Translator |
Liu Jiaolian
Title: A Scientific Approach to Estimating the Size of Bitcoin Bubbles
In this article, Giovanni Santostasi explores the micro-modeling of periodic bubbles based on the power-law growth model and the halving cycle of Bitcoin, which occurs every four years.
As we have discussed in previous articles, Bitcoin exhibits long-term power-law behavior. Due to the scale invariance property of power-law, we have a high level of confidence in predicting changes of one or two magnitudes, as Bitcoin has already exhibited nearly 9 magnitudes of scale invariance (if we include some known early dollar-to-Bitcoin transactions, where 1 dollar exchanged for 10,000 Bitcoins).
Another important characteristic of Bitcoin is its periodicity. A system with a strong known periodicity is predictable. Bitcoin shows precise periodicity over a four-year period, known as the Bitcoin cycle, which is related to the halving of its production. After the halving, there is usually a period of heightened bull market for about 1.5 years. During this period, there are significant deviations from the general power-law trend, corresponding to local maxima or peaks of the cycle. Then, the price rapidly declines for about a year, reaching the lowest point or level of the cycle. The price then slowly rises again until the next halving, and the cycle repeats. This unique sequence has occurred three times in Bitcoin’s 15-year history, and the patterns are very similar.
There is one bubble before each halving that is unrelated to any halving. It occurs within the first four years of Bitcoin’s existence, earlier than the first halving. This bubble exhibits irregular behavior (in terms of time, height, and other details), so we exclude it from the analysis.
By observing the price trend of Bitcoin, we can see that the height of each peak seems to decrease over time. One natural method to estimate this height is to observe the changes starting from the regular bottom of the trend.
The question of whether there is a specific pattern to this decrease in peak height has been discussed many times in the past. A recent notable attempt is by Peter Brandt. According to Brandt, by measuring the decline in percentage change from the bottom to the top of each cycle (including the pre-halving period), this cycle’s top is at 72k, meaning that this bull market has already peaked. He believes that the subsequent market will either consolidate or retrace to the mid-2021 low of 30k.
If we use a clock analogy, 12 o’clock is the top, 3 o’clock is the bottom, 6 o’clock is the transition from bear market to bull market, and 9 o’clock is the transition to a full bull market. We have just passed 6 o’clock and have not entered a full bull market yet, so it is still a long way from the typical time of a top in the cycle.
Brandt’s conclusion is based on the following observations. If we measure the changes from bottom to top of each cycle (including the pre-halving period), we can derive the following table:
[table]
If we represent the changes as a percentage from the bottom, it seems that the height of each cycle decreases by a factor of 5. If we exclude the pre-halving period, we only have 3 data points; if we consider the ratios, we actually only have 2 data points. These data points are not sufficient for any significant statistical analysis. However, considering that we only have these data points, it is an acceptable method to make some informed estimations about the size of the next potential Bitcoin bubble.
Thus, if we look at the table, we can conclude that this cycle’s Bitcoin bubble will only be about 4.5 times higher than the bottom of the historical cycle at $16,500, which means the top should be around $70,000. Since we have already reached this value, the conclusion is that we have already reached the peak and will only see a decline from now on.
In addition to the observed periodicity issue, there is another problem. This analysis does not take into account Bitcoin’s long-term power-law trajectory. Between the bottom and the top, there is approximately a 3-year period during which Bitcoin fluctuates significantly along the power-law trajectory, followed by a typical bull market of about 1 year.
We can use the Desmos calculator application to understand this. The formula already entered in the application tells us the estimated power-law price of a day after the Genesis Block. The bottom of the first cycle should occur around 3 years after the Genesis Block, so the trend value is approximately $0.46. The actual value of Bitcoin is around $0.3. Three years after the bottom, we have the first real bubble with a value of $1,242. The ratio between the top and the bottom should be close to 4,000 times, rather than the reported 572 times. This breaks the claimed rule of the peak decreasing by a factor of 5 from the bottom to the top.
This is due to measuring the bottoms and tops related to the periodic events in the Bitcoin cycle without considering the pre-halving bubble as a real bubble. This demonstrates the arbitrariness of this method of estimating peak size by selecting bottoms and tops of cycles.
Furthermore, the trend value at the time of the peak is close to $100. Considering the general power-law trend, it seems more natural to measure the top by the deviation from the general power-law trend. This can be achieved by calculating the percentage difference between the price and the power-law trend.
The following graph shows the relationship between percentage difference and time:
[graph]
We can observe that the bottom is very regular and seems to occur around -60% of the overall trend. The top appears to exhibit the typical decay we observe in a regular Bitcoin price chart.
Let’s measure these deviations to see if we can observe any patterns.
[graph]
Instead of calculating ratios, let’s see if we can plot these data points and find a pattern. The rapid decay suggests an exponential trend, which should appear as a straight line in a semi-log plot. We will fit the data to the number of peaks instead of a time function.
In fact, we see a good fit with an R2 value of 0.96. The Pearson coefficient needs to be at least 0.05 for the data to have statistical significance, but considering we only have 3 data points, the relatively small value of 0.12 is still promising even at this point.
After all, these are the only data points we have. Therefore, we can extrapolate the decay to the next peak, which deviates from the trend by about 78%, essentially close to doubling.
Let’s go back to the Desmos application and calculate the trend value of the next peak, which should be around the end of 2025.
By the way, here is a good way to find the number of days between two dates:
[code]
The uncertainty of the peak can be up to 2-3 months, but this should provide us with a rough estimate.
Therefore, there are approximately 6,201 days between January 3, 2009 (Genesis Block) and the projected peak of the fourth cycle. Let’s input this into the Desmos application:
[graph]
The application shows a trend value of approximately $118,066.
Thus, the estimated maximum value is:
Peak = $118,000 + 78/100 * $118,000 = $210,000.
Therefore, if everything else remains the same, this seems to be a scientifically valid method of estimating the peak of the cycle.
We also added an estimate for the bottom, which is usually around 50% of the historical trend or slightly lower. The power-law theory predicts the bottom more accurately than the peak.
The trend value is close to $165,000, so the bottom should be around half of that value. Rounded down to the nearest integer, we get:
Bottom of the next cycle = $165,000 * 0.5 = $83,000.
These are rough estimates but consistent with our full model, which attempts to include the general power-law trend, 50-60% hard bottoms, 4-year sinusoidal oscillations of the cycle, and exponential decay similar to the calculated results mentioned above.
Conclusion:
Of course, these are rough estimates, but they are based on our understanding of Bitcoin’s scaling properties and its very reliable (so far) periodicity. These predictions should be treated with caution but hopefully are useful for Bitcoin investors.
Disclaimer: This article does not constitute any investment advice. Cryptocurrencies are highly risky assets with the risk of going to zero at any time. Please participate with caution and take responsibility for yourself.
