February 5, 2023

Plan B becomes Plan A

In this article, Greg Cipolaro, CEO and editor of Digital Asset Research, shares his thoughts on the new model. high pricingprognostic ability on historical data, according to which in May next year the price of bitcoin will exceed $ 60,000. After the publication of the original PlanB study, Chipolaro and colleagues decided to independently verify the testing findings on historical data and simulate Bitcoin prices, making a few changes to the PlanB model along the way. They also analyzed previous halving cycles in order to understand what can be expected from the price of bitcoin if the story repeats itself and the model confirms its viability in intra-sample and non-sample testing.

A few months ago, a man known inTwitter and a medium under the pseudonym PlanB (@ 100trillionUSD), published a report entitled “Modeling the Bitcoin Price Based on Its Shortage.” In the described study, the relationship between the price of bitcoin and its ratio of stocks to the increase in the number of assets (Stock-to-Flow, or S2F) was analyzed in detail. The PlanB report, in our opinion, was notable for two points: an attempt to determine the future price of bitcoin and the strength of the relationship between the price (market capitalization) of bitcoin and the S2F coefficient on historical data.

Not every day you can see testing onretrospective cryptostrategy data (or estimates) with a 95% R-squared and a p-value of 2.3E-17. Therefore, we decided to replicate this study, but with more detail and a few minor adjustments. Our findings, in general, confirm the results of the initial analysis: the S2F coefficient has an explanatory power (R-square 91%) and sufficient statistical significance (t-statistic 181.3). The model predicts a Bitcoin price of $ 60,592 in May 2020 and $ 732,256 for halving in 2024.

Study Changes

In an original study, PlanB studiesmonthly data on the price and volume of the offer and excludes the first 1.018.750 issued tokens from the S2F coefficient. According to the author, these coins were created in the early months of Bitcoin and probably belonged to Satoshi or were associated with lost secret keys. We also did something similar and excluded 1,148,800 tokens from the calculations, based on the results of this analysis (English). However, we excluded these tokens from the calculation not only of the S2F coefficient, but also of market capitalization in order to obtain adjusted capitalization. We consider this approach more consistent. Regression of adjusted market capitalization with the adjusted coefficient S2F results in both a better R-squared (90.9% vs 89.9%) and a higher t-statistic (181.3 vs 171.7) compared to unadjusted indicators .

In addition, as I mentioned, we useddaily (instead of monthly) indicators of market capitalization (prices) and the number of bitcoins in circulation for the period from July 2010 to July 2019. Given the increased granularity and volatility of the price of bitcoin and its rate of release (the blocks created vary greatly from day to day), it is not surprising that our R-square turned out lower than in the original study. The monthly measurement period has a smoothing effect, which is absent when using daily data. These are statistics of double logarithmic regression, a screenshot from Excel:

: Digital Asset Research

Graphical interpretation of simulation results

Confirming the findings of the original study, webuilt a pricing model based on the results of the regression. In the chart below, we compared the actual price and the 30-day average of the simulated price (there is too much “noise” on a simple daily chart), and indicated the dates of halving. Immediately, we note that the 30-day average price of the model at the end of July was $ 4,950.

Black - model price, blue - actual price, vertical dashed lines - halvings. (: Digital Asset Research)

Premium / discount to the model

From the previous graph we can conclude thatThe actual price of bitcoin to a large extent fluctuates around the modeled one. It looks as if the market systematically underestimates the importance of halving, and then, after the fact, overestimates them. We call this a premium (or discount) to the price of the model. The following chart shows that the maximum premium to the price of the model decreases over time, which indicates an increase in the efficiency of investors' assessment of the value of Bitcoin. If such dynamics spread to the next halving cycle, then we should expect that the maximum premium to the model price this time will be much lower than the previous peak value. A reasonable assumption seems to be a premium of 200-300%.

Blue chart - actual price; black graphthe top is the price of the model; black bottom chart - premium / discount to the model; vertical dashed lines - halving; left scale: BTC price; right scale -% premium / discount. (: Digital Asset Research)

Comparison of premiums / discounts of different cycles

Bitcoin has already passed through two halving and nowthe date of the third is approaching. The duration of each halving cycle is 210,000 blocks, or slightly less than 4 years, based on a 10-minute interval between blocks. Using this information, we superimposed three halving cycles on top of each other and compared their premium / discount to the model by the days of the cycles. The third cycle is calculated until the end of July.

