## What Is Negative Correlation?

Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa. In statistics, a perfect negative correlation is represented by the value -1.0, while a 0 indicates no correlation, and +1.0 indicates a perfect positive correlation. A perfect negative correlation means the relationship that exists between two variables is exactly opposite all of the time.

### Key Takeaways

- Negative or inverse correlation describes when two variables tend to move in opposite sizes and directions from one another, such that when one increases the other variable decreases, and vice-versa.
- Negative correlation is put to use when constructing diversified portfolios so that investors can benefit from price increases in certain assets when others fall.
- Correlation between two variables can vary widely over time as correlation changes due to many conditions.
- Stocks and bonds generally have a negative correlation; therefore, traditional portfolio theory calls for investors to hold both.
- Investing in assets that are negatively correlated may reduce portfolio risk, but it also may minimize potential gains as negatively correlated assets hedge certain types of risk.

#### Correlation

## Understanding Negative Correlation

Negative correlation or inverse correlation indicates that two individual variables have a statistical relationship such that their prices generally move in opposite directions from one another. If, for instance, variables X and Y have a negative correlation (or are negatively correlated), as X increases in value, Y will decrease; similarly, if X decreases in value, Y will increase.

Though this article discusses negative correlation regarding investments, negative correlation plays a factor in many facets of business and finance. For example:

- Consider the relationship between household income and inferior products; as households make more money, they are more likely to consume less interior, more premium goods.
- Consider a human resources department noting that the less they spend on employee social events, the more likely individuals are to leave the company.
- Consider a manufacturing plant that incurs less on-the-job injuries as more training is incurring.

Negative correlation also has a loose function when considering the learning curve. As more time is spent learning something, it often takes less time to perform a given task. In this example, rework or failure decreases as proficiency due to learning increases.

The degree of correlation between two variables is not static, but can swing over a wide range—or from positive to negative, and vice versa—over time.

## Negative Correlation and the Correlation Coefficient

The degree to which one variable moves in relation to the other is measured by the correlation coefficient, which quantifies the strength of the correlation between two variables. For example, if variables X and Y have a correlation coefficient of -0.1, they have a weak negative correlation, but if they have a correlation coefficient of -0.9, they would be regarded as having a strong negative correlation.

The higher the negative correlation between two variables, the closer the correlation coefficient will be to the value -1. By the same token, two variables with a perfect positive correlation would have a correlation coefficient of +1, while a correlation coefficient of zero implies that the two variables are uncorrelated and move independently of each other.

The correlation coefficient, usually denoted by "r" or "R", can be determined by regression analysis. The square of the correlation coefficient (generally denoted by "R^{2}", or R-squared) represents the degree or extent to which the variance of one variable is related to the variance of the second variable, and is typically expressed in percentage terms.

For example, if a portfolio and its benchmark have a correlation of 0.9, the R-squared value would be 0.81. The interpretation of this figure is that 81% of the variation in the portfolio (the dependent variable in this case) is related to—or can be explained by—the variation of the benchmark (the independent variable).

## Negative Correlation and Portfolio Diversification

The concept of negative correlation is a key one in portfolio construction. Negative correlation between sectors or geographies enables the creation of diversified portfolios that can better withstand market volatility and smooth out portfolio returns over the long term. The building of large and complex portfolios where the correlations are carefully balanced to provide more predictable volatility is generally referred to as the discipline of strategic asset allocation.

Consider the generally historic long-term negative correlation between stocks and bonds. Stocks generally outperform bonds during periods of strong economic performance, but as the economy slows down and the central bank reduces interest rates to stimulate the economy, bonds may outperform stocks. In this example, investors often have a strong asset class regardless of how the economy is performing.

The ultimate goal of diversification is to find assets that are negative correlated. This may extend beyond just the asset class, as gold ETFs may act differently and have different risks than physical gold bars. All else being equal, a highly-diversified portfolio means an investor is holding negatively correlated assets.

Equities and bonds generally have a negative correlation, but like other asset classes, correlation fluctuates and these two assets become more and less correlated during certain circumstances.

## Advantages and Disadvantages of Negative Correlation

### Advantages of Negative Correlation

As mentioned above, a negative correlation is useful when attempting to diversify across assets. Holding assets that move in different directions often reduces portfolio risk of loss.

In addition to a lower risk of loss, investors may experience a lower risk of general volatility. Different industries may offset each other in the long run. By holding both electric car companies and traditional car companies, changes to one industry may be offset by opposing changes over time.

