A negative, or inverse correlation, between two variables, indicates that one variable increases while the other decreases, and vice-versa. This relationship may or may not represent causation between the two variables, but it does describe an observable pattern. A negative correlation can be contrasted with a positive correlation, which occurs when two variables tend to move in tandem.

Understanding negative correlation is important for investors since including assets in a portfolio that tend to move in opposite directions is key to achieving a well-diversified portfolio. In fact, it is because some asset classes, for instance, stocks and bonds, tend to exhibit a negative correlation with each other that diversification can increase expected returns while at the same time reducing overall portfolio risk.

Here, we dig deeper into how correlation is calculated and why negatively correlated assets work together to produce a net positive, as opposed to simply canceling each other out, for investors.

### Key Takeaways

- A negative correlation occurs between two factors or variables when they consistently move in opposite directions to one another.
- Investors can utilize assets showing negative correlation to reduce the level of risk in their portfolios without harming returns.
- Even though two variables may have a strong negative correlation, this does not necessarily imply that the behavior of one has any causal influence on the other.
- The relationship between two variables can also change over time and may have periods of positive correlation as well.

#### Correlation

## Understanding Negative Correlation

When two variables are correlated, the relative changes in their values appear to be linked. This pattern may be the result of the same underlying cause or could be pure coincidence. It is thus important to recognize the adage, "correlation does not imply causation." Nevertheless, correlation is an important statistical tool used to measure the strength of a relationship between two or more variables.

This measure is expressed numerically by the correlation coefficient, sometimes denoted by 'r' or the Greek letter rho (ρ). The values assigned to the correlation coefficients range from -1.0 and 1.0. A "perfect" positive correlation of +1.0 would mean that two variables move exactly in lockstep with one another—so if variable A increases by two, so does variable B. A "perfect" negative correlation of -1.0, by contrast, would indicate that the two variables move in opposite directions with equal magnitude—if A increases by two, B decreases by two.

In reality, very few factors are perfectly correlated either way, and the correlation coefficient will fall somewhere within the negative-one-to-one range. Note that a correlation of zero suggests that there is no relationship between two variables and their movements are completely unrelated or random to one another.

Negative correlations occur naturally in many contexts. For instance, as the amount of snowfall increases, fewer drivers appear on the road. Or, as a cow gets older, her milk production drops. As you exercise more, you tend to lose weight. The more cats there are in a neighborhood is related to fewer mice. Negative correlations also appear in the world of economics and finance.

$\begin{aligned}&r=\frac{\sum(X-\overline{X})(Y-\overline{Y})}{\sqrt{\sum(X-\overline{X})^2}\sqrt{(Y-\overline{Y})^2}}\\&\textbf{where:}\\&r=\text{The correlation coefficient}\\&\overline{X}=\text{The average of observations}\\&\qquad\text{ of variable }X\\&\overline{Y}=\text{The average of observations}\\&\qquad\text{ of variable }Y\end{aligned}$

## How Investors Use Correlations

Investors can appreciate the concept of negative correlation simply by identifying two stocks that appear to be negatively correlated. For instance, if stock A tends to fall when stock B rises, an investor who owns both shares would see the losses in one offset by gains in the other. The two stocks may be negatively correlated because they experience some negative feedback from one another directly, or because they react differently to the same external stimuli.

In the first case, imagine two competitors, such as Coca-Cola and PepsiCo. Because these two firms are locked in a perpetual battle for market share in the beverages sector, what is good for Coca-Cola may necessarily be bad news for Pepsi and vice-versa. A great new product by Pepsi may boost its share price while Coke falls. Therefore, close competitors in highly competitive markets may have a negative correlation.

In the second case, the two stocks may naturally react to the same external or indirect cause in an opposite fashion. For instance, financial stocks such as banks or insurance companies tend to get a boost when interest rates rise, while the real estate and utilities sector get hit particularly hard given the same news.

Many investors study correlations between stocks, as well as between industries, geographies, and asset type. For example, an investor in oil might hedge a portfolio with stocks in airlines. The two industries have a negative correlation. When oil prices slide, airline stocks rise. Adding more negatively correlated assets to a portfolio is the foundation of the concept of diversification. Modern portfolio theory (MPT), the formative theory behind portfolio diversification, points out that combining risky assets does not necessarily dictate that the overall portfolio risk will increase so long as there are negative correlations among them.

A correlation may or may not be meaningful. Many complex factors could be in play, and the observed correlation could end up being spurious.

