**Correlation Between Currencies**

Correlation between sets of data refers to the statistical relationship that exists between them. In forex trading, if we take two currency pairs, for example, we can calculate how closely their price is correlated, giving us insight that we may be able to exploit for future profit. This can result in improvements to our trade expectancy by refining our entry and exit strategy through analysis of highly correlated pairs, by optimization of exposure to uncorrelated currency pairs, or by several other means. If you are not sure what that means, it's ok, once you become familiar with the concept of correlation, its usefulness will be very clear. In this article, we will focus on how to calculate the "correlation coefficient", a number between -1 and +1, which indicates how closely related two currency pairs (or any other data sets) are. Follow-up articles will provide a broader study of its possible uses in extracting profit from the forex market.

There are a number of different ways to calculate dependence between time series data, such as financial instrument price feeds that are used in constructing our candle or bar charts. By far the most useful and relevant method is the calculation of linear dependence by way of the "Pearson product-moment correlation coefficient". For the purpose of this article, we will simply refer to it as the "correlation coefficient".

In order to calculate the correlation coefficient between 2 currency pairs, we would use the following equation:

where:

r_{xy} is the correlation coefficient between datasets x and y (the quantity we are calculating)

n is the number of different prices we have in the data set

x_{avg} is the arithmetic mean (average) of all the values in data set x

y_{avg} is the arithmetic mean (average) of all the values in data set y

Please note that (obviously) the prices we use for x and y must both be over the same timeframe. Also, r_{xy} = r_{yx} and -1 =< r_{xy} =< 1 for any data set x and y. A correlation coefficient r value near -1 indicates a high degree of negative correlation, meaning when one data set is moving up, the other is moving down. An r value near +1 indicates that the data move almost in lock-step.

It is highly recommended that you go through this calculation manually (on paper or a on spreadsheet) at least several times, using small data sets of 5-10 price points each. This will familiarize you with how the equation works. After this, you can use a spreadsheet to calculate the value directly (for example, using the "=CORREL(x_{1}:x_{n}, y_{1}:y_{n})" function in Excel). You can use this, along with a charting function to simulate different scenarios and automatically determine the correlation.

At this point you should be familiar enough with the concept to begin using it in your trading. There are numerous ways of using the concept of correlation, the most common being its use in portfolio theory, that dictates portfolio volatility as a function of correlation between assets. In plain English, this means that equal exposure to highly correlated assets is similar to double the exposure to any one of those assets. The details of portfolio theory are beyond the scope of this article, however, common sense also dictates that, for example, if one is long both EUR/USD and GBP/USD, with the correlation between those currency pairs fairly high, the trader is effectively almost doubling the volatility of their portfolio. This is the main reason asset managers advise clients to "diversify" their portfolios - diversification can produce a similar expected return while reducing risk.

It is also worth mentioning that in the example above, there are times when a trader may wish to exploit an expected breakdown of the correlation between EUR/USD and GBP/USD, in which case trading EUR/GBP is a better bet.

Another common use of correlation is that sentiment can be confirmed through analysis of a highly correlated asset. To use EUR and GBP as an example again, say your trading strategy produces a buy signal on EUR/USD. You can perform the same analysis on GBP/USD, and if it also produces a buy signal, barring a breakdown of correlation, you have just confirmed your chances for a winning trade. If, on the other hand, your analysis produces a neutral or sell signal on GBP/USD, you may wish to stay out of the market, or bet on a breakdown of correlation and buy EUR/GBP.

Because of its predictive value, correlation can also be used to forecast future values of certain variables. For example, a trader can analyse the correlation between the ADP US jobs report, released on the first Wednesday of each month, and the official US Labor Department Non-farm Payrolls (NFP) release on the following Friday. If the two releases are found to be highly correlated over time, that information can be used to predict, with some degree of accuracy, the results of the NFP report, and to exploit the market's expected reaction for profit.

There are numerous other uses of the correlation coefficient and related values such as covariance and linear regression. It is in your best interest to familiarize yourself with these concepts in the field of statistics, as they can be powerful tools in your quest to extract profit from the forex market.

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