Plan B is Now Plan A
TL;DR: In this piece, we will present our thoughts on an emerging pricing model that has had high predictive power in the past and that forecasts Bitcoin surpassing $60,000 in May of next year. After the original study was published, we set out to confirm the findings of the backtest and Bitcoin pricing model, and added several enhancements. We also looked past halving cycles for clues to how Bitcoin’s price could track if history repeats itself and the model proves to be valid in an out of sample test.
A few months ago, a pseudonymous individual known by the handle PlanB (@100trillionUSD) on Twitter and Medium published a report titled “Modeling Bitcoin’s Value with Scarcity.” The analysis detailed the connection between Bitcoin’s price and its Stock to Flow (SF) ratio (the inverse of its inflation rate). The report was notable for two things in our opinion: an attempt to put a future price on Bitcoin and the strength of the historical relationship between the price of bitcoin (market cap) and the SF ratio.
It’s not every day we see backtest of a crypto strategy (or valuation) with an R-Square of 95% and a P-Value of <looks closer> 2.3E-17, so we decided to replicate the study, but on a more granular level and with some slight adjustments. Our findings are broadly supportive of the original analysis: the SF ratio has had explanatory powers (R Square of 91%) and is of sufficient statistical significance (t Stat of 181.3). The model predicts a bitcoin price of $60,592 in May 2020 followed by $732,256 in the 2024 halving.
Enhancements to the Study
PlanB’s original study looked at monthly price and supply data and removed the first 1,018,750 tokens created from the SF ratio. The idea was that these coins were created in the first months of Bitcoin’s existence and likely belonged to Satoshi or were associated with private keys that have been lost. We did something similar and excluded 1,148,800 tokens based on this analysis. However, we also excluded those same token balances from the market cap calculation, not just the SF ratio, to come up with an adjusted market cap calculation. We think that removing these balances from both the SF ratio and the market cap maintains consistency in the treatment of Satoshi’s holdings. The regression of the adjusted market cap with adjusted SF ratio results in both an improved R Square (90.9% vs 89.9%) and a higher t-Stat (181.3 vs 171.7) compared with unadjusted metrics.
Also, as we mentioned we looked at daily market caps (prices) and Bitcoin outstanding starting in July 2010 through July 2019, not monthly. Given the increased granularity and volatility with the price of Bitcoin and its production rate (blocks created daily vary greatly), it’s not surprising our R Square is lower than the original study. The month-long measurement period would have a smoothing effect not present in the daily data. These are the log-log regression stats from Excel:
Graphically Interpreting Model Predictions
After confirming similar findings, we constructed a model price based on the output of the regression. We plotted actual price vs the 30 day trailing average of the model price (it’s extremely noisy on a daily basis) in the following graph along with halving dates. As a heads up, the 30-day average model price at the end of July was $4,950.
Premium/Discount to Model
A conclusion from the previous chart is the actual bitcoin price gyrates substantially around the model price. It appears to systematically underestimate halving events and then subsequently overestimate them. We call this a premium (or discount) to model price. Looking at the following chart we find that the maximum premium to model has declined over time indicating an increasing efficiency for investors to price bitcoin. If this relationship were to hold through the next halving cycle, we should expect the maximum premium to model to be well below the previous peak. A premium of 200%–300% seems like a reasonable assumption.
Comparing Premiums/Discounts Across Cycles
Bitcoin has already gone through two halving events and is about to go through its third. Each halving cycle lasts 210,000 blocks, which should be a little less than 4 years based on 10 minute block times. Using that information, we stacked the three halving cycles and compared their premiums/discounts to model on similar days in the cycles. The third cycle is through the end of July.
There are three interesting observations from the preceding chart. The first is that premiums to the model have peaked about a third of the way through a cycle. Given that we’re about to end one cycle and start another (the third cycle is still ongoing and will complete at the next halving), that implies the peak actual price with respect to the model price is still ahead of us. A third of the way through the next halving cycle would be around September 2021. The second observation is that the steep discount to model in a cycle has occurred about two-thirds of the way through a cycle. This has also marked the bottom of a drawdown in the price of Bitcoin. Our final observation is that a premium to model has occurred around the current period in the cycle in all three halving cycles. We don’t know if the current cycle will play out like the last two, but it’s an interesting observation.
First Out of Sample Test Coming Up
When Bitcoin undergoes its third halving next May, the model predicts a price of $60,595. This represents a market cap of $1,248B, up significantly from the $208B today. To put this in context, Bitcoin’s peak market cap from the December 2017 high was $327B, with a dominance (share of total crypto industry market cap) of about 46% according to Coinmarketcap.com. For reference, the crypto industry’s total market cap peaked at $828B in January 2018. Today, Bitcoin’s dominance is nearly 69% with a total industry market cap of $304B. While the model predicts $60,595 in May 2020, in the two previous halvings the actual price didn’t reach 100% of model price until well after the halving. Based on an estimated halving date of 5/17/20, that puts model parity sometime in the year 2021 based on a similar lag. In other words, we’re still a ways off from knowing if these predictions will hold.
Where Does $1T Come From?
$1T of flow into the asset is by no means trivial and should not be underestimated. This represents ~11% of the value of all the gold ever mined (190,040 metric tons at $1,500/oz or about $9T), an asset that has been viewed as a store of value for thousands of years. Where would this $1T inflow into Bitcoin come from? That is hard to know but if the current macroeconomic and geopolitical conditions continue, it could come from a number of sources: currencies that are devalued or lose purchasing power, gold investors that view Bitcoin as a higher beta version of gold, or from currently negative-yielding debt, which recently topped $15T worldwide. The following chart shows the magnitude of M1 (currency in circulation and overnight deposits), M2 (M1+deposits with an agreed maturity of up to two years and deposits redeemable at notice of up to three months), and negative-yielding debt around the world.
