Correlation in The Context of Cryptocurrencies

Over the past few years, there are some very interesting things to note about the correlation between Bitcoin (and cryptocurrencies as a whole) and the traditional market (SP500 and gold in particular).

We all know what correlation is, even if we all have not really studied statistics: “In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data” - Wikipedia

Now, it does not mean, as we always hear, people say correlation does not imply causation. That is because two variables may be correlated and yet there may not be a relationship between them, as we will talk about.

When scientists and mathematicians speak about correlation, the metric you normally use is a “correlation coefficient” and this is a number somewhere between minus one (-1) and plus one (1). If the correlation is a positive one, that means that the two variables move together very smoothly. If the correlation coefficient is equal to 0, it means that the two variables are completely uncorrelated. And if the correlation is -1, it means that the variables are completely anti-correlated.

Is Bitcoin correlated to another market?

Generally speaking, no, they are not. We can look at some graphs such as SP500 vs BTC:

Source: blockchaincenter.net

Some bitcoiners like to say “Bitcoin is an uncorrelated asset”, implying that its price movement is completely decoupled from the price movement of other asset classes. Investing in combinations of uncorrelated assets can reduce the overall risk in a portfolio and even boost the overall return. But is that really the case? With this tool, data is analyzed with the aim to back up or dismiss the claim.

The Pearson correlation coefficient is a beneficial mechanism to measure this correlation and assess the strength of a linear relationship between two data sets. It takes values between -1 and 1. -1 is a strong negative correlation, 0 implies no correlation at all (uncorrelated) and +1 stands for a strong positive correlation.

Looking at this tool, a coefficient of 1 essentially equates: if one asset goes up, the one we are comparing it to tends to go up, as well. This also happens vice versa. A good example for a coefficient of almost 1 is the comparison between the SP 500 and the Dow Jones stock index. Both track the performance of blue-chip stocks. Consequently, it comes as no surprise that the correlation chart for SP vs. Dow Jones looks like the following:

Source: blockchaincenter.net

According to Trader University, if you look at returns, Bitcoin and the stock e382af97-dad0-4901-a538-6063a63d886d are only loosely correlated. But because Bitcoin and the stock market (as measured by the SP 500) are cointegrated, one must instead look at price correlation between the price of Bitcoin and the price of the SP 500. Following Plan B's analysis, I conclude that Bitcoin and the stock market are indeed both cointegrated and correlated, with a very high R-squared of 95%.

This makes sense, since both the stock market and Bitcoin are increasingly driven by Fed money printing, quantitative easing, and the debasement of the US dollar. The more the Fed prints, the higher both the stock market and Bitcoin should go.

According to Plan B's regression equation, Bitcoin can be viewed as a levered version (416x) of the SP 500, with only 100% downside. Thus a very small allocation to Bitcoin should be able to give an investor equivalent exposure to a stock index fund.

The Fed's balance sheet, the US stock market, and Bitcoin should continue to rally as the Fed continues to sterilize the US current budget deficit, as well as massive future entitlement spending.

If we look at the 2 previous years correlation, here are the results:

Source: blockchaincenter.net

Let’s take BTC vs SP500, we see it is 0.36. If we take BTC vs Gold, it is fairly close to 0, 0.13, so the correlation is even smaller. So when you see numbers like this, numbers that are not >0.8 or <-0.8, you can say yes, Bitcoin SP500 are uncorrelated. But the story does not stop there.

During some periods, Bitcoin and the stock market have been correlated and extremely correlated sometimes, as the data shows, it is not often longer than 6 months or so. But yes, sometimes, when stocks fall, Bitcoin falls and when stocks rally, Bitcoin rallies.

Our take here is to remind you that yes Bitcoin and stocks could have been correlated during a precise period of time, during the liquidity crisis for example, where people have been dumping everything and trying to raise US dollars. But people were even dumping gold for example. The thing is that over longer periods of time, Bitcoin is not correlated.

Source: PlanB

So of course, we can be surprised when we see such kinds of graphs and tweets saying that BTC SP500 are actually correlated and cointegrated.

The analogy that is always used to illustrate cointegration is the drunk and his dog:

Source: eco.uc3m.es

So we do not know where the drunk is going to end up because he is just wandering all over the place and he is staggering around in the dark at midnight after drinking a lot but we do know that wherever he ends up, his dog is gonna be within one leash distance from him. This is a good way of visualizing what cointegration is in statistical terms.

“Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables. First, all of the series must be integrated of order d (see Order of integration). Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d, then X, Y, and Z are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends—either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends” - Wikipedia

So what PlanB pointed out and what we may have not realized is that when cointegration between two variables like the price of bitcoin and the price of the SP500 you need to look a t price level correlation rather than correlation of percentage returns.

When you look at the correlation of the price of bitcoin and how it is correlated with the price of the SP500, you find that they are extremely correlated and have an R-squared value of 95 percent which is extremely high and shows a very strong correlation. The fact that they are cointegrated implies that this is probably not a spurious correlation and means there is a real correlation here between these two variables.

Source: PlanB

Basically, what it means is that:

• When SP500 doubles, BTC goes up 416x

• When SP500 goes up 10%, BTC goes up 2.29x

Investing in Bitcoin in many ways, looks like a leverage version of the SP500. A nice thing about bitcoin is that you can allocate a very small amount because the worst thing that can happen is BTC going to 0 and you lose 100% of your investment, which is why you want to seize it accordingly. But if it goes up and if the SP500 doubles, the BTC will go up 416 times.

There is then a very good reason why BTC the SP500 are correlated: both are driven by the FED policy. As the FED was printing a lot of new dollars to try to stabilize the economy, it has impacted all the markets.

Conclusion

We know that the FED’s balance sheet is going to have to keep going up until something really major breaks. The FED will continue to monetize the debt by printing new money and buying treasuries for the most part.

Gold is not correlated with any of the other data sets including Bitcoin.

Cryptocurrencies amongst each other are positively correlated. Bitcoin and the SP 500 showed no correlation until the Corona Crisis hit both stocks and Bitcoin hard, resulting in a growing correlation.

Over time the correlation grew stronger. Bitcoin SP500 are cointegrated.

Everything is going up, so risk assets are going up. They will not go up in real terms but they will be going up in nominal terms, especially stocks. The purchasing power of the dollar will go down as stocks go up.

Statistics do not care about these elements and as a result this correlation will continue between the FED balance sheet and risky assets.

Disclaimer: This article is for educational purposes only and is not intended as investment advice. Qualified professionals should be consulted prior to making financial decisions.

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