Investors may find that pursuing negative correlation is a more engaging way to invest. Consider only investing in one asset class such as airlines. Instead, by expanding into equities for healthcare providers, streaming services, or financial services, investors may find the research of these new industries more enjoyable.

Considering companies, businesses may decide to expand into differentiating goods with a negative correlation to maximize revenue. Instead of cannibalizing one product line with another, two negatively correlated product lines may never compete. This may also allow the company to deploy different resources instead of having to rely on a single failure point.

### Disadvantages of Negative Correlation

Though a negative correlation may be insightful, it may also be misleading if the associated assets are not actually negatively correlated. Consider the negative correlation between ski lift tickets and shark attacks. One may make misleading decisions based on negative correlations. In addition, be mindful that the correlation of two items today may be widely different tomorrow due to a change of circumstance.

For portfolio management, a negative correlation also indicates that very different assets are being held. This may mean an investor is not an expert on an asset they are holding and may be unaware of asset risks. For example, though farmland may have a negative correlation to equities, investors may not have tremendous experience in the agriculture industry.

Last, negative correlation in a portfolio means different asset classes are being held to reduce risk. In exchange for lower risk, investors are willing to sacrifice potentially higher returns by not diversifying. For example, buying bonds may result in negative correlation but also in lower returns.

### Negative Correlation

May reduce a portfolio's short-term risk of loss

May reduce a portfolio's long-term risk of volatility

May be a more enjoyable strategy to investing for retail investors

May allow a company to have multiple non-competing product lines

May be misleading if data suggests correlation means causation

May expose an investor to asset classes they do not have adequate knowledge of

Often results in lower potential portfolio returns in exchange for greater risk protection

## Macroeconomics and Negative Correlation

It should be noted that this investment thesis may not work all of the time, as the typical negative correlation between oil prices and airline stocks might occasionally turn positive. For example, during an economic boom, oil prices and airline stocks may both rise; conversely, during a recession, oil prices and airline stocks could slide in tandem.

When negative correlation between two variables breaks down, it can play havoc with investment portfolios. For example, US equity markets experienced their worst performance in a decade in the fourth quarter of 2018, partly fueled by concerns that the Federal Reserve (Fed) would continue to raise interest rates.

When assets that are often negatively correlated move in the same direction, this is an example of systematic risk. Systematic risk can not be diversified away; it will exist in financial markets and is the inherent risk present in investing. Though asset classes may traditionally be negatively correlated, macroeconomic conditions may result in asset classes acting similarly due to broader impacts to the market.

## Example of Negative Correlation

Examples of negative correlation are common in the investment world. A well-known example is the negative correlation between crude oil prices and airline stock prices. Jet fuel, which is derived from crude oil, is a large cost input for airlines and has a significant impact on their profitability and earnings.

If the price of crude oil spikes up, it could have a negative impact on airlines' earnings and hence on the price of their stocks. But if the price of crude oil trends lower, this should boost airline profits and therefore their stock prices.

Here's how the existence of this phenomenon can help in the construction of a diversified portfolio. As the energy sector has a substantial weight in most equity indices, many investors have significant exposure to crude oil prices, which are typically quite volatile. As the energy sector, for obvious reasons, has a positive correlation with crude oil prices, investing part of one's portfolio in airline stocks would provide a hedge against a decline in oil prices.

## Why Is Correlation Important?

Correlation is important because it is often an indicator of portfolio risk. When a collection of securities is negatively correlated, they pose less risk because when one security falls in value, another often increases. Investors may also actively seek out greater risk in exchange for greater potential returns; using this strategy, correlation is important because they may want to maximize correlation to yield the greatest risk and reward.

## How Is Correlation Calculated?

Correlation is first calculated by finding the covariance of each of the variables. Then, the correlation coefficient is determined by dividing the covariance by the product of the variables' standard deviations.

## What Are the Types of Correlation?

There are three types of correlation: positive, negative, and no correlation. There are also several types of correlation calculation methods including Pearson correlation, Kendall rank correlation, Spearman correlation, and the Point-Biserial correlation.

## Is Negative Correlation Better Than Positive Correlation?

For some investors, negative correlation is better than positive correlation. This means that investors are exposed to less risk, have the chance to invest in different types of securities, and often experience less portfolio volatility. For others, negative correlation means hedging their investment which minimizes potential gains.

## The Bottom Line

A negative correlation is an event of two variables moving in the opposite direction. As one variable increases in value, the other decreases. This relationship is measured by the correlation coefficient, and the concept of negative correlation is central to portfolio diversification theory. For most investors, negative correlation across portfolio assets is favorable.