conversely, a correlation coefficient of -1 implies a perfectly negative correlation, meaning the two variables will always move in the opposite direction in the same proportions.

In the real world, most variables don't have a perfect correlation, so the correlation coefficient will fall somewhere in the middle of the range.

Height and weight are a good example of two correlated variables that don't have a perfect linear correlation. In other words, the taller a person is, the heavier they are likely to be, but it isn't a perfect relationship. Someone who is 170cm tall can certainly be heavier than someone who is 180cm tall.

## Different versions of the correlation coefficient

The correlation coefficient has several variations, but the Pearson coefficient is the most commonly used. The Pearson coefficient measures the strength of linear correlations between two variables, but it is possible for two variables to have a nonlinear correlation as well.

We'll spare you the mathematics behind how correlation coefficients are calculated, but the general takeaway is the closer to zero a correlation coefficient is, the weaker the correlation between the two variables. And the closer to 1 or -1 it is, the stronger the correlation.

## Why does it matter to investors?

There are several reasons correlation coefficients can be meaningful to investors. Portfolio diversification is one reason. Financial advisors might check to see if an investor's portfolio is filled with investments whose performance is closely correlated. If there is too much correlation, they might take steps to diversify.

A popular investing metric known as 'beta' is a close cousin of the correlation coefficient. It expresses how volatile a stock's performance is compared with the market as a whole. For example, a beta of 1 means that if the S&P/ASX 200 Index (ASX: XJO) rises by 1%, we can expect the stock to lift by the same amount. On the other hand, a beta of 2 implies that a stock is twice as reactive to market movements.

## Example of using correlation coefficients

Let's say you own three ASX shares, which we'll call Company A, Company B, and Company C. All three are growth stocks in the technology space. Company A and Company B have share price movements with a coefficient of 0.95, indicating a very strong correlation. Companies B and C have a correlation of 0.92, and Companies A and C correlate 0.93 with one another.

The problem is that when one of these stocks performs poorly, it's highly probable that the other two will do the same.

So you may look to diversify by adding a stock that has a low, or even a negative, correlation with your other investments to help offset the risk involved with your entire portfolio moving in the same direction.

This article contains general educational content only and does not take into account your personal financial situation. Before investing, your individual circumstances should be considered, and you may need to seek independent financial advice.

To the best of our knowledge, all information in this article is accurate as of time of posting. In our educational articles, a 'top share' is always defined by the largest market cap at the time of last update. On this page, neither the author nor The Motley Fool have chosen a 'top share' by personal opinion.

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The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Scott Phillips.