EBF 301
Global Finance for the Earth, Energy, and Materials Industries

Correlation

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Correlation is a measure of the strength of the linear relationship between two quantitative variables. The equation for the correlation coefficient is:

r=∑(xi−ˉx)(yi−ˉy)√∑(xi−ˉx)2√∑(yi−ˉy)2

Correlation coefficient takes a value between -1 and 1. As you can see in the following video, a correlation coefficient of 1 indicates a strong positive linear relationship between two variables and a correlation coefficient of -1 shows a strong negative linear relationship. And if two variables are not related or not linearly related, the correlation coefficient can take a value close to zero.

Strength of linear association

Strength of linear association (no sound
Click here for a text description of what is observed in the video

The video shows a graph with the explanatory variable on the x-axis and the response variable on the y-axis. There are many points on the graph. The correlation value is shifted from -1 to 1. What the correlation is -1 the points are in a linear, negatively sloped line. As the correlation value changes until the correlation value reached +1 where the points are now in a linear, positively sloped line.

Penn State Statistics Department

As we learned in a previous lesson, a high correlation between spot and futures market prices makes the hedging efficient. Note that in the case of backwardation, the correlation between spot and futures would be lower.

Example:

The following chart shows the last 10 prices of February 2018 crude oil spot and futures from EIA.

Date NYMEX Futures$/bbl Spot$/bbl
Feb 14, 2018 60.7 60.6
Feb 15, 2018 61.48 61.34
Feb 16, 2018 61.89 61.68
Feb 20, 2018 61.91 61.9
Feb 21, 2018 61.73 61.68
Feb 22, 2018 62.72 62.77
Feb 23, 2018 63.52 63.55
Feb 26, 2018 63.81 63.91
Feb 27, 2018 62.94 63.01
Feb 28, 2018 61.43 61.64

The following chart displayed the data and, as you can see, they are closely related.

Chart of prices of February 2018 crude oil spot and futures from EIA displayed in previous table
NYMEX futures and Spot Market data over a two week period.
Credit: NYMEX

As the following graph shows, we can use the Excel function CORREL() to calculate the correlation between spot and futures for these price data as 0.994, which shows a strong relationship between them.

screen grab of excell and using CORREL( ) function to yield a correlation of 0.994
Excel document showing the correlation between spot and futures.
Credit: NYMEX

Note that cross hedging is using futures contracts (for commodity A) in order to hedge the price risk for the commodities (commodity B) that don’t have futures contract market. And cross hedging is possible when the futures price of commodity A are highly correlated with spot prices of commodity B.

Note that we can calculate the correlation of the returns in a similar way to what we did to calculate the volatility (calculating the standard deviation for the returns).