Over the years, on-chain analysis has matured a lot. Institutional-level data providers have come to market, while a lot of very valuable data is also still available for free and utilized by the many analysts in the space. However, it is rare for fundamentally new ideas to emerge. August 24th, 2023, was one of those days on which the field of on-chain analysis was upgraded by a fascinating new concept. David Puell of investment management firm Ark Invest and James Check of data-provider Glassnode published a set of reports (1, 2) called ‘Cointime Economics’, in which they introduce a new approach that sheds new light on a broad set of existing on-chain metrics.

In this article, I will first attempt to reframe the rationale behind Cointime Economics in my own terms, which may hopefully help others to grok the rather abstract concepts in the framework. Then, I will reflect on how the newly introduced metrics may not only be used to estimate ‘fair price’ and ‘floor price’ levels, but also quantify to what extent current or historic market values are (ab)normal.

Why did we need a new approach in the first place?

A lot of the existing on-chain analysis techniques use the bitcoin supply. Since a part of the total bitcoin consists of coins that are (likely) lost (e.g., Satoshi’s coins, coins in lost wallets or provably burned coins), metrics that utilize the bitcoin supply in an attempt to say something useful on current or historic market prices do not optimally reflect those market conditions.

An example of this is the Realized Price (Figure 1; orange) that is derived from the Realized Cap, which was introduced by Nic Carter and Antoine Le Calvez in 2018. The realized price is the dollar value of all bitcoin at the price at which they last moved (= Realized Cap), divided by the total bitcoin supply. The result is a dollar-denominated value that is often described as the market’s average cost basis. Soon after in 2018, Murad Mahmudov and David Puell iterated upon this with the Market Value to Realized Value (MVRV) ratio, by dividing Bitcoin’s Market Cap by the Realized Cap (Figure 2; red). The MVRV ratio therefore reflects the extent in which historic market prices are overextended or undercooled in comparison to the estimated average cost basis of the market, and thus aimed to express to what extent the average market participant is in profit or at a loss.

Since many of the bitcoin that were lost in the early days of the network last moved at very low prices, the calculated realized price is much lower than it would have been if lost coins were excluded. The realized value metric aims to describe the average cost basis of the available bitcoin — since those are the only ones that matter from a market-perspective — but actually provides an underestimation of that number because it uses the total bitcoin supply without accounting for lost coins. Chapter 8 of Glassnode’s report provides several case studies of how many bitcoin may be lost and comes to a best estimate of between 18.5% (3.897M BTC) and 23.2% (4.871M BTC) of the circulating supply. Since the actual number of lost coins is and will remain unknown, there is a need for a different and preferably more dynamic approach. Enter Cointime Economics.

What is the new approach in Cointime Economics?

Cointime Economics iterates on ‘liveliness’ (Figure 2), a metric that was introduced by the late Tamas Blummer in late 2018 and became famous in 2019 for its use in calculating the unrealized profit and loss metrics in a collaboration with Tuur Demeester and Michiel Lescrauwaet. Liveliness itself utilizes another metric called Coin Days Destroyed (CDD), which was one of the first ever on-chain metrics and introduced in 2011. CDD is calculated by taking the number of bitcoin in a transaction and multiplying it by the number of days since those bitcoin were last spent. Hence, CDD is particularly high when a large number of old bitcoin transact, and low when only a limited number of bitcoin that are relatively young move on-chain. Liveliness takes the sum of all CDD, divided by the sum of all coin days that were ever created. Liveliness therefore increases when long term holders liquidate positions and decreases when market participants are increasingly holding onto their bitcoin. It can therefore be seen as a reflection of how willing the bitcoin holder base is to part with their coins.

What’s new in Cointime Economics is the concept of ‘Coinblocks’ (Figure 3). Coinblocks are similar to CDD, and are calculated by multiplying the number of coins that are transacted by the number of blocks that have passed since those coins last moved.

Similar to coin days, Coinblocks can also be described as ‘created’, ‘destroyed’ and ‘stored’. The number of Coinblocks created (CBC) simply increases with each newly mined bitcoin that comes into circulation and each block that passes. Coinblocks destroyed (CBD) represent the number of Coinblocks that are wiped out when coins transact on-chain, whereas Coinblocks stored (CBS) represents the number of Coinblocks that were not destroyed (=CBC — CBD).

