## 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. ### Benchmark For Correlation Values

A benchmark or point of reference chosen by an investment fund ...
2. ### Covered Interest Arbitrage

Covered interest arbitrage is a strategy where an investor uses ...
3. ### Mean-Variance Analysis

The process of weighing risk against expected return. Mean variance ...
4. ### Coefficient of Determination

A measure used in statistical model analysis to assess how well ...
5. ### Time Value of Money - TVM

The time value of money is the idea that money presently available ...
6. ### Continuous Compounding

Continuous compounding is the process of calculating interest ...
Related Articles

### 4 Reasons Why Market Correlation Matters

Learn about how correlation can be used to measure how broader markets move in relation to each other. See how correlation is used to manage risk.
2. Investing

### Is the Stock Correlation Strategy Effective?

The synchronized movement among stocks and markets in recent years is challenging diversification.

Knowing the relationships between pairs can help control risk exposure and maximize profits.
4. 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.
5. Investing

### The Market Is Assessing Trump Implications

Stocks are no longer moving in unison, and active fund managers are cheering.
6. 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.
7. Investing

### How to Create a Risk Parity Portfolio

Learn about how risk parity uses leverage to create equal exposure to risk among different asset classes in portfolio construction.
8. Investing

### Apple's iPhone X Is Sold Out in Many Major Cities

The new iPhone X hit store shelves this weekend and quickly sold out in at least 20 major cities.
RELATED FAQS
1. ### 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 >>
2. ### 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 >>
3. ### 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 >>
4. ### 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 >>
5. ### 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 >>
Hot Definitions
1. ### Leverage

Leverage results from using borrowed capital as a source of funding when investing to expand the firm's asset base and generate ...
2. ### Financial Risk

Financial risk is the possibility that shareholders will lose money when investing in a company if its cash flow fails to ...
3. ### Enterprise Value (EV)

Enterprise Value (EV) is a measure of a company's total value, often used as a more comprehensive alternative to equity market ...
4. ### Relative Strength Index - RSI

Relative Strength Indicator (RSI) is a technical momentum indicator that compares the magnitude of recent gains to recent ...
5. ### Dividend

A dividend is a distribution of a portion of a company's earnings, decided by the board of directors, to a class of its shareholders.
6. ### Inventory Turnover

Inventory turnover is a ratio showing how many times a company has sold and replaces inventory over a period.