Correlation Coefficient

What Is the Correlation Coefficient?

The correlation coefficient is a metric that measures the strength and heading of a relationship between two securities or variables, for example, a stock and a benchmark index, commodities, bonds, or different types of assets with data series. It can likewise be utilized to compare the performance of two unique types of asset classes: a foreign currency and gold, the S&P 500 Index and a bond yield, an exchange-traded fund and crude oil, or even cryptocurrency and a benchmark tech stock index. This article centers around stocks.
Correlation measures the relationship of two stocks based on their returns (percentage gains or losses), not their historical prices, which is comparable in how beta is measured. Numerous investors and analysts use correlation to determine whether one stock is moving in a similar bearing as another stock or benchmark index. As part of an investment strategy, it very well may be useful in affirming the heading of a stock to its benchmark, or on the other hand whether the stock and benchmark are moving in inverse headings.

Step by step instructions to Calculate the Correlation Coefficient

A simple calculation method is to utilize what's known as the Pearson correlation coefficient calculator, named after the English mathematician Karl Pearson.
In this formula, r addresses Pearson's correlation coefficient. Find the covariance of two variables, which will be called x and y. Take that number, and afterward partition by the product of the standard deviation of x and the standard deviation of y.
r = covariance of two variables x and y/(standard deviation of x) * (standard deviation of y)

In any case, that might be seen as the long-hand method of computing correlation. The most efficient method for working out correlation is through calculation sheet. Requiring 5 days' worth of data probably won't be basically as meaningful as 5 months, so having a sizable series will be key. A few investors and analysts use around 90 or 100 days' worth of historical prices for adequate quantitative analysis. A more limited period, however, could be utilized to compare long-term correlation.
Below is an instance of computing the coefficient correlation among Apple and the S&P 500 Index, a benchmark measure for U.S. stocks.
Step 1: Collect daily data returning 91 days. The correlation target is for 90 days, yet the principal day fills in as the base price for the primary percentage change. Compute daily percent change for Apple and the S&P 500. Note: The formula is displayed in the cell as well as in the field area on the upper left corner of the bookkeeping sheet. Apple's closing stock price accounts for adjustments, including splits, dividends, and additionally capital gain distributions.
Step 2: Calculate the 90-day correlation of Apple and S&P 500 by involving the shorthand command in the bookkeeping sheet. It won't make any difference whether Apple is the first or second exhibit, just as long as the data range between the two matches. For comparison on a more limited duration, work out the 30-day correlation utilizing the last 30 days of data.
Note: Some bookkeeping sheets allow for the comparison of at least three variables by means of a matrix.

The most effective method to Interpret the Correlation Coefficient

The coefficient of the correlation goes from - 1 to 1. A number at - 1 or close to - 1 demonstrates that the two stocks have an inverse correlation. All in all, when one goes up, the other goes down and vice versa. At 1 or close to 1, two stocks are moving in a similar heading, with 1 meaning that they are moving lockstep with one another. It's rare to see two stocks with either a perfect coefficient correlation of - 1 or 1. A correlation of 0 shows a neutral position, with no relationship demonstrated in terms of strength and bearing.
Graphically, a correlation of greater than 0 would have a positive slant, while a correlation under 0 would have a negative incline.
A Quick Guide to Correlation Coefficient Values

Correlation Value	Strength	Direction
1	Perfect positive correlation	Same
0.75	High	Same
0.50	Moderate	Same
0.25	Low	Same
0	No Correlation	None
-0.25	Low	Opposite
-0.50	Moderate	Opposite
-0.75	High	Opposite
-1	Perfect negative correlation	Opposite

Suppose that a stock and a benchmark index have a correlation of 0.75. That means the relationship between the two is strong and both will generally move in a similar heading more often than not. One more method for expressing it is that the two move in a similar bearing 75 percent of the time. On the other hand, a - 0.75 correlation demonstrates that the two move the other way 75 percent of the time. A correlation of 0.5 recommends that the strength between the two is moderate and they move in a similar course half the time, while 0.25 proposes low correlation however they actually move in a similar heading a portion of the time. Negative correlations of - 0.5 and - 0.25 demonstrate moderate and low strength, separately, however recommend the stock and the benchmark will generally move in inverse bearings. **Note:** In a bear market, in the event that two stocks decline in a similar course, their correlation stays positive. In the above model, Apple and the S&P 500 have a correlation coefficient of 0.73817, which shows a strong relationship between the two over the 90 days of data. On the off chance that the number of days is diminished to the last 30, the correlation is 0.84602, which proposes a stronger relationship than over the 90-day period. During the 30-day period, sentiment in the market turned bearish. As Apple's stock fell, without a doubt so did the S&P 500. Apple had the greatest market capitalization of any U.S. stock at that point, and that means its weighting in the S&P 500 had more influence on the benchmark's course than any of its other part stocks. ## The most effective method to Use the Correlation Coefficient An investors use correlation to measure risk in a portfolio. A high correlation between of one stock to the benchmark could mean higher risk, compared to one with no correlation, on the grounds that the two are closely related and would move in a similar heading. A negative correlation could help in enhancing investment on the view that one stock's losing returns means another's gain. Correlation can be utilized related to other technical measures and metrics, for example, [relative strength index](/rsi), [moving average](/movingaverage), [beta](/beta) and standard deviation. ## What Are the Limitations of the Correlation Coefficient? Since the correlation coefficient is limited to historical data, it would be trying to involve it as a forecasting instrument. Correlation is utilized in quantitative analysis (rather than fundamental analysis, which utilizes data gathered from an organization's financial statement), and hence is limited to data series, like a stock's price history.

Highlights

Pearson correlation is the one most regularly utilized in statistics. This measures the strength and heading of a linear relationship between two variables.
Correlation coefficients are utilized to measure the strength of the relationship between two variables.
Correlation coefficient values under +0.8 or greater than - 0.8 are not thought of as critical.
Values generally range between - 1 (strong negative relationship) and +1 (strong positive relationship). Values at or close to zero suggest a weak or no linear relationship.

FAQ

How Is the Correlation Coefficient Used in Investing?

Correlation coefficients are a broadly involved statistical measure in investing. They play a vital job in areas like portfolio composition, quantitative trading, and performance evaluation. For instance, some portfolio managers will monitor the correlation coefficients of individual assets in their portfolios to guarantee that the total volatility of their portfolios is kept up with inside acceptable limits.Similarly, analysts will in some cases use correlation coefficients to anticipate what a particular asset will be meant for by a change to an outside factor, for example, the price of a commodity or an interest rate.

How Do You Calculate the Correlation Coefficient?

The correlation coefficient is calculated by first determining the covariance of the variables and afterward partitioning that quantity by the product of those variables' standard deviations.

What Is Meant by the Correlation Coefficient?

The correlation coefficient portrays how one variable maneuvers corresponding to another. A positive correlation demonstrates that the two move in a similar course, with a +1.0 correlation when they move in tandem. A negative correlation coefficient lets you know that they rather move in inverse bearings. A correlation of zero recommends no correlation by any means.