Tamas Blummer’s liveliness metric can be recalculated by dividing the total number of Coinblocks destroyed by the total number of Coinblocks that were ever created. At a first glance, this finding may seem insignificant, but has the clear advantage that these inputs can now be calculated purely based on inputs that are available on the blockchain itself, which results in a metric that is more accurately reproducible across data providers. Furthermore, it enables the possibility to not only weigh metrics by price but also by time, as we will see in the two new metrics that will be described below.

How was this used to iterate on Realized Price and the MVRV ratio?

As described above, the Realized Price is often interpreted as the market’s average cost basis, but actually represents an underrepresentation of that value because it does not account for lost coins. In Cointime Economics, a new metric was introduced that uses liveliness to weigh the new metric for the extent in which the total market is actually ‘alive’. Because the creators of the new metric chose to do so based on a derivate of the Realized Cap instead of the Realized Cap itself, we will first briefly explain the Thermocap and Investor Cap before diving into the new metric.

Realized cap is the total price of all existing bitcoin at the price at which they last moved (Figure 4; orange). As a reflection of the total market, this includes both coins that were mined, as well as bought on the market (e.g., at exchanges). The portion of the Market Cap (Figure 4; black) that consists of the value that has been paid to miners to secure the network via the issuance of new coins is called the ‘Thermocap’ (previously introduced by Nic Carter), and can be calculated as the aggregated dollar-value of each bitcoin at the time it was mined (Figure 4; blue). By subtracting the Thermocap from the Market Cap, the ‘Investor Cap’ (previously introduced by Ark Invest) can be found (Figure 4; red). The Investor Cap represents the portion of the total Market Cap that was not introduced via the issuance of new coins by miners, but that actually moved on-chain at a certain market price. As such it is seen as a more appropriate reflection of the average price that was paid for each existing bitcoin by market participants.

Cointime Economics introduces a new alternative for the Realized Price called the ‘True Market Mean Price’, which is calculated by dividing the Investor Cap that was described above by the Active Supply, which is the total bitcoin supply multiplied by the liveliness (Figure 5; purple).

Similarly to how the MVRV ratio divides the bitcoin Market Cap by the Realized Cap, a new metric that utilizes the Investor Cap and Liveliness-weighted Market Cap was proposed. Puell and Check implicitly proposed the following 2 adaptations to the original MVRV ratio:

• Numerator: Instead of using just the Market Cap, weigh the Market Cap by liveliness (Market Cap * Liveliness) to create a new metric called ‘Active Cap’ that accounts for the extent in which the market can be seen as ‘alive’, and thus dynamically accounts for potentially lost coins.
• Denominator: Instead of dividing this number by the Realized Cap, divide it by the Investor Cap that excludes the portion of the value that was introduced by newly mined coins from the Realized Cap and thus only uses coins that actually moved on-chain at a certain market price.

By doing so, the new metric called Active-Value-to-Investor-Value (AVIV) Ratio (Figure 5; blue) provides a more accurate reflection for the degree in which the average active market participant is in profit or at a loss by dynamically accounting for lost coins. AVIV ratio values above 1 suggest that the market price is above the average active market participant’s cost basis, whereas values below 1 indicate that the average active market participant is at a loss.

What properties of these metrics are interesting?

As expected, the True Market Mean Price is significantly higher than the Realized Price and is positioned much more ‘in the middle’ of historic price action. In fact, according to Chapter 6 of Glassnode’s report, the True Market Mean Price is so ‘in the middle’ that both the mean (1.018) and median (1.038) AVIV ratio values are very close to 1, which is the average active market participant’s estimated break-even point. Historically, the bitcoin price trades above an AVIV ratio value of 1 53.3% of the time, and 46.7% below it. This property makes the AVIV ratio quite unique, and makes the True Market Mean Price an ideal ‘fair value’ estimate as the basis for over- and undervaluation modeling. However, there are two aspects of the AVIV ratio metric that can be improved for use in statistical valuation modeling.

