Negative CorrelationDefined along with Formula & How to Calculate

## What is Negative Correlation?

Negative correlation is a relationship between two variables where the variables have an inverse relationship.

Basically, with negative correlation, as one variable increases, the other variable decreases.

Negative correlation is often described by a correlation coefficient that is between 0 and -1.

Two variables with a perfectly negative correlation would have a correlation coefficient of -1.

If the two variables have a correlation coefficient of 0, then there is no correlation.

Whereas, if the variables have a correlation coefficient of +1, they have a perfectly positive correlation.

### Negative Correlation Explained

Negative correlation exists when two variables have an inverse relationship; one variable moves in one direction, and the other variable moves in the opposite direction.

As an example, suppose a negative correlation exists between variables A and B.

This means that if A has an increase in value, B will decrease in value, and vice versa.

The strength of the relationship that exists between the two variables is measured by the correlation coefficient.

If variables A and B had a correlation coefficient of -0.9, it would indicate a very strong negative correlation.

In contrast, a correlation coefficient of -0.1 would indicate a very weak negative correlation.

The stronger the negative correlation is between any two variables, the closer the correlation coefficient will get to -1.

Whereas the stronger the positive correlation between two variables is, the closer the correlation coefficient will get to +1.

If two variables have a correlation coefficient of 0, there is no correlation between the variables.

## Calculating Correlation Coefficient

This is the formula for calculating the correlation coefficient:

∑ (x(i) – x̅)(y(i) – ȳ) / √ ∑(x(i) – x̅) ^2 ∑(y(i) – ȳ)^2

With

x(i) = value of x

y(i) = value of y

x̅ = mean of the value of x

ȳ = mean of the value of y

Although this formula can be used to calculate the correlation coefficient, there are other methods that can be used, such as using one of the many online calculators available for calculating the correlation coefficient.

Or, if you are just trying to find out if your variables have a negative correlation, you could use a scatter plot.

If you use a scatter plot, a line that slants downward from left to right indicates a negative correlation.

The correlation coefficient is indicated by an “R” or “r.”

The square of the correlation coefficient, which is generally indicated by either R-squared or R2, is generally given as a percentage and shows the extent to which the variance in the dependent variable is explained by the independent variable.

The degree of correlation that exists between two variables can change over time.

It can even change from positive to negative or negative to positive.

## Why Is Negative Correlation Important?

Correlation is frequently used when constructing and managing portfolios.

Many people prefer a diverse portfolio that has investments with different levels of risks and returns.

This is because people with too many of the same types of securities in their portfolios are more vulnerable to market volatility.

Investors with a diverse portfolio are more likely to have only part of their portfolio impacted by a major event rather than their entire portfolio.

In order to build portfolios that are better able to withstand market volatility, the correlations need to be carefully balanced.

This process is typically called the discipline of strategic asset allocation.

## Example of the Use of Correlation in a Portfolio

One example of this is the proportion of stocks to bonds in a portfolio.

There is a negative correlation between stocks and bonds in the long term.

Stocks typically perform better than bonds when the economy is doing well.

However, when the economy is declining, and interest rates are being reduced in an attempt to improve the economy, bonds may perform better than stocks.

For example, consider an investor with a carefully balanced portfolio of \$200,000 that has 55% in stocks and 45% in bonds.

During a year with a strong economy, assume the stock portion of the portfolio is generating a 10% return.

Whereas, due to the increasing interest rate, the bond portion of the portfolio has a -3% return.

This means the overall return of the portfolio is 4.15% (10% * .55) + (-3% * .45).

However, instead, consider how the same portfolio might do in a year with a slow economy with the interest rates moving lower.

The stock portion of the portfolio generates a return of -4%, and the bond portion of the portfolio generates a return of 9%.

This would mean a return of 1.85% for the portfolio as a whole.

If the same investor had instead had all bonds with the same two sets of economic conditions, the portfolio would have had a return of -3% in the year with a strong economy and 9% in the year with a weak economy.

These returns are far more volatile than the returns of 4.15% and 1.85%.

## Key Takeaways

• Negative correlation is useful when developing a portfolio in order to make sure it is diverse.
• Negative correlation, or as it is sometimes called inverse correlation, is a situation in which two variables move in opposite directions.
• The correlation that exists between two variables can change considerably over time.

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1. Boston University “The Correlation Coefficient (r)” Page 1 . August 24, 2022

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