An Old Statistical Trick Might Help Better Explain the Apparent Correlation Between Bitcoin and Gold

The relationship between Bitcoin and Gold is one of the dynamics that seems to constantly capture the minds of financial analysts. Recently, there have been a series of new articles claiming an increasing “correlation” between Bitcoin and Gold and the phenomenon seems to be constantly debated in financial media outlets like CNBC or Bloomberg.

From a mathematical standpoint, the recent apparent correlations between Bitcoin and Gold might be explained by one of the most intriguing dynamics in statistics: the confounding bias.

There is nothing like a nascent asset class to show the mysteries of statistics in action. In the case of crypto, every week we discover new speculations about factors that could be correlated with the price of a specific crypto-asset sometimes “sidestepping” the principles of statistics.

Among those hopeful correlations, the possible relationships between Bitcoin and Gold as two prominent stores of value seems to be one of the favorite ideas of the finance community to try to explain the behavior of former.

After all, what better ways to explain an unknown asset like Bitcoin than by correlating with one of the oldest and best understood asset types in history.

The Bitcoin and Gold Correlation

In recent days, there have been a series of news in financial media outlets claiming an increasing correlation between Bitcoin and Gold. Bloomberg recently reported a notable 0.827 correlation between the two stores of values in the last three months. Financial analysis website Seeking Alpha, claimed that “The statistically reality is that gold and bitcoin are usually positively correlated and becoming more so by the day.” Forbes also drums the positive correlation between Bitcoin and Gold. Of course, some crypto analysts are already using Gold to explain the recent decline in prices in Bitcoin.

The idea of finding correlations between two asset classes is only interesting if you can use one to explain the behavior of the other. As two of the most prominent stores of value in the market, there is going to be times in which Bitcoin and Gold appear positively correlated but you can make similar arguments for almost any other combinatorial pair of assets in the market.

The “apparent correlation” between Bitcoin and Gold has been typically seen an a sign of maturity of the crypto markets but the true might be simpler than that.

The hope to find strong predictors for the price of Bitcoin might be causing analysts to ignore one of the most interesting phenomenon’s in causality theory.

Confounding Bias

One of the oldest dynamics in statistics and one of the most ignored ones, confounding bias describes the scenario in which a hidden variable(or many) influences other two variables that have been selected for the treatment of an experiment.

The hidden variable is often referred as the confounder and is represented by Z in the following diagram.

The term confounding originally meant “mixing” in English. In the previous diagram, the apparent causal effect is X →Y is “mixed” with a spurious correlation between X and Y induced by the fork X ←Z →Y. In other words, the apparent correlation between X and Y is only relevant if Z exists.

Despite being a well-known dynamic in causal relationships, the confounding bias is often ignored when discovering correlations between different factors. One of my favorite examples of confounding bias was described by statistical legend Judea Pearl in his famous masterpiece “The Book of Why”.

In 1998, a study in the New England Journal of Medicine revealed an association between regular walking and reduced death rates among retired men. The researchers used data from the Honolulu Heart Program, which has followed the health of 8,000 men of Japanese ancestry since 1965.

The researchers, led by Robert Abbott, a biostatistician at the University of Virginia, wanted to know whether the men who exercised more lived longer. They chose a sample of 707 men from the larger group of 8,000, all of whom were physically healthy enough to walk.

Abbott’s team found that the death rate over a twelve-year period was two times higher among men who walked less than a mile a day (I’ll call them “casual walkers”) than among men who walked more than two miles a day (“intense walkers”). To be precise, 43 percent of the casual walkers had died, while only 21.5 percent of the intense walkers had died.

Although detailed, the experiment is subject to confounding bias given that it ignored some external factors that might be dictating the correlation between the length of the daily walk and the health of the patient. One obvious confounding factor is age: younger men might be more willing to do a vigorous workout and also would be less likely to die.

If confounding bias is often ignored in sophisticated statistical studies, what do you think happens in basic financial articles trying to explain the correlation between Bitcoin and Gold? 😉

A Different Explanation of the Bitcoin and Gold

The consideration of confounding bias shades a different perspective between the possible correlation between Bitcoin and Gold. Instead of assuming that the apparent relationship is a sign of the maturity of Bitcoin, maybe we should think about the different confounders that are present in the current market conditions.

The analysis for a well-known asset like Gold is simpler than more a nascent an unstable asset like Bitcoin.

History tells us that the price of Gold is influenced by a plethora of factors such as a weakening dollar, geo-political tensions, increasing volatility or changes in the interest rates.

Nobody really understands the quantitive factors that move the price of Bitcoin but there are factors like regulatory news, geo-political tensions or changes in the crypto-ecosystem that have proven to be highly influential.

If there are market conditions that cause those factors to move in the same direction, then we will see an apparent, and yet misleading, correlation between Bitcoin and Gold.

The current economic climate and the rapid development of the crypto market is creating a statistically ideal environment for confounding biases between Bitcoin and Gold.

Pick your favorite: the escalating economic tensions between the United States and China, the sudden collapse of the Argentinian macro-economic indicators, the increasing volatility of the Chinese Yuan, the fears of a recession facing some European economies, etc.

All those elements could be seen as confounders of a positive correlation between Bitcoin and Gold.

However, it would only take those factors to dissipate of other non-confounding factors to move in the opposite direction for that correlation to disappear.

Correlating the behavior of different asset classes is a brutally difficult exercise that should be subjected to the most rigorous statistical models. What seems to be a strong correlation today, could change drastically under different market conditions.

This is even more relevant in the case of a nascent asset class like crypto. Confounding bias teaches us that sometimes what you don’t see is as important as what you see.