Negative Correlation

Negative Correlation Meaning

In layperson’s terms, a negative correlation is a relationship between two variables. They are part of a function in which dependent and independent variables move in different directions regarding value. For example, if the independent variable increases, the dependent variable decreases, and vice versa.

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Negative correlation can be described by the correlation coefficientCorrelation CoefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more when the value of this correlation is between 0 and -1. The amount 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, correlate -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 the x variable will result in a difference of 0.1 unit only in the cost of variable y.

Negative Correlation Explained

To understand the strong negative correlation better, we need to have a basic understanding of correlation. CorrelationCorrelationCORREL function is a statistical function in Excel. The CORREL formula finds out the coefficient between two variables and returns the coefficient of array1 and array2. The correlation coefficient determines the relationship between the two properties.read more 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 person’s value also increases. Therefore, it indicates a positive correlation between height and weight because as one variable increases, other variables also increase. 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, the temperature decreases.

The formula gives correlation:

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. The negative sign indicates a negative correlation, while the positive sign indicates a positive correlation. Zero correlation means that there is no relationship between the two variables.

Thus, one should use the correlations 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 one should not use negative correlation psychology to investigate the change in one variable due to other variables because multiple factors will always impact that relationship. For example, consumer spending in the market and the revenue of an FMCGFMCGFast-moving consumer goods (FMCG) are non-durable consumer goods that sell like hotcakes as they usually come with a low price and high usability. Their examples include toothpaste, ready-to-make food, soap, cookie, notebook, chocolate, etc.read more company. They may show a positive correlation, but that company’s revenue may increase because of some other reason, like the launch of a new product or expansion into an emerging economy.

Why Negative Correlation Matters?

This concept of negative correlation psychology is widely used in the financial market for various purposes as given below.

• Portfolio Management: Correlation is widely used in the management of portfolios. Often, it is said that portfolios should be diverse. It should consist of multiple investments involving different risks and returns. If we have the same type of securities in our portfolio, any major event will impact not just one security but the whole portfolio. For that purpose, we find a correlation between the returns of securities. One should not purchase deposits with perfectly positive correlationsPerfectly Positive CorrelationsPositive Correlation occurs when two variables display mirror movements, fluctuating in the same direction, and are positively related. In layman's terms, if one variable increases by 10%, the other variable grows by 10% as well, and vice versa.read more together. Often, the stakes with negative correlations add to diversify the portfolio. 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 movements can be helpful for matters relating to economic policies. For example, unemployment and consumer spending. As spending increases, unemployment decreases (generally).

How To Interpret?

Given below are some steps to identify the strong negative correlation between two variables. Let us study the same in details.

• Variable identification -The first step is to be able to identify the variable sthat we are analysing in the process. This is very important so that we can understand the relation later on.
• Coefficient calculation – Then we need to calculate the correlation coefficient for the variables, which is the value of r. There are different softwares and statistical tools to do the same. The resultant value will be between positive 1 and negative 1. If the value of r is near -1, then it shows a perfect negative correlation.
• Evaluation – The sign of the coefficient is very important for evaluation. In case the correlation is negative, the sign of r will be negative. We also need to evaluate the magnitude or the strength of the value. In case the value is very close to -1, the negative correlation is very strong.
• Understand the direction and plot data – This will further help in understanding the relationship. Since in this case, the value of one variable will move in the opposite direction of the other, the negative correlation graph will show a downward sloping line.
• Use of examples – Examples taken from real life scenarios help to understand the concept better. In this article, we have taken some useful and interesting examples that will clear our understanding. However, it is to be kept in mind that there are some other factors also which may influence the correlation.

Thus, we can see that the above steps are taken to successfully interpret the results of the calculation and the examples can be used to compare the values and identify situation where this concept is applicable.

Examples

Let us understand the concept of perfect negative correlation with the help of some suitable examples.

Example#1

• Oil prices and stocks of airline companies: Oil is a major raw material for airline companies. As the oil prices increase, their profitabilityProfitabilityProfitability refers to a company's ability to generate revenue and maximize profit above its expenditure and operational costs. It is measured using specific ratios such as gross profit margin, EBITDA, and net profit margin. It aids investors in analyzing the company's performance.read more starts decreasing, reflected in their stock prices. Hence, they show a negative correlation.
• Stock market and gold prices (most of the time, not always): Gold always acts as an alternative investmentAlternative InvestmentAlternative investments refer to investments made in assets classified as non-traditional investment vehicles.read more option for equity investors. Thus, whenever the stock market seems to be declining, investors get interested in investing in gold. Thus, gold prices start to increase.

Example#2

Suppose two stocks have provided the following returns annually in the period 2011-16:

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

Calculation of variable xy

Calculation of variable X²

Calculation of variable Y²

Sum

Calculation of Correlation coefficientCalculation Of Correlation CoefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more (r)

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

Refer to the Excel sheet given above for detailed calculations.

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

At times, other factors may cause the variables to behave in a particular manner. In the example discussed above, one can deduce that when x increases, y decreases. But it would be wrong to suppose that the rise in ‘x’ is causing the ‘y’ to decrease because both companies may be involved in entirely different businesses and impacted by different economic conditions.

Negative Correlation Vs Positive Correlation

Both are statistical concepts that help in establishing a relation between two variables. So, we can identify how change in one variable affects another one. However, let us identify the differences between the two above concepts.

• In the former if the value of one variable increases, the other variable will decrease in value, due to which the relation in negative. But for the latter, with increase in the value of one variable, the other variable will also increase.
• If we plot a negative correlation graph of both the concepts the former will show a curve or a line that slopes downwards, whereas the latter will show a curve or a line that is upward sloping.
• The former is represented by the coefficient (r) that is less than zero, which signifies that the negative correlation will be stronger if the coefficient is closer to -1. But for the latter, the case is just the opposite, the coefficient is greater than zero. So, the closer the value of the coefficient is to 1, the stronger is the correlation.

However, it is important to note that both the concepts simply show a statistical relationship between both the variables on case of negative as well as positive correlation. There is no fixed rule that one variable will definitely cause another variable to change in value.

Frequently Asked Questions (FAQs)

Recommended Articles

This article is a guide to Negative Correlation and its meaning. We explain it with examples, differences with positive correlation & how to interpret it. You can learn more from the following statistics articles: –

• Equity Investor
• Pearson Correlation Coefficient
• Create Correlation Matrix in Excel
• Compare – Correlation vs Covariance