## Positive Correlation vs. Inverse Correlation: An Overview

In the field of statistics, correlation is a relationship between two variables. Variables are correlated if a change in one is accompanied by a change in the other. Correlation shows if the relationship is positive or negative and how strong the relationship is.

- Positive correlation is the relationship between two variables that change together.
- Inverse correlation is the relationship between two variables that change in opposite directions.

Inverse correlation is sometimes referred to as negative correlation.

### Key Takeaways

- A positive correlation is evident when two variables move in the same direction.
- An inverse correlation is evident when two variables move in the opposite direction.
- When the strength of the correlation is measured, a positive correlation will be a positive number while a negative correlation will be a negative number.
- Investors who want to hedge against risk often seek out stocks in sectors that have a negative price correlation with their other investments.
- Correlation can be accidental. Investors look for rational reasons why one sector moves in tandem with another sector or in the opposite direction. That makes it more likely that the correlation will occur consistently.

## Positive Correlation

When two related variables move in the same direction, their relationship is positive. This correlation is measured by the coefficient of correlation (r). When r is greater than 0, it is positive. When r is +1.0, there is a perfect positive correlation.

Examples of positive correlations occur in our daily lives. The more money a company spends on advertising, the more product it sells. In this example, the coefficient of correlation might be difficult to measure. It would likely be less than +1.0.

A stronger correlation would exist in the case of an hourly employee and the employee's pay. The more hours the employee works, the larger the person's paycheck will be.

Looking for correlation is reasonable when analyzing the relationship between significant, quantifiable data.

## Inverse Correlation

When two related variables move in opposite directions, their relationship is negative. When the coefficient of correlation (r) is less than 0, it is negative. When r is -1.0, there is a perfect negative correlation.

Inverse correlations describe two factors that seesaw relative to each other. A consumer's increase in personal spending is correlated with a decline in the consumer's bank balance. An increase in a driver's driving speed is correlated with a decrease in the vehicle's fuel efficiency.

One key example of an inverse correlation in the financial world is the relationship between stocks and bonds. As stock prices rise, the bond market tends to decline, just as the bond market does well when stocks underperform.

## Special Considerations

Correlation does not necessarily imply causation.

Variables A and B might rise and fall together, or A might rise as B falls. However, the rise of one factor may not have directly caused the rise or fall of the other. Both may be caused by an underlying third factor, such as commodity prices. The apparent relationship between the variables might even be a coincidence.

The total number of people connected to the Internet, for example, greatly increased year over year from its inception in the early 1990s until 2015. During the same period of time, the price of oil generally trended upward.

This is a positive correlation but the two factors almost certainly have no meaningful relationship. That both the population of Internet users and the price of oil increased is likely to be a coincidence.

## Is an Inverse Relationship the Same as a Negative Correlation?

Inverse relationship and negative correlation are synonymous.

Both can be used to describe any two variables that reliably move in opposite directions.

When an inverse relationship is measured, the result will be a negative number.

## What Is the Difference Between Inverse and Direct Relationships?

The direct relationship is a concept in mathematics that may be a positive correlation or an inverse correlation.

Two variables have a direct relationship if they measurably increase or decrease in tandem.

## What Are Inversely Correlated Assets?

Inversely correlated assets predictably move in different directions.

Stock investors look for inversely correlated sectors in order to mitigate risk in their portfolios. For example, an investor may see great opportunity in the transportation sector and might buy stocks in airlines, shipping companies, and railroads. But to hedge against risk, the investor might also put some money into energy stocks. If gasoline prices soar, the profits of the transportation companies may suffer but energy companies should do well.

## What Is an Example of an Inverse Correlation?

A classic example of an inverse relationship is the price of gold versus the price of stocks. Gold is seen as the ultimate safe haven. When stocks fall, investors will bail out and move their money into gold.

Another inverse relationship can be seen in the reaction of stocks to an increase in inflation. In inflationary times, companies that sell discretionary goods, like vacation packages or second homes, may see sales fall as inflation increases. Companies that are in the business of supplying staples like food and utility services should at least stay steady.

So-called discretionary stocks have an inverse relationship with value stock.

## What Is the Opposite of an Inverse Relationship?

The opposite of an inverse relationship, or inverse correlation, is a positive correlation.

Low-interest rates have a positive correlation with increased home purchases. Increased home purchases have a positive correlation with increased sales of appliances and home furnishings.

Warm weather has an inverse relationship with the demand for home heating oil. But warm weather has a positive correlation with sales of ice cream and flip-flops.