Dark blue - the first cycle; blue - the second cycle; blue - the third cycle; X axis - days of the cycle; Y axis -% premium / discount. (: Digital Asset Research)

From this graph you can make three interestingobservations. First, premiums to the model peaked around the third of the cycle. Given that we are at the end of one cycle and about to move on to the next (the next cycle will complete the third cycle), this means that the peak of the actual price premium relative to the modeled one is still ahead. The first third of the next halving cycle will take place approximately in September 2021. The second observation is that the maximum discount to the model was achieved after passing through two-thirds of each cycle. This also coincided with the formation of a price “bottom” for bitcoin. And our last observation is that approximately in the current period, inside each of the three halving cycles, Bitcoin was trading at a premium in relation to the price of the model. We cannot know in advance whether the current cycle will continue to develop according to the scenario of the two previous ones, but this is an interesting observation.

The first non-sampling test on the way

At the time of the next halving expected in Maynext year, the Bitcoin price predicted under this model is $ 60,595. This corresponds to a market capitalization of $ 1,248 billion, which is significantly higher than today's 208 billion. To better describe the context, at the highs of December 2017, the market capitalization of Bitcoin, according to Coinmarketcap.com, reached $ 327 billion, with a dominance index (share in the total capitalization of the crypto industry) of about 46%. For reference: the maximum value of the total cryptocurrency market capitalization was recorded in January 2018 and amounted to $ 828 billion. Today, the Bitcoin dominance index is almost 69% with a total cryptocurrency market capitalization of $ 304 billion. While the BTC price predicted under this model in May 2020 is $ 60,595, it should be noted that in the two previous halving cycles, the actual price reached 100% of the modeled one only some time after the halving. Based on the estimated halving date of 05.17.2020 and with a delay similar to the previous halving cycles, the actual price of BTC will have to reach parity with the one simulated somewhere in 2021. That is, we will not know soon whether these forecasts will materialize.

Where can a trillion dollars come from?

The influx of a trillion dollars in assets is a phenomenonit is by no means trivial and cannot be underestimated in any way. This amount represents ~ 11% of the value of all gold ever mined (190,040 metric tons at a price of $ 1,500 per ounce, which gives about $ 9 trillion), an asset that has been used as a means of preserving the value of thousands of years. Where does this trillion dollars come from in Bitcoin? It’s hard to know for sure, but if the current macroeconomic and geopolitical conditions continue, there may be several sources: currency depreciating or losing their purchasing power, gold investors considering Bitcoin as its digital counterpart, or negative yield on government bonds, whose recent global volume exceeded 15 trillion dollars. The table below shows the size of the money supply M1 (currency in circulation and short-term deposits), M2 (M1 + deposits with an agreed maturity of up to two years and deposits paid with advance notice of up to three months) and the total global volume of debt securities with negative profitability.

and: Digital Asset Research, Board of Governors of the Federal Reserve, European Central Bank, Bloomberg

Is $ 1 trillion worth of fiat money really needed?

It may happen that the inflow into the asset is 1 billiondollars and is not needed to ensure that its price rises to $ 60 thousand. CoVenture published an analysis (English), which showed that in order to get a real (albeit short-term) impact on the actual price of bitcoin, a factor of 11.37 should be applied to the amount of fiat inflow. Using a 10-fold or even 5-fold multiplier shows that to get the required growth in market capitalization of up to $ 1 trillion, an inflow of “only” $ 100 or 200 billion is enough.

Does this model work for other digital assets?

We used a double logarithmicregression to check if S2F has an explanatory power relative to the LTC price. Litecoin has the same emission model prescribed in the program code as Bitcoin, with the exception that the interval between Litecoin blocks is 4 times less (2.5 minutes) than Bitcoin, and the emission volume, on the contrary, is limited to 4 times number (84 million LTC). Halving in it occurs every 840,000 blocks instead of 210,000, which is the same for about 4 years, given the 4 times smaller interval between blocks. Unfortunately, the R-square of the regression was only 42.8% - this is clearly not enough to describe the LTC price movements.

(: Digital Asset Research)

We think there is an explanation for this: Lightcoin to Bitcoin price correlation. Bitcoin, of course, is the dominant cryptocurrency market capitalization asset. This means that price movements of other digital assets, such as Litecoin, are very often determined by fluctuations in the price of bitcoin. We suggest that the price movements of the lightcoin may be partly explained by its S2F coefficient, however, other factors, like, probably, the bitcoin S2F coefficient, are also giving them decisive attention. This is how the 90-day average correlation coefficient between BTC and LTC looks like:

: Digital Asset Research

Criticism of the model

The original PlanB model was expressedsome well-thought-out criticisms, especially here (English) and here (English, we plan to publish the translation in the near future). The author of the first analysis disagrees with the distribution of residuals, which can be somewhat leveled out by our observation about the cyclical nature of the premium / discount of the actual price to the model. We do not think that this is a sufficient reason to reject the null hypothesis. The second analysis, as it were, fully confirms the conclusions reached by PlanB, albeit with a heading that, at first glance, implies disagreement with them. Perhaps the best that the reader could do is to read both articles and draw independent conclusions.

