## 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 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 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: –

**r = n (∑xy) – ∑x ∑y / √ [n* (∑x ^{2} – (∑x)^{2})] * [n* (∑y^{2} – (∑y)^{2})]**

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. If both variables share a different number of data sets employed, then it would be termed as heterogeneous.
- The calculation of correlation for the homogenous dataset is easier and less complex as compared with heterogeneous datasets.

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For eg:

Source: Inverse Correlation (wallstreetmojo.com)

### Inverse Correlation Numerical Example

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

- 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
- ∑(X
^{2})=(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 portfolioDiversified PortfolioPortfolio diversification refers to the practice of investing in a different assets in order to maximize returns while minimizing risk. This way, the risk is kept to a minimal while the investor accumulates many assets. Investment diversification leads to a healthy portfolio.read more 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 inherentRisk InherentInherent Risk is the probability of a defect in the financial statement due to error, omission or misstatement identified during a financial audit. Such a risk arises because of certain factors which are beyond the internal control of the organization.read more 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 a 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 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 perform similarly 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 consider the odd behavior of a few data points taken up in the data set chosen for 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.
- An inverse correlation between two variables does not mean 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 correlationA Positive CorrelationPositive 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 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 riskMeasure Of Unsystematic RiskUnsystematic risk refers to risk that is generated in a specific company or industry and may not be applicable to other industries or the economy as a whole. There are two types of unsystematic risk: business risk and financial risk.read more.

### Recommended Articles

This article has been a guide to what is Inverse Correlation and its Definition. Here we discuss formula to calculate the inverse correlation along with examples, advantages, and disadvantages. You can learn more about from the following articles –

- Excel Inverse Matrix
- Negative Correlation Matters
- Pearson Correlation Coefficient Formula
- Correlation Matrix in Excel

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