The phenomenon of financial bubbles has always been a hot topic among industry insiders, and there have been multiple academic papers discussing it, the earliest of which can be traced back to Professor Didier Sornette's research on financial bubbles in 2014.
In fact, the paper defines a "bubble" as an unsustainable growth phase where the price increases at an accelerating rate, meaning the growth exceeds exponential levels. Clearly, by definition, a bubble is destined to burst, causing prices to fall back to their starting values or even lower.
In recent years, Bitcoin has experienced multiple periods of growth that surpassed exponential levels, followed by extremely sharp declines, referred to as the "crypto winter," where the market for Bitcoin and other assets fell silent, and the industry seemed frozen, with prices plummeting. The previous declines in Bitcoin's price after bubble phases were -91%, -82%, -81%, and -75% during the last crypto winter.
So far, Bitcoin's price trend has followed a clear cycle of halving every 210,000 blocks, approximately every four years, with this rhythmic pattern determining the cycle of decline, recovery, and then exponential growth.
In 2011, Diaman Partners and Professor Ruggero Bertelli published a paper on a deterministic statistical indicator—the Diaman Ratio. This indicator performs a linear regression of price against time on a logarithmic scale (as shown in the figure above).
Without delving into the indicator itself, it is very useful for those using quantitative tools for investment decisions. The first part of this analysis aims to verify whether and how Bitcoin has entered a bubble phase in the past.
Specifically, 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 indicates that growth exceeds exponential levels, which aligns with Sornette's definition of a bubble.
Diaman Partners collected daily historical data series for Bitcoin, calculated the one-year DR, and checked when it was greater than 1.
The chart clearly shows that there have been phases of growth exceeding exponential levels in previous cycles, while in the most recent cycle, apart from the unprecedented phenomenon of the U.S. approving ETFs and Bitcoin breaking the 2021 high before the 2024 halving, the Diaman Ratio has rarely been significantly above 0.
Does this mean that Bitcoin cycles will no longer follow the four-year pattern, and that crypto winters will not reappear at the end of the second year? It is still too early to draw conclusions, but it is likely that the growth structure of Bitcoin has changed.
To verify this hypothesis, we calculated Bitcoin's volatility using a four-year observation window (equivalent to the halving cycle) and slid this window over time to observe whether volatility remains constant or gradually decreases.
The chart shows a sharp decline in volatility, with annual volatility exceeding 140% in the early development stages, then gradually decreasing to around 50% or lower today. While lower volatility also means lower expected returns, it indicates that future prices may be more stable, with fewer surprises.
In fact, if we look at the rolling annual return chart, which takes one year's performance from 2011 and then calculates the annual return day by day, it is clear that past returns have decreased over time, with the last three years remaining relatively stable, confirming the theory of Bitcoin cycles, where years of prosperity are followed by years of disaster, has been somewhat broken.
The above figure shows that the average annual return has gradually declined, with no peaks in the most recent cycle, confirming that the risk-return structure of Bitcoin has changed. However, Bitcoin's price rose from $15,000 in December 2022 to a recent high of $126,000, achieving very attractive returns in this cycle, but without the fanfare seen in previous cycles.
The average annual return chart for the four-year observation period shows a clear trend of declining returns over time, which is understandable when considering Bitcoin's total market capitalization, as doubling an asset worth $20 billion is one thing, while doubling an asset worth $2 trillion is another.
On the other hand, assuming we can consider the rise of the fourth halving cycle to be over, although no one can confirm or deny this, the total wealth generated so far has been greater than in other cycles, confirming that Bitcoin, both as a network and as an asset itself, has generated more wealth in its short 15-year history than any other type of investment.
From a statistical perspective, we conclude:
In four instances, Bitcoin can be considered to be in a "bubble" phase, meaning returns exceeded exponential levels, but unlike traditional bubbles that burst within months, Bitcoin has shown resilience in its growth, with an average Diaman Ratio of less than 1, indicating high but not exponential growth. In fact, power laws can describe Bitcoin's price growth quite well.
It is also clear that the intensity and duration of these "bubble" phenomena have decreased over time, to the extent that in the last cycle starting in 2024 (at least so far), there has been no price growth exceeding exponential levels.
Both returns and volatility are declining, indicating that reaching a value exceeding one million (if at all) may take 15 years, making many predictions of Bitcoin reaching $13 million by 2040 statistically very unlikely.
The U.S. approval of ETFs, with BlackRock's IBIT spot Bitcoin ETF reaching $100 billion in assets under management in less than three years, becoming the fastest-growing financial product in history, has broken the cycle of growth, super-growth, and crypto winter predictions for Bitcoin cycles, with new highs expected to be reached after the next halving.
The greater stability of returns and lower volatility suggest that the crypto winter may not be "very cold" like in previous cycles, with losses exceeding 50%-60%, but may alternate between declines and new highs, without the exponential jumps seen in the past.
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Original: “Bitcoin (BTC) ‘Four-Year Cycle’ is Broken—And This Time, Data Proves It”
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