Bitcoin and S&P 500 correlation is decoupling
Across Twitter in the last couple days, there have been several tweets about Bitcoin and its correlation to traditional markets or stocks. Some say there is no correlation, while others say they are highly correlated; It was correlated, now it is not. Which one is it? Additionally, some of the tweets I came across appeared to misunderstand what a correlation is. In this article, I will settle the debate on whether Bitcoin and the S&P 500 are correlated or not. I start by breaking down what a correlation is and then analyze Bitcoin and the S&P 500's correlation across the last year.
What is a correlation?
If you already know what correlations are, then skip to the "Bitcoin and the S&P 500" section. A correlation, or a correlation coefficient, is a number between the range negative one (-1.0) and positive one (+1.0). Alternatively, -1.0, -0.9,..., -0.1, 0, 0.1,..., 0.9, 1.0. Values are typically written like so: ".643" or "r = -.793", without a zero in front of the decimal and with two-to-three decimal places. In this article, I use the Person correlation for all the calculations.
Person correlation formula and notes (Mindrila and Balentyne, 2020).
Correlations measure the relationship (i.e., strength and direction) between two variables. The closer the correlation is to +1.0, the stronger and more direct the relationship is. In other words, if one variable goes up, the other variable is likely to go up too (i.e., a direct, or positive, correlation). This is also true vice versa. The closer the correlation is to -1, the stronger and more in-direct the relationship is. In other words, if one variable goes up, the other variable will likely go down (i.e., an in-direct, or negative, correlation). This is also true vice versa. The closer a correlation is to 0, the weaker the relationship is and, when closer to zero, no clear direction can be inferred.
Qualitative description of correlation strength (Mindrila and Balentyne, 2020).
When it comes to correlations, it is incorrect to say that two variables are not correlated. This is because variables will always have some degree of correlation (unless they have a perfect correlation of zero). Rather, what should be said is that the variables are weakly or strongly correlated. Additionally, one can also describe a correlation as statistically significant or insignificant. Now that we know what a correlation is, I will not look at the correlation between Bitcoin and the S&P 500.
Bitcoin and the S&P 500
Now that we know two variables (such as, the Bitcoin and S&P 500 daily closing price) always have some degree of correlation, we know that Bitcoin and traditional markets or stocks do too. The question then shifts away from "are they correlated or are they not correlated" to "is that correlation weak, strong, significant, or insignificant and what interpretations can be made with that information?"
Below, I plotted the correlation between Bitcoin and S&P 500 daily closing price across each month for a year. I also tested each monthly correlation for its significance level (two images down).
Bitcoin and S&P 500 monthly correlation chart.
The current month of May 2020 is only based on 10 data points. It is too early to tell if Bitcoin and S&P 500 are correlated for this month. It would be ideal to wait until the end of May to determine the result. However, the preliminary result suggests that the relation is very weak and insignificant, r(9) = .017, p = .963. I understand why Twitter was blowing up on the "no correlation" news given this result. Also, notice how the trend is going down for both monthly correlations and the 3-month moving average. I would wait until the end of May before describing Bitcoin and the S&P 500 as very weakly correlated for the month. See image below for each month's significance level.
Monthly correlations and significance.
Out of the last twelve months (not including this May), 50% of the correlations have been significant. All the correlations that were significant were at least in the |.6|'s, while all those that were insignificant were below the |.4|'s (I am using absolute values here).
Another way to analyze Bitcoin and the S&P 500 daily closing price is to convert them into z-scores. If you do not know what these are, see my previous article on the Bitcoin 2020 Halving where I explain z-scores. Basically, z-scores let you compare two completely different things, like apples and bananas. Z-scores normalize the two different things on to the same scale. This allows for a true comparison between the variables. I did this comparison below.
Bitcoin and S&P 500 daily closing price in z-scores.
Currently, Bitcoin and the S&P 500 are divergent. That is, they are moving away from each other. This explains the preliminary result of a very weak correlation between Bitcoin and the S&P 500. Given the Bitcoin is rising as the S&P 500 is falling, the correlation at the end of May 2020 could turn out to be negative, or indirectly correlated. As one goes up, the other goes down.
Notice that the last three months (i.e., Feb - April), Bitcoin and the S&P 500 were following the same trend. This explains the moderate-to-strong correlations they had the last few months. However, when we look at December through the end of January, it is clear there is a gap between Bitcoin and the S&P 500 price. No surprise, the correlations for those months were weak and insignificant. A similar story is true for the remainder of the months.
In this article, I reviewed what correlations are and analyzed the correlation between Bitcoin and S&P 500 closing prices across the last twelve months. In short, I argued that there is always a correlation between two variables (unless a true zero). It is incorrect to say that two variables have no correlation. Rather, describing the correlation in terms of strength and significance is more appropriate and objective. Preliminary results suggest that Bitcoin and S&P 500 closing prices for the month of May 2020 share a very weak and insignificant correlation, r(9) = .017, p = .963. Given that this result is only based on ten data points, it is best to wait until the end of the month for a more robust sample. Lastly, it is true that for the last three months Bitcoin and the S&P 500 have been moderately-to-strongly (and significantly) correlated. Current trends suggest a decoupling in price is developing. With this, I expect a negative correlation for the month of May 2020 as Bitcoin and S&P 500 prices are divergent.
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