## What Is Positive Correlation?

A positive correlation is a relationship between two variables that move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

### Key Takeaways

- A positive correlation is a relationship between two variables that tend to move in the same direction.
- A positive correlation exists when one variable tends to decrease as the other variable decreases, or one variable tends to increase when the other increases.
- In finance, correlations are used to describe how individual stocks move with respect to the wider market.
- Beta is a common measure of market correlation, usually using the S&P 500 index as a benchmark.
- A beta of 1.0 describes a stock that is perfectly correlated with the S&P 500. Values higher than 1.0 describe stocks that are more volatile than the S&P 500, while lower values describe stocks that are less volatile.

#### Correlation

## Understanding Positive Correlation

A perfectly positive correlation means that 100% of the time, the variables in question move together by the exact same percentage and direction. A positive correlation can be seen between the demand for a product and the product's associated price. In situations where the available supply stays the same, the price will rise if demand increases.

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

Additionally, gains or losses in certain markets may lead to similar movements in associated markets. As the price of fuel rises, the prices of airline tickets also rise. Since airplanes require fuel to operate, an increase in this cost is often passed to the consumer, leading to a positive correlation between fuel prices and airline ticket prices.

A positive correlation does not guarantee growth or benefit. Instead, it is used to denote any two or more variables that move in the same direction together, so when one increases, so does the other. But the existence of a correlation does not necessarily indicate a causal relationship between variables.

Correlation is a form of dependency, where a shift in one variable means a change is likely in the other, or that certain known variables produce specific results. A general example can be seen within complementary product demand. If the demand for vehicles rises, so will the demand for vehicular-related products and services, such as tires. An increase in one area has an effect on complementary industries.

In some situations, positive psychological responses can cause positive changes within an area. This can be demonstrated within the financial markets, in cases where general positive news about a company leads to a higher stock price.

### Correlation vs. Causation

Correlation among variables does not necessarily imply causation.

## Positive Correlation in Finance

A simple example of positive correlation involves the use of an interest-bearing savings account with a set interest rate. The more money that is added to the account, whether through new deposits or earned interest, the more interest that can be accrued. Similarly, a rise in the interest rate will correlate with a rise in interest generated, while a decrease in the interest rate causes a decrease in actual interest accrued.

Investors and analysts also look at how stock movements correlate with one another and with the broader market. Most stocks have a correlation between each other's price movements somewhere in the middle of the range, with a coefficient of 0 indicating no relationship whatsoever between the two securities. A stock in the online retail space, for example, likely has little correlation with the stock of a tire and auto body shop, while two similar retail companies will see a higher correlation. This is because businesses that have very different operations will produce different products and services using different inputs.

A brick-and-mortar book retailer, on the other hand, is likely to have a negative correlation with the stock of Amazon.com, as the online retailer's popularity is typically bad news for traditional book stores. The stock of the popular payment processor PayPal is likely to be positively correlated with the stocks of online retailers that use its services. If the stocks of eBay, Amazon, and Best Buy pick up due to increased online revenue, it is likely that PayPal will experience a similar boost as its fee-driven income picks up and positive earnings reports encourage investors.

## Beta and Correlation

Beta is a common measure of how correlated an individual stock's price is with the broader market, often using the S&P 500 index as a benchmark. If a stock has a beta of 1.0, it indicates that its price activity is strongly correlated with the market. A stock with a beta of 1.0 has a systematic risk, but the beta calculation can’t detect any unsystematic risk. Adding a stock to a portfolio with a beta of 1.0 doesn’t add any risk to the portfolio, but it also doesn’t increase the likelihood that the portfolio will provide an excess return.

A beta of less than 1.0 means that the security is theoretically less volatile than the market, meaning the portfolio is less risky with the stock included than without it. For example, utility stocks often have low betas because they tend to move more slowly than market averages.

A beta that is greater than 1.0 indicates that the security's price is theoretically more volatile than the market. For example, if a stock's beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks and small caps tend to have higher betas than the market benchmark. This indicates that adding the stock to a portfolio will increase the portfolio’s risk, but also increase its expected return.

Some stocks even have negative betas. A beta of -1.0 means that the stock is inversely correlated to the market benchmark as if it were an opposite, mirror image of the benchmark’s trends. Put options or inverse ETFs are designed to have negative betas, but there are a few industry groups, like gold miners, where a negative beta is also common.

### Beta

A beta of +1.0 indicates a stock that moves in the same direction as the rest of the market. A beta of -1.0 indicates that a stock moves opposite to the rest of the market.

## Positive Correlation vs. Inverse Correlation

In statistics, positive correlation describes the relationship between two variables that change together, while an inverse correlation describes the relationship between two variables which change in opposing directions. Inverse correlation is sometimes described as negative correlation. Examples of positive correlations occur in most people's daily lives. The more hours an employee works, for instance, the larger that employee's paycheck will be at the end of the week. The more money is spent on advertising, the more customers buy from the company.

Inverse correlations describe two factors that seesaw relative to each other. Examples include a declining bank balance relative to increased spending habits and reduced gas mileage relative to increased average driving speed. One example of an inverse correlation in the world of investments 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 are underperforming.

It is important to understand that correlation does not necessarily imply causation. Variables A and B might rise and fall together, or A might rise as B falls, but it is not always true that the rise of one factor directly influences the rise or fall of the other. Both may be caused by an underlying third factor, such as commodity prices, or the apparent relationship between the variables might be a coincidence.

The number of people connected to the Internet, for example, has been increasing since its inception, and the price of oil has generally trended upward over the same period. 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 have increased is explainable by a third factor, namely, general increases due to time passed.

## What Is an Example of Positive Correlation?

One example of positive correlation is the relationship between employment and inflation. High levels of employment require employers to offer higher salaries in order to attract new workers, and higher prices for their products in order to fund those higher salaries. Conversely, periods of high unemployment experience falling consumer demand, resulting in downward pressure on prices and inflation.

## What Is the Relationship Between Beta and Positive Correlation?

Beta is a common measure of the correlation between an individual stock and the wider market, often using the S&P 500 index as a benchmark. A beta value greater than zero indicates that the stock is positively correlated with the market, meaning that its share price tends to rise when the market rises. If a stock has a beta less than 1.0, its movements will be smaller than the movements of the wider market. A beta higher than 1.0 indicates that the stock will fluctuate more than the market as a whole.

## What Is Inverse Correlation?

A positive correlation describes a relationship between variables that move together, and an inverse correlation describes variables that tend to move in opposite directions. This may also be referred to as a negative correlation. In investing, negative correlations are indicated by beta values below zero: a beta of -1.0 indicates a stock whose movements are a mirror opposite of the benchmark's trends.

## Does Correlation Imply Causation?

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