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Correlation coefficient

how to calculate coefficient of correlation

Is a statistical method using a number that describes the degree of a linear relationship between two assets that either move together, or inversely, or are not related at all. The correlation coefficient is a way to measure the strength of the relationship between two assets, useful because analysis of one market can sometimes help us infer things about the other market.

A correlation coefficient is a single number that describes the degree of linear relationship between two sets of variables. If one set of data (say, gold) increases at the same time as another (say, gold stocks), the relationship is said to be positive or direct. If one set of data increases (gold) as the other decreases (USD), the relationship is negative, or inverse.

Let’s follow a simple example from everyday life. How much electricity do you use in balmy spring day as opposed to a rainy winter day? You probably would say that in a sunny day you use less electricity. On a rainy day you use artificial light and are more likely to stay at home. So where do we spot correlation in this example? According to statistics, demand for electricity is positively correlated with the amount of rain on a given day. We use more electricity on rainy days than in sunny days.

Why correlation coefficient is so important and why we should use it in our analysis?

We live in a globalized world and financial markets are generally integrated - none of them moves on its own, but rather they move together, or in an inverse fashion (with turning points taking place at the same time). Consequently, even if you're just interested in gold or silver, it's best to analyze many markets.

Analyzing many markets already gives you an advantage over most investors who focus on gold or silver only. But

we think this analysis could go one step further. In order to make this multi-market analysis even more efficient, we try to estimate the strength of "influence" that particular non-PM market has on gold, silver and corresponding equities. Consequently, we’re able to pay greater attention to markets that are more important at a particular moment.

One of the ways to measure the strength of the "influence" is to use the linear correlation coefficient. We have put "influence" into quotation marks, because the correlation coefficient does not tell us which market influences which - still, we have common sense to know that. For instance, the price of gold determines earnings and therefore share prices of gold mining companies and not the other way around.

What this number really tells us, is "how much" have the markets moved together in the past, without telling us why. The shape of a given relationship usually does not change along with change in the prices, so what we could infer based on analysis of one market, could help us analyze other markets. For instance, if gold moved opposite to the USD index lately and we have just seen a verification of a very bullish formation on the USD Index chart, then it's likely that we will see a decline in gold even though the situation in gold itself doesn't suggest that on its own.

Correlation coefficient takes values from -1 to 1 where:

  • -1 means that there is a very strong negative correlation between markets that are moving in opposite directions
  • 0 means that there is no correlation between market moves
  • 1 means that there is a strong positive correlation. Markets are moving in the same direction

Below you can find a table that shows individual values of correlation coefficient and their meaning/ description.

Category: Forex

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