Negative Correlation

Negative Correlation Definition

In layman terms, Negative Correlation is a relationship between two variables. 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 variableIndependent VariableIndependent variable is an object or a time period or a input value, changes to which are used to assess the impact on an output value (i.e. the end objective) that is measured in mathematical or statistical or financial modeling.read more increases, the dependent variable decreases, and vice versa.

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 x variable will result in a difference of 0.1 unit only in the cost 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 value 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.

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

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For eg:
Source: Negative Correlation (wallstreetmojo.com)

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. 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 a correlation between the returns of securities. The 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 should not be purchased together. To diversify the portfolio, often, the stakes with negative correlations 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 movements 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 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, 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 investmentAlternative InvestmentA financial asset that is different from the conventional investment categories such as stocks and cash is referred to as an alternative investment. Private equity, hedge funds, venture capital, real estate/commodities, and tangibles such as wine/art/stamps are all examples of alternative investments.read more 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 two stocks have provided the following returns annually in the period 2011-16:

Year	Stock Return (%)	Year	Stock return (%)
2011	43	2011	63
2012	21	2012	82
2013	25	2013	74
2014	42	2014	67
2015	57	2015	47
2016	59	2016	43

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 calculation.

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

Conclusion

At times, there may be 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 suppose that the rise in ‘x’ is causing the ‘y’ to decrease because it is possible that both the companies concerned are involved in entirely 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 –

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