### 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

### BREAKING DOWN Negative Correlation

Negative correlation is used in statistics to measure the amount that a change in one variable can affect an opposite change in another variable. Analysts perform a regression analysis to quantify predictability of the negative relationship between the two variables. This procedure provides analysts with a calculation of R-squared (R2), which is the statistical measure of how well one variable predicts the value of another variable. If the R2 between two separate items is 1, it means the independent variable accurately predicts the dependent variable without error. An R2 of 0 implies that the independent variable cannot predict the dependent variable. An R2 that falls between 0 and 1 measures the extent to which the independent variable predicts the dependent variable. For example, if R2 is 0.4, this implies that the independent variable can predict the dependent variable with 40% accuracy.

For example, the more time a person devotes to purchasing goods at the mall, the less money he will have in his checking account. The higher an investor's mutual fund expense ratio, the lower his investment returns. The more hours a person spends at the office, the less time he or she has for other activities. All of these variables have a negative R2.

### The Importance of Negative Correlation

Negative correlation is important for any analyst, investor or person looking to diversify and hedge his bets. If an investor is able to find an investment class that moves opposite to another set of assets he is holding, he can invest in both to stabilize his portfolio. Commodities, for example, are known to move in the opposite direction of the stock market, on average. If an investor holds a portfolio with a 100% allocation of public equities, he can sell some of his stock to purchase precious metals, thus balancing his portfolio from volatility.

However, while negative correlation can be used to reduce the risk of a portfolio, it can also create a situation where an investor cannot win. If the two asset classes are perfectly negatively correlated, any gains in one class are completely offset by the other. Therefore, it is important to find two different investments that have a small, negative correlation. This way, if the relationship between stocks and commodities is -0.40, an investor can reduce, but not completely offset, his losses in times when stocks are moving downward and still earn a positive return when stocks increase in value.