First, the AVIV ratio values during the early days of Bitcoin are incredibly high (Figure 5, blue values on the left). The explanation is simple: after bitcoin received its first price of a few cents in July 2010, the initial exchanges were very illiquid, which was fertile ground for a massive run-up in price — its first hype cycle. One can argue that the AVIV ratio values of that first hype cycle are heavily skewed by market inefficiencies and initial price discovery, and should not be used as part of a historical ‘measuring stick’ to compare more recent values to. A solution could be to only use AVIV ratio values after January 1st, 2012, when the Bitcoin hype cycle went through its first rapid bull-bear cycle, and the average active market participant was just back to its break-even point.

Second, the blue graph in Figure 5 shows that AVIV ratio values fluctuate around 1, but on this linear chart deviate farther away above 1 during bull-runs than they deviate downwards during bear markets. Again, the reason for this is evident: due to how the metric is calculated, the theoretical upside of the scale is infinite, whereas the downside of the scale is 0. For data-visualization purposes this can simply be corrected for by placing the y-axis on a logarithmic scale (as the authors of Cointime Economics have done), but if you want to use this data for statistical calculations, applying the logarithmic transformation to the data itself can be helpful.

In Figure 6, both suggested adaptations were applied. A (natural) logarithmic transformation was performed on the AVIV ratio (blue) values since January 1st, 2012. The AVIV ratio is exactly the same as the regular AVIV ratio when visualized on a logarithmic y-axis (e.g., as depicted on page 18 of Ark Invest’s report), but now fluctuates around a value of 0, where values above 0 signal profitable market conditions and values below 0 suggest that the average active market participant is at a loss.

How can this be used for statistical modeling?

The log-transformed AVIV ratio that we created above represents the degree in which the current average bitcoin market participant is estimated to be in profit (values >0) or at a loss (<0). Even if the AVIV ratio is considered to be the best available model for this, it remains an estimate of the actual average cost basis. The fun thing with statistics is that we can actually express how certain we are that a finding is correct — in this case if historical bitcoin market prices are abnormally discounted or overvalued.

Since the log-transformed AVIV ratio has a distribution that is symmetrical around a mean (of in in this case 0) where values around it are more frequently occurring than values further away from it, it has a ‘normal’ or ‘Gaussian’ distribution. In fact, that is its literal definition according to Investopedia. As a result, the metric can be used for ‘parametric’ statistical analysis, which is a fancy word for the most common form of statistical analysis, often using the variable’s mean and standard deviation. This for instance enables the same z-score based modeling approaches that I’ve written about before (e.g., Bitcoin Price Temperature, MVRV Bands and MVIV + MVLV Bands) — but it will work in a more clean way for the AVIV ratio due to its more appropriate statistical properties.

With a normal distribution, we can use z-scores to calculate ‘confidence intervals’. A confidence interval is a range of values that is likely to contain the ‘true answer’ to a question. The ‘null hypothesis’ (/base case) for the log-transformed AVIV ratio is that historical bitcoin market prices are on average at ‘fair value’, as most values tend to be close to 0. The ‘alternate hypothesis’ is that a certain market value is not at fair value and thus abnormally priced. Since bitcoin can be both over- and underpriced in comparison to this ‘fair value’, we need our confidence interval to be two-sided.

Mathematically, we know that in a normal distribution, 95% of the values are within -1.96 and +1.96 standard deviations of the mean. Therefore, when the log-transformed AVIV ratio is 1.96 standard deviations above its mean, we can state that we are 95% certain that bitcoin is abnormally overpriced compared to its fair value. And similarly, when the log-transformed AVIV ratio is 1.96 standard deviations below its mean, the conclusion would be that with 95% certainty, bitcoin is underpriced. This 95% confidence interval is the most common in statistical testing in most academic fields, but the 90%, and to a lesser extent 80% and 99% confidence intervals can also be used (e.g., depending on sample size or expected effect size). Figure 7 shows an example of a normal distribution with two-sided 80%, 90%, 95% and 99% confidence intervals.

Enough theory — what does this look like for AVIV?

