What does 'Inverse Correlation' mean
An inverse correlation, also known as negative correlation, is a contrary relationship between two variables such that they move in opposite directions. For example, with variables A and B, as A increases, B decreases and as A decreases, B increases. In statistical terminology, an inverse correlation is denoted by the correlation coefficient "r" having a value between 1 and 0, with r = 1 indicating perfect inverse correlation.
BREAKING DOWN 'Inverse Correlation'
In financial markets, the best example of an inverse correlation is probably the one between the U.S. dollar and gold. As the U.S. dollar depreciates against major currencies, gold is generally perceived to rise, and as the U.S. dollar appreciates, gold declines in price. Two points need to be kept in mind with regard to negative correlation. First, the existence of negative correlation, or positive correlation for that matter, does not necessarily imply a causal relationship. Second, the relationship between two variables is not static and fluctuates over time, which means the variables may display an inverse correlation during some periods and a positive correlation during others.Inverse Correlation Calculation Example
Calculating correlation is important because the risk reduction benefits of portfolio diversification rely on this statistic. The below example shows how to calculate the statistic.
Assume an analyst needs to calculate the correlation for the following two data sets:
X: 55, 37, 100, 40, 23, 66, 88
Y: 91, 60, 70, 83, 75, 76, 30
There are three steps involved in finding the correlation. First, add up all the X values to find SUM(X), add up all the Y values to find SUM(Y) and multiply each X value with its corresponding Y value and sum them to find SUM(X,Y):
SUM(X) = (55 + 37 + 100 + 40 + 23 + 66 + 88) = 409
SUM(Y) = (91 + 60 + 70 + 83 + 75 + 76 + 30) = 485
SUM(X,Y) = (55 x 91) + (37 x 60) + (100 x 70) + ... (88 x 30) = 26,926
The next step is to take each X value, square it and sum up all these values to find SUM(x^2). The same must be done for the Y values:
SUM(X^2) = (55^2) + (37^2) + (100^2) + ... (88^2) = 28,623
SUM(Y^2) = (91^2) + (60^2) + (70^2) + ... (30^2) = 35,971
Noting there are seven observations, n, the following formula can be used to find the correlation coefficient, r:
r = (n x (SUM(X,Y)  (SUM(X) x (SUM(Y))) / Square Root((n x SUM(X^2)  SUM(X)^2) x (n x SUM(Y^2)  SUM(Y)^2))
In this example, the correlation is:
r = (7 x 26,926  (409 x 485) / Square Root((7 x 28,623  409^2) x (7 x 35,971  485^2)) = 9,883 / 23,414 = 0.42
The two data sets have an inverse correlation of 0.42.

Correlation Coefficient
A measure that determines the degree to which two variable's ... 
Negative Correlation
In statistics, a perfect negative correlation is a relationship ... 
Serial Correlation
The relationship between a given variable and itself over various ... 
Pairs Trade
A pairs trade is a trading strategy that involves matching a ... 
Cluster Analysis
An investment approach that places securities into groups based ... 
Coefficient of Determination
A measure used in statistical model analysis to assess how well ...

Investing
The Risks of Investing in Inverse ETFs
Discover analyses of the risks inherent to inverse exchangetraded funds (ETFs) that investors must understand before considering an investment in this type of ETF. 
Investing
Tales From The Trenches: Perfectly Negative Profitability
Use correlations to profit when two specific instruments move in opposite directions. 
Investing
Regression Basics For Business Analysis
This tool is easy to use and can provide valuable information on financial analysis and forecasting. Find out how. 
Tech
Are Bitcoin Price And Equity Markets Returns Correlated?
Is there a correlation between bitcoin's price and the equity markets? We investigate. 
Investing
How does crude oil affect gas prices?
Understand the origins of oil, how its price is determined and where its correlation with gas prices falls in the global economy. 
Investing
How to Diversify Your Portfolio Beyond Stocks
Find out how to get diversified in asset classes beyond stocks to reduce portfolio risk. Learn how diversification can help you reach your financial goals. 
Financial Advisor
Do Bear Market Funds Make Sense for Investors?
Bear market funds have their place. But are they right for individual investors? 
Investing
The Long and Short of Inverse ETFs
When applied properly, inverse ETFs can be a useful tool for traders. 
Investing
Portfolio Diversification, Done Right
Diversifying your portfolio by means of different securities and asset classes is an essential approach to lower the overall risk of a portfolio.

Does a negative correlation between two stocks mean anything?
Learn what the concept of negative correlation means, understand how it is generally calculated and see how it is used in ... Read Answer >> 
How can you calculate correlation using Excel?
Find out how to calculate the Pearson correlation coefficient between two data arrays in Microsoft Excel through the CORREL ... Read Answer >> 
How is correlation used differently in finance and economics?
Take a look at the similarities and differences between how statistical correlation is applied in economics as opposed to ... Read Answer >> 
What Does it Mean if the Correlation coefficient is Positive, Negative, or Zero?
When a coefficient is greater than zero, it is a positive relationship; when the value is less than zero, it is a negative ... Read Answer >> 
How should I interpret a negative correlation?
Learn more about correlation and how businesses analyze variables. Find out how negative correlations are interpreted by ... Read Answer >>