### 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, a 0 indicates no correlation, and a +1 indicates a perfect positive correlation. A perfect negative correlation means the relationship that exists between two variables is negative 100% of the time.

#### Correlation

### Understanding Negative Correlation

Negative correlation or inverse correlation is a relationship between two variables whereby they move in opposite directions. If 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. 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).

It is important to note that 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. Equities and bonds generally have a negative correlation, but in the 10 years to 2018, their correlation has ranged from approximately -0.8 to 0.2, according to BlackRock.

### Key Takeaways

- Negative correlation or inverse correlation is a relationship between two variables whereby they move in opposite directions. This relationship is measured by the correlation coefficient "r", while the square of this figure "R-squared" indicates the degree to which variation in one variable is related to the other.
- Negative correlation is a key concept in portfolio construction, as it enables the creation of diversified portfolios that can better withstand portfolio volatility and smooth out returns.
- Correlation between two variables can vary widely over time. Stocks and bonds generally have a negative correlation, but in he decade to 2018, their correlation has ranged from -0.8 to 0.2.

### The Importance of Negative Correlation

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.

Consider the 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.

As an example, assume you have a $100,000 balanced portfolio that is invested 60% in stocks and 40% in bonds. In a year of strong economic performance, the stock component of your portfolio might generate a return of 12%, while the bond component may return -2% because interest rates are on a rising trend. Thus, the overall return on your portfolio would be 6.4% ((12% x 0.6) + (-2% x 0.4). The following year, as the economy slows markedly and interest rates are lowered, your stock portfolio might generate -5% while your bond portfolio may return 8%, giving you an overall portfolio return of 0.2%.

What if, instead of a balanced portfolio, your portfolio was 100% equities? Using the same return assumptions, your all-equity portfolio would have a return of 12% in the first year and -5% in the second year, which are more volatile than the balanced portfolio's returns of 6.4% and 0.2%.

### Examples 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 (energy only constitutes about 5% of the S&P 500 but makes up close to 20% of Canada's TSX Composite index, for instance), 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.

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 may 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 may slide in tandem.

When negative correlation between two variables breaks down, it can play havoc with investment portfolios. For example, US equity markets had their worst performance in a decade in the fourth quarter of 2018, partly fueled by concerns that the Federal Reserve would continue to raise interest rates. Fears of rising rate fears also took their toll on bonds, which fell along with stocks, as the normal negative correlation between stocks and bonds fell to its weakest levels of the past two decades. At such times, investors often discover to their chagrin that there is no place to hide.