Figure 8 [the parameters for the Glassnode Workbench graphs can be found in the Appendix underneath this article] shows a graph of the log-transformed AVIV ratio (black), a zero-line that represents the ‘True Market Mean Price’ (grey), and the 90% and 95% confidence intervals. The confidence intervals are drawn by calculating the all-time rolling mean and standard deviation of the log-transformed AVIV ratio values since January 1st, 2012. By using all-time rolling values, historic values in the graph itself do not change when calculated on different dates, and the confidence intervals gradually adapt, as they widen during increased volatility (in the AVIV ratio values) and tighten if volatility decreases over time. From that perspective they are a bit similar to Bollinger Bands, but more stable over time as they use a much larger and dynamically expanding timeframe.

So far, the 95% confidence intervals for the log-transformed AVIV ratio have signaled both under- and overvalued market prices during each of the 3 market cycles that have occurred since 2012. It is important to realize there are no guarantees that price movements will remain as volatile in the future, and thus that the AVIV ratio values will not necessarily become as abnormal (in both directions) again in the future. However, when it does occur again in the future, we now have a tool that we can use to express how abnormal those prices are in a historical context.

Similarly to how we have utilized z-scores to plot related price levels on the bitcoin price chart for the Bitcoin Price Temperature, MVRV Bands and MVIV + MVLV Bands, we can now also do so based on the log-transformed AVIV ratio values. The result could be called ‘AVIV Confidence Bands’ and is shown in Figure 9.

Just for fun, as an alternative data-visualization, since the Glassnode Workbench software that was used to create these graphs now also allows annotations when a certain condition is met. Figure 10 shows the historical bitcoin price (black) with color-coded annotations when the log-transformed AVIV ratio is below the bottom 90%, 95% or 99% confidence interval (green shades) or the top ones (red shades). This figure shows that historically, it has not always been wise to for instance sell bitcoin as soon as the upper boundaries of the 90% or 95% confidence intervals were reached, as abnormal prices tend to occur over somewhat longer time-periods during both bull- and bear-markets.

Did Cointime Economics introduce other models?

In Cointime Economics, Puell and Check also introduced a new ‘floor model’, that aims to model the ‘price floor’ that the bitcoin price sometime briefly dips below, but always relatively soon bounces back above. The new model, which is described as both the ‘Cointime Price’ and ‘Blummer Price’ by the authors, utilizes the coinblocks that were introduced above. It is calculated by first calculating the all-time cumulative sum of all Cointime Value Destroyed (CVD), and then dividing it by the all-time cumulative sum of all coinblocks destroyed. The rationale behind this has not been as thoroughly documented as the one behind the AVIV ratio, but the model itself does not dissappoint. Figure 10 visualizes the Cointime Price / Blummer Price in green, and shows that it is consistently lower than the Realized Price (orange).

Can confidence intervals also be used for this?

In the introduction to confidence intervals above, we reflected on the situation where the null hypothesis was that the bitcoin market price is around ‘fair value’, and can deviate from it in both directions. In the case of the Cointime Price / Blummer Price, the basic premise is that the floor model represents the bottom of the price range, and thus that market values can only abnormally deviate from it to the upside. For this situation, it is possible to use one-sided confidence intervals, for which slightly different z-scores are used. In the same style as the normal distribution with two-sided confidence intervals was displayed in Figure 7, Figure 12 shows an example distribution that utilizes one-sided confidence intervals.

To properly align with the approach that we used for the log-transformed AVIV Ratio above, we first need to calculate a similar indicator to the AVIV ratio. Since we want to estimate to what extent the current market value is overvalued against the floor price of the Cointime Price / Blummer Price, we can calculate the Market-Value-to-Cointime-Value (MVPV) or Market-Value-to-Cointime-Value (MVBV) ratio by simply dividing the bitcoin market price by the Cointime Price / Blummer Price. Then we plot the one-sided confidence intervals by first calculating the all-time rolling mean and standard deviation of this new metric, and plotting the lines on the chart (rolling mean + [z-score of the one-sided confidence interval] * rolling standard deviation), as is done in Figure 13.

Similar to before, these confidence intervals can also be plotted on the price chart (Cointime Price + z-score * all-time rolling standard deviation of MVPV ratio) in Figure 14.

