# Correlation

## What is 'Correlation'

Correlation, in the finance and investment industries, is a statistic that measures the degree to which two securities move in relation to each other. Correlations are used in advanced portfolio management. Correlation is computed into what is known as the correlation coefficient, which has value that must fall between -1 and 1.

Next Up

## BREAKING DOWN 'Correlation'

A perfect positive correlation means that the correlation coefficient is exactly 1. This implies that as one security moves, either up or down, the other security moves in lockstep, in the same direction. A perfect negative correlation means that two assets move in opposite directions, while a zero correlation implies no relationship at all.

For example, large-cap mutual funds generally have a high positive correlation to the Standard and Poor's (S&P) 500 Index, very close to 1. Small-cap stocks have a positive correlation to that same index also, but it is not as high, generally around 0.8.

However, put option prices and underlying stock prices tend to have a negative correlation. As the stock price increases, the put option prices go down. This is a direct and high-magnitude negative correlation.

## Correlation Calculation Example

Investment managers, traders and analysts find it very important to calculate correlation, because the risk reduction benefits of diversification rely on this statistic. Financial spreadsheets and software can calculate the value of correlation quickly.

Assume an analyst needs to calculate the correlation for the following two data sets:

X: 41, 19, 23, 40, 55, 57, 33

Y: 94, 60, 74, 71, 82, 76, 61

There are three steps involved in finding the correlation. The first is to add up all the X values to find SUM(X), add up all the Y values to fund SUM(Y) and multiply each X value with its corresponding Y value and sum them to find SUM(X,Y):

SUM(X) = (41 + 19 + 23 + 40 + 55 + 57 + 33) = 268

SUM(Y) = (94 + 60 + 74 + 71 + 82 + 76 + 61) = 518

SUM(X,Y) = (41 x 94) + (19 x 60) + (23 x 74) + ... (33 x 61) = 20,391

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) = (41^2) + (19^2) + (23^2) + ... (33^2) = 11,534

SUM(Y^2) = (94^2) + (60^2) + (74^2) + ... (61^2) = 39,174

Noting that 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))) / SquareRoot((n x SUM(X^2) - SUM(X)^2) x (n x SUM(Y^2) - SUM(Y)^2))

In this example, the correlation would be:

r = (7 x 20,391 - (268 x 518) / SquareRoot((7 x 11,534 - 268^2) x (7 x 39,174 - 518^2)) = 3,913 / 7,248.4 = 0.54

RELATED TERMS
1. ### Inverse Correlation

A contrary relationship between two variables such that they ...
2. ### Negative Correlation

A relationship between two variables in which one variable increases ...
3. ### Positive Correlation

A relationship between two variables in which both variables ...
4. ### Correlation Coefficient

A measure that determines the degree to which two variable's ...
5. ### Covered Interest Arbitrage

The practice of using favorable interest rate differentials to ...
6. ### Serial Correlation

The relationship between a given variable and itself over various ...
Related Articles

### Correlation

In the world of finance, correlation is a statistical measure of how two securities move in relation to each other.

### What's the Correlation Coefficient?

The correlation coefficient is a measure of how closely two variables move in relation to one another. If one variable goes up by a certain amount, the correlation coefficient indicates which ...
3. Markets

### Understanding the Oil & Gas Price Correlation

Learn how the correlation between the commodity prices for natural gas and oil changed from 2004 to 2015 due to increased natural gas production.
4. Managing Wealth

### Diversification: Protecting Portfolios From Mass Destruction

This investing strategy retains its charm as a protection against random events in the market.

### Explaining Autocorrelation

Autocorrelation is the measure of an internal correlation with a given time series.

### Managing Currency Exposure In Your Portfolio

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

### Calculating Future Value

Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.
8. Investing

### Pairs Trade Example

As with nearly any investment, taking a pairs trade involves more than just hitting the buy and sell button. Here we examine, in very broad terms, the steps required to enter and exit a pairs ...
9. ETFs & Mutual Funds

### How I Learned to Stop Worrying and Love the Bond

Though U.S. Treasuries are not as expensive as government bonds, U.S. bonds are offering a relatively paltry real return, even after adjusting for low inflation.
10. Managing Wealth

### Diversification Beyond Stocks

If you think holding several stocks means you're diversified, think again - there's much more to be done to reduce portfolio risk.
RELATED FAQS
1. ### 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 >>
2. ### 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 >>
3. ### What is the difference between a copay and a deductible?

Learn how the correlation coefficient may be used to predict the relationship between the returns of two stocks, but also ... Read Answer >>
4. ### How do I calculate correlation between market indicators and specific stocks?

Discover how to calculate the correlation coefficient between market indicators and stock prices, a critical skill in technical ... Read Answer >>
5. ### How does correlation affect the stock market?

Learn about the role correlation plays in prudent stock market investing, and how the correlation coefficient is used to ... Read Answer >>
6. ### How do you calculate r-squared in Excel?

Calculate R-squared in Microsoft Excel by creating two data ranges to correlate. Use the Correlate formula to correlate both ... Read Answer >>
Hot Definitions
1. ### Sell-Off

The rapid selling of securities, such as stocks, bonds and commodities. The increase in supply leads to a decline in the ...
2. ### Brazil, Russia, India And China - BRIC

An acronym for the economies of Brazil, Russia, India and China combined. It has been speculated that by 2050 these four ...
3. ### Brexit

The Brexit, an abbreviation of "British exit" that mirrors the term Grexit, refers to the possibility of Britain's withdrawal ...
4. ### Underweight

1. A situation where a portfolio does not hold a sufficient amount of a particular security when compared to the security's ...
5. ### Russell 3000 Index

A market capitalization weighted equity index maintained by the Russell Investment Group that seeks to be a benchmark of ...
6. ### Enterprise Value (EV)

A measure of a company's value, often used as an alternative to straightforward market capitalization. Enterprise value is ...