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 example presented below 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(x2). The same must be done for the Y values:

SUM(X2) = (552) + (372) + (1002) + ... (882) = 28,623

SUM(Y2) = (912) + (602) + (702) + ... (302) = 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(X2) - SUM(X)2) x (n x SUM(Y2) - SUM(Y)2))

In this example, the correlation is:

r = (7 x 26,926 - (409 x 485) / Square Root((7 x 28,623 - 4092) x (7 x 35,971 - 4852))

r = 9,883 / 23,414

r = -0.42

The two data sets have an inverse correlation of -0.42.

RELATED TERMS
  1. Correlation

    Correlation is a statistical measure of how two securities move ...
  2. Correlation Coefficient

    The correlation coefficient is a statistical measure that calculates ...
  3. Serial Correlation

    Serial correlation is the relationship between a given variable ...
  4. Pairs Trade

    A pairs trade is a trading strategy that involves matching a ...
  5. Intermarket Analysis

    Intermarket analysis looks at related asset classes or financial ...
  6. Regulation X

    Regulation X is a rule that limits the amount of credit foreign ...
Related Articles
  1. Investing

    How To Trade Currency And Commodity Correlations

    Relationships between currencies and commodities exist throughout the financial markets. Find out how to trade these trends.
  2. Trading

    Managing Currency Exposure In Your Portfolio

    The value of your investments is impacted by changes in global currency exchange rates. Find out how.
  3. Investing

    Tales From The Trenches: Perfectly Negative Profitability

    Use correlations to profit when two specific instruments move in opposite directions.
  4. Tech

    Are Bitcoin Price And Equity Markets Returns Correlated?

    Is there a correlation between bitcoin's price and the equity markets? We investigate.
  5. 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.
  6. Investing

    Commodities: The Portfolio Hedge

    These diverse asset classes can provide downside protection and upside potential. Find out how to use them.
  7. Investing

    A Guide to Using Inverse ETFs for Diversification

    A look at how inverse ETFs can help investors diversify their portfolios.
  8. Investing

    Apple Will Kill Off iPhone X This Year: Analyst

    Mirabaud Securities, citing excess chip inventory, predicts Apple will discontinue the iPhone X.
  9. Investing

    Apple: Slow iPhone 8 Sales May Not Be a Bad Thing

    A sluggish start may be a good thing if Asian consumers are waiting for the pricier iPhone X.
  10. Managing Wealth

    Does International Investing Really Offer Diversification?

    Historically, international investing has worked out well for investors, but this may no longer be the case.
RELATED FAQS
  1. What is the difference between positive correlation and inverse correlation?

    Learn the difference between a positive correlation and a negative, or inverse, correlation and the way they apply to the ... Read Answer >>
  2. 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 >>
  3. 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 >>
  4. How is correlation used in modern portfolio theory?

    Discover how modern portfolio theory and the efficient frontier use correlation between investment assets to predict an optimal ... Read Answer >>
  5. What are some examples of positive correlation in economics?

    Learn the most common examples of positive correlation in macroeconomics and microeconomics, including demand and price, ... Read Answer >>
Hot Definitions
  1. Yield Curve

    A yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but ...
  2. Portfolio

    A portfolio is a grouping of financial assets such as stocks, bonds and cash equivalents, also their mutual, exchange-traded ...
  3. Gross Profit

    Gross profit is the profit a company makes after deducting the costs of making and selling its products, or the costs of ...
  4. Diversification

    Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
  5. Intrinsic Value

    Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
  6. Current Assets

    Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
Trading Center