## Negative Correlation Definition

In layman terms, Negative Correlation is a relationship between two variables such that they are part of a function in which dependent and independent variables move in different directions in terms of value. For example, if the independent variable increases, the dependent variable decreases, and vice versa.

Negative correlation can be described by the correlation coefficient when the value of this correlation is between 0 and -1. The value of a perfect negative correlation is -1. The strength of the correlation between the variables can vary. For example, suppose two variables x and y have a correlation of -0.8. It means, as x increases by 1 unit, y will decrease by 0.8. Now consider that the negative correlation between these variables is -0.1. In this case, every unit change in the value of x variable will result in a change of 0.1 unit only in the value of variable y.

### Understanding Negative Correlation

To better understand the Negative Correlation, we need to have a basic understanding of correlation as well. Correlation is a statistical tool that is a measure of the degree of relation between two different functions. For example, the weight and height of a person. Generally, as the height increases, the weight of the person increases as well. It indicates that there is a positive correlation between height and weight because as one variable increases, other variables also increases. But the correlation is negative if the two variables move in opposite directions. For example, height from the seal level and temperature. As the height increases, temperature decreases.

Correlation is given by the formula:

Here,

- r = correlation coefficient;
- = Mean of variable X;
- = Mean of variable Y

Rearranging gives us this formula:

Correlation can take any value between -1 to 1. Negative sign indicates a negative correlation while a positive sign indicates a positive correlation. Zero correlation means that there is no relationship between the two variables.

### Why Negative Correlation Matters?

**Portfolio Management**: Correlation is widely used in the management of the portfolios. It is often said that portfolios should be diverse. It should consist of multiple investments involving different risks and returns. This is because if we have the same type of securities in our portfolio, anyone major event will impact not just one security but the whole portfolio. For that purpose, we find correlation between the returns of securities. The securities with perfectly positive correlations should not be purchased together. To diversify the portfolio, often the securities with negative correlation are added. Consider the above-discussed example of airline stocks and oil prices. If a portfolio has energy stocks, the management can consider buying airline stocks to hedge against the decline in oil prices.**Economics**: Many trends associated with economics involve negative correlation. This relationship between the trends can be helpful for matters relating to economic policies. For example, unemployment and consumer spending. As for spending increases, unemployment decreases (generally).

### Real-Life Examples of Negative Correlation

- Oil prices and stocks of airline companies: Oil is a major raw material for airline companies. As the oil prices increase, their profitability starts decreasing, which gets reflected in their stock prices as well. Hence, they show a negative correlation
- Stock market and gold prices (most of the time, not always): Gold always acts as an alternative investment option for equity investors. Thus, whenever the stock market seems to be declining, investors get interested in investing in gold and thus, gold prices start to increase

### Practical Example of Negative Correlation

**Suppose there are two stocks, that have provided the following returns annually in the period 2011-16:**

Considering the stock returns of first stock as variable ‘x’ and that of second stock as ‘y’.

**Calculation of variable xy**

**Calculation of variable X ^{2}**

**Calculation of variable Y ^{2}**

**Sum**

Calculation of Correlation coefficient (r)

- =((6*14311)-(247*376))/(((6*11409)-(247^2))^0.5*((6*247160-(376^2))^0.5)
**=Correlation Coefficient (r) = -0.97608**

Refer to excel sheet given above for detail calculation.

The negative value of correlation coefficient shows that the variables are negatively correlated.

### Conclusion

At times, it is possible that there are other factors involved that cause the variables to behave in a particular manner. In the example discussed above, it can be deduced that when x increases, y decreases. But it will be wrong to deduce that the increase in ‘x’ is causing the ‘y’ to decrease. Because it is possible that both the companies concerned are involved in completely different businesses and get impacted by different economic conditions.

Thus, correlations should be used only to determine a cause. The executives can use it to understand the relationship between variables, such as, market demand and consumer spending, that already exists as part of the analysis. But it should not be used to investigate the change in one variable due to other variables because there will always be multiple factors impacting that relationship. For example, consumer spending in the market and revenue of an FMCG company. They may show a positive correlation but it is possible that the revenue of that company increased because of some other reason like the launch of a new product or expansion into an emerging economy.

### Recommended Articles

This has been a guide to Negative Correlation and its definition. Here we discuss how to interpret negative correlation along with practical examples and its usage in real life. You can learn more from the following statistics articles –

- Definition of Unemployment Compensation
- Calculate Pearson Correlation Coefficient
- Examples of Correlation
- Create Correlation Matrix in Excel
- Compare – Correlation vs Covariance

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