Correlation coefficient

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. We use the correlation phenomenon in our analyses and alerts.

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. In other words, if gold moves in tune with USD (in percentage terms the sizes of moves are at least similar), one can speak of gold's positive correlation coefficient with the USD, and if they move in the opposite directions, one can speak of gold's negative correlation coefficient with the USD.

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.

Correlation Coefficient	Type / strength of correlation
-1   -   -0.9	Strongly negative
-0.9   -   -0.7	Negative
-0.7   -   -0.4	Fairly negative
-0.4   -   -0.2	Slightly negative
-0.2   -   0	Very weak and negative
0	No correlation
0   -   0.2	Very weak and positive
0.2   -   0.4	Slightly positive
0.4   -   0.7	Fairly positive
0.7   -   0.9	Positive
0.9   -   1	Strongly positive

Real market example

To better understand the concept of the correlation coefficient, please consider the following examples of different kinds of correlation. The screenshots have been taken from our gold and silver correlations video - you might want to watch it for additional explanations.

Positive correlation

Probably nobody will argue that gold and HUI index move in the same direction on average.

On the graphic below you can easily notice that there is a strong positive correlation. We say that correlation is positive when correlation coefficient takes value from o to +1. We see that gold and HUI reach peaks and bottoms almost in the same time.

Negative correlation

Negative correlation means that markets are moving on average in different direction. If the correlation is negative it takes values from -1 to 0. On the graphics below you can easily spot a negative correlation between US Dollar and Euro. You see that peaks of the dollar occur when the euro reaches bottoms and vice versa.

Zero correlation

We say there is zero correlation when there is no noticeable relationship between markets. At the graph below you can see that there are no similar or totally opposite moves between Us Dollar and Canadian Venture Exchange. They are independent and their correlation coefficient is “0”.

Restrictions

We would not recommend using correlation coefficients to calculate the exact sizes of one's positions or to estimate the size of the position that one would want to hedge. Most statistical coefficients are biased as a result of assuming normal distribution of returns. It does not pose a serious threat as long as you only use the results for comparison between assets or to as an additional technique that doesn't directly calculate prices of assets. One should also check the raw data for rare (but significant) events.

- Moreover, by simply using correlations we cannot define the influence that one market has on another. We can only notice that relationship occurs. We are not able to tell (based on the coefficient value alone) if gold influences the dollar or vice versa.

- We cannot make detailed price forecast based on correlation coefficients alone, because we will get results that cannot be interpreted in a useful way. However, we can use correlation analysis to find important connections between the markets and use them in connection with other types of analysis, which would increase the efficiency of the latter.