### Negative Correlation Between Stocks and Bonds

One of the most widely recognized negative correlations among asset classes is that of stocks and bonds. Traditionally, financial experts have recommended owning both stocks and bonds with weights that vary with investment goals, time horizon, and risk tolerance. The reason behind holding both stocks and bonds is that when stocks fall, bonds tend to rise. This generates a risk reduction through diversification.

Why are stocks and bonds thought to be negatively correlated? The theory posits that inflation, which is a general rise in prices, benefits stock prices because increased costs will be passed on to consumers and translate into greater nominal profits. Bonds, on the other hand, which often pay a fixed interest rate, will see the value of those coupon payments erode with inflation, making them less valuable. Moreover, the amount initially invested in a long-term bond, known as the principal, will have less purchasing power when it is returned several years from now than it is today. As a result, inflation plays an important role in understanding the relationship between stock and bond prices.

A second reason has to do with relative riskiness. Bonds are often seen as less volatile and more conservative, in general, than stocks. If investors feel that stocks are overbought or the economy is shaky and a selloff is likely, they may shift funds out of riskier assets like stocks and invest that money in bonds. This is known as "flight to safety", where selling pressure in stocks accelerates downward prices while bonds get bid up.

Researchers looking at the price relationship between stocks and bonds, however, suggest the assumed negative correlation is not so straightforward and could be merely an illusion. Empirical research looking at the historical movement of the two asset classes shows that there are periods of negative correlation, but mostly they are positively correlated. Research looking as far back as 1926, in fact, shows that the stock/bond correlation has been positive for the vast majority of the time, with just three significant periods of negative correlation: from 1929–1932, 1956–1965, and from 1998-2003.

### Negative Correlations and Forex Trading

The foreign exchange, or forex market, involves trading currencies that are priced in pairs. As such, no single pair trades completely independent of the others. Once you are aware of the correlations among and between different currencies and how they change, you can use them to your advantage.

The reason for the interdependence of currency pairs has a lot to do with the nature of international trade and global financial flows. Countries with large trade deficits have currencies that tend to be negatively correlated with countries showing a surplus. Likewise, the currencies of commodity-rich exporters will often be negatively correlated with countries that rely heavily on imports.

### Negative Correlations and Business Management

In business, negative correlations can be identified by management as a way to naturally offset risks of doing business. These are known as natural hedges. Executives may also look at existing relationships, such as between marketing expenditures and sales, as part of market analysis.

For example, if an expensive marketing campaign is met with declining sales, it could signal that the marketing is backfiring or alienating customers, and should be reconsidered. However, correlations should not be too quickly interpreted as evidence of one variable causing a change in another variable. Business environments often present highly complex causes and correlations that may or may not be meaningful.

While computing correlation can be time-consuming, you can calculate it easily with software like Excel.

## Negative Correlation FAQs

### What Does Negative Correlation Mean?

Negative correlation describes an inverse relationship between two factors or variables. For instance, X and Y would be negatively correlated if the price of X typically goes up when Y falls; and Y goes up when X falls.

### What Is an Example of Negative Correlation?

In addition to the examples provided above, an often-cited example of a negative correlation is between the U.S. dollar and gold. As the U.S. dollar depreciates against major currencies or due to inflation, the dollar price of gold is generally observed to rise; and as the U.S. dollar appreciates, gold declines in price. This is why gold is considered a good hedge against inflation.

### What Do You Mean by Positive or Negative Correlation?

A positive correlation would be the opposite type of relationship to negative correlation. In other words, X and Y would be positively correlated if they both rise together or fall together. Note that correlations can and often do change over time, and the fact that X and Y are positively correlated now does not mean they will remain so. They may become negatively correlated in the future.

### What Is Considered a Weak Negative Correlation?

The strength of a correlation relationship is quantified by its correlation coefficient, the strongest possible being "perfectly" correlated. A perfect negative correlation has a value of -1.0 and indicates that when X increases by z units, Y decreases by exactly z; and vice-versa. In general, -1.0 to -0.70 suggests a strong negative correlation, -0.50 a moderate negative relationship, and -0.30 a weak correlation. Remember that even though two variables may have a very strong negative correlation, this observation by itself does not demonstrate a cause and effect relationship between the two.

## The Bottom Line

Negative correlations describe a relationship between factors that move in opposite directions. While negative correlations occur in several contexts, they are particularly of interest in the financial world since negatively correlated assets are fundamental to portfolio diversification and risk-reduction strategies. Even though inverse relationships may persist, correlation does not necessarily mean causation. Furthermore, correlations tend to shift and change in both strength and direction over time.