The phenomenon of financial bubbles is hotly debated among industry operators, and there are several academic papers on the subject, starting with Professor Didier Sornette’s 2014 study of financial bubbles.
In fact, the paper defines a “bubble” as a period of unsustainable growth with prices rising faster and faster, i.e., growing more than exponentially. Obviously, bubbles by definition are destined to burst and bring prices back to their starting value or worse.
In the recent past, Bitcoin (BTC) has experienced periods of more than exponential growth, followed by very sharp declines, called “crypto winter,” a period when no one talked about Bitcoin and other assets anymore, meaning there was a freeze around the sector, and prices collapsed. Previous declines following the Bitcoin price bubble were -91%, -82%, -81%, and -75% in the last crypto winter.
So far, the price trend of Bitcoin has followed a distinct cycle marked by halving every 210,000 blocks, equal to about four years, which has rhythmically determined periods of decline, recovery and then exponential growth.
In 2011, together with Professor Ruggero Bertelli, Diaman Partners published a paper on a deterministic statistical indicator called the Diaman Ratio. This indicator creates a linear regression between prices on a logarithmic scale (as shown above for the price of Bitcoin) and time.
Without going into detail about this indicator, which is actually very useful for those who use quantitative tools to make investment decisions, the purpose of this first part of the analysis is to verify how much and how Bitcoin has entered a bubble in the past.
To do this, if DR < 0, it means that the price is falling; if DR < 1, it means that growth is sustainable; if DR = 1, it means that growth is exponential; if DR > 1, it means that growth is more than exponential, which corresponds to Sornette’s definition of bubbles.
Diaman Partners took the daily historical series of Bitcoin, calculated the one-year DR, and checked when it was greater than 1.
The graph clearly shows that in previous cycles there were periods of more than exponential growth, while in the recent cycle, apart from an attempt when ETFs were approved in the United States and the price of Bitcoin exceeded the 2021 high before the 2024 halving, a phenomenon that had never happened before, the Diaman Ratio was never much higher than 0.
Does this mean that Bitcoin cycles will no longer follow the four-year rule, with crypto winter starting toward the end of the second year of the cycle? It is too early to say, but most likely the growth structure of Bitcoin has changed.
To test this hypothesis, we took the volatility of the Bitcoin price with a four-year observation window, equal to the halving cycle, and slid this volatility calculation window over time to see if it remains constant or decreases over time.
The graph shows a sharp decline in volatility, which in the early years of development was over 140% on an annual basis, then gradually declined to a current value of about 50% or less. While lower volatility also means lower expected returns, it means greater price stability for the future and fewer surprises.
Related: Estimating Bitcoin’s support levels for the next cycle bottom
In fact, if we take the rolling annual return chart, i.e., take the performance of one year in 2011 and then calculate the return for one year on a day-by-day basis, it is clear that in the past there were returns that have decreased over time and in the last three years have in fact remained flat, confirming that the theory of the Bitcoin cycle, with fantastic years followed by a catastrophic year, has been somewhat broken.
The chart above shows that average annual returns have gradually declined, with no peaks at all in the last cycle, confirming the hypothesis that Bitcoin's risk-return structure has changed. Yet the price of Bitcoin has risen from $15,000 in December 2022 to $126,000 at recent highs, so a very attractive return has still been achieved in this cycle, but with less fanfare than in previous cycles.
The graph of average annual returns over a four-year observation period shows a clear trend toward declining Bitcoin returns over time, which is understandable when considering the total market cap of Bitcoin, as it is one thing to double an asset worth $20 billion, but quite another to double an asset worth $2 trillion.
On the other hand, assuming that we can consider the rise of the fourth halving cycle to be over, which no one can deny or affirm with certainty, the total wealth generated so far is greater than in other cycles, confirming, if confirmation were needed, that Bitcoin, understood both as a network and as an asset in itself, has generated more wealth than any other type of investment in just 15 years of history.
Drawing conclusions from this analysis, from a statistical point of view:
On four occasions, Bitcoin can be considered to be in a “bubble” phase, i.e., with more than exponential returns, but unlike traditional bubbles that then burst in a few months, Bitcoin has shown resilience in its growth, which on average has a Diaman Ratio of less than 1 with high but not exponential growth. In fact, a power law can describe the growth of Bitcoin's price very well.
It can also be clearly seen that these “bubble” phenomena have decreased in intensity and duration over time, so much so that in the last cycle that began in 2024, there has been (at least for now) no more than exponential price growth.
Both returns and volatility are decreasing, suggesting that reaching values above one million (if ever) will probably take 15 years, and therefore, many predictions of Bitcoin reaching $13 million in 2040 are statistically very unlikely.
The approval of ETFs in the United States, with BlackRock's IBIT spot Bitcoin ETF reaching $100 billion in assets under management in less than three years, becoming by far the fastest-growing financial product in history, has broken the Bitcoin cycle that predicted periods of growth, hypergrowth and crypto winter, with new highs being reached after the next halving.
Greater stability in returns and lower volatility suggest that the crypto winter will not be “very cold” with losses exceeding 50%-60% as in previous cycles, but could alternate periods of decline with new highs without the exponential jumps seen in the past.
This article is for general information purposes and is not intended to be and should not be taken as legal or investment advice. The views, thoughts, and opinions expressed here are the author’s alone and do not necessarily reflect or represent the views and opinions of Cointelegraph.