Combining model with premium / discount

As we showed earlier, the actual price, likethe rule either surpasses or falls short of simulated. If we combine 1) the forecasts within our model, 2) the tendency of investors to overestimate and underestimate the asset in relation to the price of the model, and 3) timing within the cycles, this opens up new opportunities for interesting forecasts. Of course, this should be taken with a healthy share of skepticism and not be regarded as an investment recommendation. We have too little data (only 3 cycles, 1 of which has not yet been completed, only 2 of which [current and previous], in our opinion, are relevant for the description of the upcoming cycle) to make convincing conclusions based on them. Nevertheless, we find such an experiment worthy of attention as one of the many possible ways to further develop the idea.

We shared the upcoming cycle (after May Halving2020) into three phases: parity with the model, premium to the model and discount to the model. Based on the second and third (current) cycles and using the model of the ratio of stocks to growth, we developed a potential scenario for the movement of the BTC price, presented in the picture below. All this with the caveat that this is only a predictive model of the future price (the forecast may not be justified) and the distribution of premium / discount to the model in the upcoming cycle is repeated here in accordance with the two previous cycles (again, in reality, everything may turn out differently). I repeat: several levels of assumptions are used here, which in the future may very well not be justified.

: Digital Asset Research

Parity with the model

The parity phase with the model is the stage at whichthe actual price rises to the simulated one and remains equal to it. This would mean an increase from the current ~ $ 10,150 to the level predicted by the model. Other features of this phase include increased self-confidence, a willingness to communicate with strangers, and interest in new activities (such as woodwork or bird watching). In the second cycle, this phase began on the 124th day of the cycle, in the third cycle it happened on the 398th day. If we assume that the date of the next halving, 05.17.2020, does not change, then by this day we should reach the price of the model in the range of $ 61398-63469 (the price of the model is constantly increasing with an increase in the S2F coefficient and, as a result, a decrease in the inflation rate).

Model Award

In the phase of the premium to the model, the actual price of bitcoinrises above the simulated, much higher than the simulated. This phase is characterized by an extreme degree of self-confidence (you are still a living embodiment of success) and the interest in extreme hobbies that woke up in you, such as mixed martial arts or falconry. You only wear shirts from Cryptograffitti and are in a dozen groups on Telegram, all of whose avatars are exclusively with masks - Bane, Daft Punk or Scorpio. You begin to wonder more often about how to get a sleeping volcano for an underground lair. In the forthcoming fourth cycle, we expect a decrease in this premium, as the market becomes more and more efficient. But everyone who has been following the cryptosphere for some time knows how irrational the market can sometimes be. We assume that the maximum premium will drop to 200%, although on our part this is nothing more than a hunch. We did not derive any equation that would explain the sequence of 2452%, 909%, 517%. In the previous two cycles, these peaks were reached on the 366th and 526th days, which for the next cycle will approximately correspond to the middle of 2021.

Discount to the model

The last stage is the phase of discount to the model. Common signs of this phase include a return to religious beliefs, conversations with inanimate objects with prayers that “so that the price simply returns to the level of two weeks ago,” drawing countless lines and triangles in TradingView and increasing the time spent with the family. In the previous two cycles, the maximum discount in relation to the price of the model was reached on the 777th and 901th days. This corresponds to a decrease of 78% and 87% of the maximum values, and something similar happened in each of the last 3 cycles.


After reviewing the critical comments addressedPlanB research and by doing our own analysis, we came to the conclusion that the initial PlanB research was correct, but possibly incomplete. Shrinking premiums to the price of the model and rhyming cycling lead us to believe that some other term or function may be missing or not yet disclosed. Or, perhaps, as Professor Asvat Damodaran says, the value of Bitcoin as an asset can never be determined, at best it can be somehow valued. It seems that the extension of the model in time can give incredible results, but you and I are unlikely to see what will happen in 2140. We are quite sure of this.

However, we consider the conclusions of PlanB andOwn model is an interesting addition to the tools of the perspicacious crypto investor. We hope to see further criticism and updates to this model, as we believe that open discussions contribute to our understanding of this asset. And we look forward to testing our model in in-sample and out-of-sample testing during the next halving in May 2020. Until then, focus on the target.