What is Inverse Correlation?

Inverse correlation is 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, the other variables will 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 determine 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, one can display the correlation coefficient as below: –

r = n (∑xy) – ∑x ∑y / √ [n* (∑x2 – (∑x)2)] * [n* (∑y2 – (∑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 homogenous. If both variables share a different number of data sets employed, it would be termed heterogeneous.Correlation calculation for the homogenous dataset is easier and less complex than with heterogeneous datasets.

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Inverse Correlation Numerical Example

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

  • X: 22, 20, 110Y: 70,80,30

To calculate the correlationCalculate The CorrelationCorrelation is a statistical measure between two variables that is defined as a change in one variable corresponding to a change in the other. It is calculated as (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2.read more 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 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. As a result, the portfolio provides an inverse correlation of -0.99.

Inverse Correlation in Portfolio Diversification

Diversification is a process that reduces concentration risk and helps allocate investment capital to more than one asset. A portfolio of assets formulates diversifying the 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 ensuring stable returns. A portfolio signifies a collection of financial assetsFinancial AssetsFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more, such as bondsBondsBonds refer to the debt instruments issued by governments or corporations to acquire investors’ funds for a certain period.read more, stocks, or commodities.

The diversification achieved for a portfolio of assets is an example of an inverse correlation. Therefore, 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 that one can use both for hedgingHedgingHedging is a type of investment that works like insurance and protects you from any financial losses. Hedging is achieved by taking the opposing position in the market.read more purposes as well as for investment. Gold as an asset shares an inverse correlation-based relationship with the United States dollar.

The gold can 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 riskDiversifiable RiskA diversifiable risk refers to the firm-specific uncertainty that impacts an individual stock price rather than affecting the whole industry or sector in which the firm operates. Such risk can be mitigated or reduced by adopting diversification strategies to ensure that the returns are not affected.read more 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.Each industry does not necessarily perform similarly, resulting 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 in the data set chosen for analysis.Various factors and variables 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 static but dynamic and 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 and an inverse correlation for the next period.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. If one variable appreciates its characteristics, the other variable will 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.

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

  • Excel Inverse MatrixNegative Correlation MattersPearson Correlation Coefficient FormulaCorrelation Matrix in Excel