# What Is Positive Correlation and How to Measure It?

## What is Positive Correlation?

A positive correlation is a relationship between two variables moving in the same direction. Two different variables are moving in the same direction, they are theoretically affected by the same external forces.

## KEY TAKEAWAYS

A positive correlation is a relationship between two variables moving in the same direction.

A positive correlation exists when one variable decreases as the other variable decreases, or one variable tends to increase as the other increases.

In finance, correlation is used to describe how individual stocks move relative to the broader market.

Beta is a common measure of market correlation, and the S&P 500 is usually used as a benchmark.

Beta 1.0 identifies a stock fully correlated with the S&P 500. Values greater than 1.0 identifies the most volatile stocks of the S&P 500, while values lower identifies the least volatile stocks.

## Understanding Positive Correlation

An absolutely positive correlation means that 100% of the time, the variables involved move together in exactly the same percentage and direction. A positive correlation can be seen between the demand for a product and the relative price of the product. In cases where available supply remains the same, if demand increases, price will increase.

In addition, gains or losses in some markets may trigger similar movements in related markets. As the price of fuel goes up, so do airfares. Because aircraft require fuel to operate, this cost increase is often passed on to consumers, resulting in a positive correlation between fuel prices and airfares.

A positive correlation does not guarantee growth or benefits. Instead, it is used to refer to any two or more variables that move together in the same direction, such that when one increases, so does the other. The presence of an association does not necessarily indicate a causal relationship between the variables.

Correlation is a form of dependence, where a change in one variable means that another variable is likely to change, or that some known variable produces certain results. A common example can be seen in the demand for complementary products. If the demand for automobiles increases, so will the demand for automobile-related products and services, such as tires. Growth in one area affects complementary industries.

In some cases, a positive psychological response can lead to positive changes in an area. This can be demonstrated in the financial markets, where generally positive news about a company causes the share price to rise.

## Positive Correlation Measure

In statistics, a perfect positive correlation is denoted by a correlation coefficient value of +1.0, while 0 indicates no relationship, and -1.0 indicates a perfect (negative) inverse correlation.

Positive correlations can also be easily identified by displaying the data set graphically using a scatter plot. Each point on the scatter plot represents a sample element at the intersection of the x-axis variable and the y-axis variable. Positive correlation is evidenced on a scatter plot by a series of points pointing upwards that show that as the x-axis variable increases, so does the y-axis variable.

When analyzing a statistically positive correlation, it is important to understand the p-value of a data set. The P-value is a statistical measure of how statistically significant the results are. In general, a higher probability value indicates more evidence that the two data points are more strongly associated.

## Positive Correlation in Finance

A simple example of a positive correlation involves using a fixed-rate savings account. The more money added to the account, whether through new deposits or interest earned, the more interest can be earned. Similarly, an increase in interest rates is associated with an increase in interest generated, while a decrease in interest rates leads to a decrease in real interest.

Investors and analysts also look at how stock movements relate to each other and to the broader market. Most stocks have a correlation somewhere in the middle of the range between each other’s price movements, where a coefficient of 0 indicates no correlation between two securities.

For example, stocks in the online retail space have little to do with stocks in a tire and body shop, while two similar retail businesses will see a significant correlation. This is because firms with different functions will produce different products and services using different inputs. Each of these companies faces different operational risks, opportunities and challenges.

## Positive Correlation and Diversity

Modern portfolio theory is rooted in diversification, the idea that an investor should hold broadly unrelated assets to reduce risk at the portfolio level. This contradicts the positive correlation. In general, investment theory states that investors should be wary of positive broad-based correlations in their investment portfolios.

For most investors, the ideal investment strategy is to avoid positive correlations between assets and asset classes. While each individual must evaluate their own investment strategy, owning assets with positive correlations increases the risk of loss.

## Beta and Correlation

Beta is a general measure of how an individual stock’s price relates to the broader market, and the S&P 500 is often used as a benchmark. If a stock has a beta of 1.0, this indicates that its price activity is closely related to the market.

The 1.0 beta stock has systematic risk, but the beta account can’t detect any unsystematic risk. Adding stocks to a beta 1.0 portfolio does not add any risk to the portfolio, but it also does not increase the likelihood that the portfolio will provide excessive return.

A lower beta of 1.0 means the security is theoretically less volatile than the market, which means the portfolio is less risky with the stocks included than without. For example, utility stocks often have lower betas because they move more slowly than the market average.

A beta greater than 1.0 means the security is theoretically more volatile than the market. For example, if a stock has a beta of 1.2, it is considered to be 20% more volatile than the market. Technology stocks and small-cap stocks have betas above the market standard. This indicates that adding stocks to the portfolio will increase the risk of the portfolio, but also increase its expected return.

Some stocks also have a negative beta. Put options or inverse ETFs are designed to have a negative beta, but there are some industry groups, such as gold mining, where negative betas are also common.

## Positive Correlation vs Negative Correlation

Negative correlation is sometimes described as inverse correlation. In statistics, positive correlation describes the relationship between two variables that change together, while inverse correlation describes the relationship between two variables that change in opposite directions.

Examples of positive correlation can be found in most people’s daily lives. The more hours an employee works, for example, the higher the employee’s weekend pay. The more money spent on advertising, the more customers will buy from the company.

Inverse correlation describes two factors that are related to each other. Examples include lower bank balances relative to increased spending habits and lower fuel mileage relative to average driving speeds. An example of an inverse relationship in the investment world is the relationship between stocks and bonds. In theory, as stock prices go up, the bond market goes down, just as the bond market works well when stocks are underperforming.

It is important to understand that correlation does not necessarily imply causation. Variables A and B may rise and fall together, or A may rise with B falling, but it is not always true that the appearance of one factor directly affects the rise or fall of the other. Both may be due to a third underlying factor, such as commodity prices, or the apparent relationship between the variables may be serendipitous.

The number of people connected to the Internet, for example, has been increasing since its inception, and oil prices have generally increased over the same period. This is a positive correlation, but these two factors have almost no meaningful relationship. Both the increase in the number of Internet users and the rise in oil prices can be explained by a third factor, which is the general growth resulting from the passage of time.

## What Is an Example of a Positive Correlation?

An example of a positive correlation is the relationship between employment and inflation. Higher levels of employment require employers to offer higher wages to attract new workers, and to offer higher prices for their products to finance their higher wages. On the contrary, during periods of high unemployment, consumer demand falls, which leads to downward pressure on prices and inflation.

## What Does Correlation 1.0 Mean?

A correlation coefficient of 1.0 means that two variables have a completely positive correlation. When one variable changes, the other changes. Although this does not mean that one variable directly affects the outcome or changes the other, the two variables always go together and are likely to be correlated.

## How Do You Know If a Correlation Is Strong or Weak?

The association between two variables can be evaluated by determining the correlation coefficient and the p-value for the data set. Both scales are analyzed together to show the strength of the relationship between the variables and the reliability of the data.

## Does Correlation Mean Causation?

Correlation does not require causation, and it is a common logical fallacy to believe otherwise. When two variables are positively correlated, it does not necessarily mean that one variable causes change in the other. Both variables may be affected by an unknown third factor, or the apparent relationship between the variables may be coincidental.

## Bottom Line

When two variables move together, the two variables are said to be positively correlated. Although one variable may not directly affect the other, two variables may change at least in the same direction. Investors trying to reduce portfolio risk often try to eliminate positive correlations through diversification. This is done by analyzing the correlation coefficient, beta, and other statistical measures for each variable.