Does $1T of Fiat Really Need to Come In?
It may be the case that $1B in fiat need not come into the asset to move it to $60K. CoVenture previously published an analysis that showed an 11.37x multiplier of fiat inflows to bitcoin prices, albeit over a short term time range. Using a 10x or even 5x multiplier implies “only” $100B or $200B of fiat inflows to get the requisite $1T increase in market cap.
Does the Model Work for Other Digital Assets?
We used a log-log regression to see if the SF ratio had explanatory powers for Litecoin’s price. Litecoin has a similar programmatic supply issuance model as Bitcoin, except Litecoin has 1/4 the expected block creation time (2.5 minutes) and 4 times the max supply (84M LTC). Cutting edge stuff, we know. It also goes through reward halvings every 840,000 blocks instead of 210,000 blocks, which still amount to roughly every 4 years given the target block time. Unfortunately, the regression’s R Square was only 42.8%, not nearly high enough to describe the price movement of LTC.
We think there’s an explanation for this: Litecoin’s price correlation to Bitcoin. Bitcoin is by far the dominant asset in the crypto landscape by market cap. As such, other digital asset’s price movements, like Litecoin, are very often determined by the movement in Bitcoin. Our guess is that part of Litecoin’s price movement can be explained by its SF ratio, but also by other factors, like perhaps Bitcoin’s SF ratio. Here is BTC-LTC 90 day rolling correlation ratios:
Critiques to the Model
There have been several well thought out critiques to the original model, notably here and here. The first analysis seems to take issue with the distribution of residuals, to which our observation of the cyclicality of premium/discount to model might be of some aid. This is not a reason to reject the null, in our view. The second analysis seems to confirm PlanB’s original findings in an exhaustive manner, although with a title that at first glance seems to disconfirm it. We encourage readers to review both of these critiques and draw their own conclusions.
Combining the Model with Premium/Discount
As we showed previously, actual prices tend to overshoot and undershoot the model. If we combine 1) model predictions 2) investor tendency to overshoot and undershoot the model on actual price and 3) timing within the cycle, some interesting predictions emerge. Take this with a grain of salt and do not consider this investment advice. There are far too few observations (3 cycles in total, 1 of which is still being completed, 2 of which we think are relevant (the current cycle and previous) to describe the upcoming cycle) to draw strong conclusions. Still, we think it’s interesting as one of many possible paths forward, which is why we’ve devoted some analysis to it.
We break the upcoming cycle (post-May 2020 halving) into three phases: Parity to Model, Premium to Model, and finally Discount to Model. Using cycles two and three (current cycle) as guides plus the stock to flow model, the following chart potentially gives a guide to the path ahead. This is all with the caveat that the model is predictive of future prices (it may not) and the actual price premium/discount to model repeats in the upcoming cycle in a similar manner as the past two cycles (again, it may not). To repeat, there are several layers of assumptions here that very well may not prove to be accurate in the future.
Parity to Model
In the Parity to Model phase, this catch up phase where actual prices rises to and then equals the model price. That would mean rising from the current price of ~$10,150 to the predicted model. Other characteristics of this phase include increased personal confidence, willingness to talk to strangers, and interest in new hobbies, like woodworking and bird watching. In the second cycle, this happened on day 124. In the third cycle, this happened on day 398. Assuming 5/17/20 holds as the halving day, we could reach the model prices of $61,398 or $63,469 (the model price continually goes up as SF goes up (inflation rate goes down)) on the noted dates.
Premium to Model
In the Premium to Model phase, this is where investors have bid the actual price of Bitcoin above model price, way above model price. Characteristics of this phase include extreme confidence (you are the living embodiment of alpha after all) and interest in extreme hobbies, like mixed martial arts and falconry. You exclusively wear shirts from Cryptograffitti and are in dozens of Telegram groups with people who only wear masks, like Bane, Daft Punk, and Scorpion. You often wonder how to acquire a dormant volcano for an underground lair. In the upcoming fourth cycle, we assume this premium declines as the market gets more efficient in the future. But anyone that has been in crypto for any amount of time knows how irrational the market can be at times. We assume this maximum premium declines to 200%, which is honestly just a guess. We have found no equation to explain the sequence of 2,452%, 909%, and 517%. Based on the past two cycles, those peaks were reached on days 366 and 526, which would equate to the middle of 2021.
Discount to Model
The final step is the Discount to Model phase. Signs of this phase include renewed spiritual beliefs, bargaining with inanimate objects to “just make the price go back to where it was 2 weeks ago”, excessive line and triangle drawing on TradingView, and increased time with your family. Based on the past two cycles, the trough discount (maximum discount) to model has occurred on day 777 and 901. This equates to a peak to trough decline of 78% and 87%, something that has happened in each of the past 3 cycles.
Conclusion
Our reading of the critiques combined our own analysis informs our belief that PlanB’s original research was correct, but perhaps incomplete. Looking at declining premiums to model and rhyming cyclicality lead us to believe that some other term or function is perhaps missing or undiscovered. Or it may simply be the case that Bitcoin as an asset can never be valued, merely priced, in the words of Professor Aswath Damodaran. It does seem that pushing the model at extreme boundaries produces some unbelievable outcomes, but we’re unlikely to be around to see what happens in the year 2140. That fact we’re fairly certain of.
Nevertheless, we find PlanB’s original findings and subsequent model an interesting addition to the discerning crypto investor’s tool kit. We look forward to further critiques and updates to the model and believe that open discussions can push our understanding of this asset forward. We look forward to testing the model with an out sample test at the next Bitcoin halving in May 2020. Until then, stay on target.
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