Inverse Correlation (Definition, Formula)

What is Inverse Correlation?

Inverse correlation is defined as the mathematical relationship between two variables wherein their positions are opposite to each other. It signifies that if one variable displays an increase in its position then the other variables would display a decrease. A negative correlation coefficient signifies inverse correlation and the value presented by the correlation coefficient signifies the strength of a linear or non-linear relationship between two variables.

How to Find Inverse Correlation?

The correlation coefficient helps in determining the relationship between two variables using statistical and mathematical relationships as an inverse correlation (when the coefficient is negative).

For two variables X and Y, the correlation coefficient can be expressed as displayed below: –

Here the number of variables for determining the correlation coefficient is represented as n.

If both variables (X and Y) share the same number of data sets employed to determine correlation, it would be termed as homogenous in nature whereas if both variables share a different number of data sets employed then it would be termed as heterogeneous in nature.
The calculation of correlation for the homogenous dataset is easier and less complex as compared with heterogeneous datasets.

Inverse Correlation Numerical Example

Suppose an investor holds two assets X and Y have the following returns: –

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X: 22, 20, 110
Y: 70,80,30

To calculate the correlation coefficient of X and Y, perform the following steps: –

∑X = 22 + 20 + 110 = 152
∑Y = 70 + 80 + 30 = 180
∑(X²)=(22)²+(20)²+(110)²= 12,984
∑(X×Y) = (22×70) + (20×80) + (30×110) = 6,440
∑(X)²= (152)²= 23,104
∑(Y)²= (180)²= 32,400

r = – 0.99

Therefore, the Investor holds a diversified portfolio of two assets. The portfolio provides an inverse correlation of -0.99.

Inverse Correlation in Portfolio Diversification

Diversification is a process that reduces concentration risk and helps in the allocation of investment capital in more than one asset. A portfolio of assets is formulated to achieve diversification of risk inherent in holding such assets and ensure stable returns. A portfolio of assets signifies a collection of financial assets. Such financial assets maybe bonds, stocks or commodities.

The diversification achieved for a portfolio of assets is an example of an inverse correlation. When the correlation coefficient is at -1, it is said that the diversification is at maximum and there is minimum risk involved in the portfolio of assets formulated.

Inverse Correlation – Gold and Dollar Example

Gold is a commodity that is a very popular instrument which can be used both for hedging purpose as well as for the purpose of investment. The gold as an asset shares an inverse correlation-based relationship with the United States dollars.

The gold can be used to curb the rising levels of inflations and hence curb any potential loss in the value of US dollars. Whenever a dollar collapses in front of rising inflation, gold can be utilized as an alternative investment tool to curb inflation, stop the loss of value and reduce the potential impacts of a dollar collapse.

Advantages

It offers diversification to the portfolio of financial assets.
Diversifiable risk is defined as the risk that is specific to the firm.
A portfolio holds assets that are not specific to one firm or industry but caters to multiple firms or industries.
It is not necessary that each industry would perform in a similar fashion and hence results in an inverse correlation.
An inverse correlation between the two assets can help in the hedging positions.

Limitations

The analysis of the inverse correlation does not account for potential outliers.
Additionally, the analysis does not take into consideration the odd behavior of a few data points taken up in the data set chosen for the purpose of analysis.
There can be various factors and variables that might not be a part of the determination and analysis of inverse correlation.
Extrapolating the results of reference data onto the new data can give rise to errors and high levels of risk.
Inverse correlation between two variables does not mean that there is a cause and effect relationship between the two variables.

Important Points

This analysis is not a static analysis but a dynamic analysis that modifies itself with time.
The two variables taken up for analysis can display a positive correlation for a specific period of time and inverse correlation in the next period of time.
It does not describe the cause and effect relationship between the two variables.
If the correlation is not calculated correctly, it can present skewed results.

Conclusion

The correlation analysis tells us how two variables taken up for analysis behave with each other. In this, if one variable displays appreciation in its characteristics the other variable would display deterioration in its value. The best way to determine the inverse correlation between two variables is to employ regression analysis and plot the results using a scatter plot.

The portfolio of assets that offers an inverse correlation is said to be diversified. A diversified portfolio reduces the measure of unsystematic risk.