To close off, the MVCV/MVBV ratio and confidence bands can also be plotted using the color-coded annotations that we utilized above for the AVIV ratio, as is done in Figure 15.

Are there any caveats with this approach?

There are several differences between the approaches used for the log-transformed AVIV ratio and MVCV/MVBV confidence bands:

• The fundamental reasoning behind the AVIV ratio has been more clearly described than for the Cointime Price / Blummer Price.
• The assumption that market value can be expected to stick close to the AVIV ratio based ‘fair value’ (basically; mean reversion) appears to be more fundamentally sound than the assumption that the market value should not dip far and/or long below the Cointime Price / Blummer Price floor model.
• An approach that utilizes two-sided intervals (e.g., admitting that we don’t know in what price can or cannot deviate from its fair value) is more conservative than one that assumes value can only deviate up.

As such, I personally see the AVIV ratio and related models that were discussed above as more fundamentally sound and trustworthy than the Cointime Price / Blummer Price related models.

In both cases, it is important to realize that historic price movements and -volatility do not necessarily reoccur in the future. Although the bitcoin price has historically moved eerily consistent on a 4-year cycle that appears to be related to the halving schedule (and/or the global liquidity cycle that has been flowing with a similar beat since Bitcoin was born), it is also reasonable to expect that as a result of the maturing market, volatility should be expected to gradually become less extreme.

The confidence intervals and bands that were introduced in this article may appear to represent hard cut-off points for when the bitcoin market cycle should be expected to bottom or top, but there are no such clear limits in reality — especially during extreme bear- or bull-market conditions where fear and FOMO tend to skew rational thinking. Similar to how some academic fields are moving from a traditionally ‘frequentist’ (e.g., drawing binary conclusions depending on if a value is above or below a pre-set threshold, e.g. p<.05) to a ‘Bayesian’ approach (e.g., using available evidence to estimate the probability of a certain result being true), it is healthy to interpret these metrics with a more probabilistic mindset when aiming to analyze the market, ideally in combination with other metrics.

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Disclaimer: This article was written for educational, informational and entertainment purposes only and should not be taken as investment advice.

Appendix: Glassnode Workbench parameters

Required: Glassnode Tier 2 subscription

Figure 8 — AVIV confidence bands (indicator)

Metrics: [m1] BTC: Price; [m2] BTC: Liveliness; [m3] BTC: Circulating Supply; [m4] BTC: Investor Capitalization

Formulae: [f1] f10-f10; [f2] cummean(f10) + 2.57 * cumstd(f10); [f3] cummean(f10) + 1.96 * cumstd(f10); [f4] cummean(f10) + 1.64 * cumstd(f10); [f5] cummean(f10) + 1.28 * cumstd(f10); [f6] cummean(f10) -1.28 * cumstd(f10); [f7] cummean(f10) -1.64 * cumstd(f10); [f8] cummean(f10) -1.96 * cumstd(f10); [f9] cummean(f10) -2.57 * cumstd(f10); [f10] log(subset(m2*m3*m1/m4, “2012”, “2099”))

Figure 9 — AVIV confidence bands (price)

Metrics: [m1] BTC: Liveliness; [m2] BTC: Circulating Supply; [m3] BTC: Investor Capitalization; [m4] BTC: Price

Formulae: [f1] m3/(m1*m2); [f2] log(subset(m1*m2*m4/m3, “2012”, “2099”)); [f3] (2.7182818284590452353602874713527^(cummean(f2) + 2.57 * cumstd(f2)))*f1; [f4] (2.72^(cummean(f2) + 1.96 * cumstd(f2)))*f1
[f5] (2.7182818284590452353602874713527^(cummean(f2) + 1.96 * cumstd(f2)))*f1; [f6] (2.7182818284590452353602874713527^(cummean(f2) + 1.64 * cumstd(f2)))*f1; [f7] (2.7182818284590452353602874713527^(cummean(f2) + 1.28 * cumstd(f2)))*f1; [f8] (2.7182818284590452353602874713527^(cummean(f2) -1.28 * cumstd(f2)))*f1; [f9] (2.7182818284590452353602874713527^(cummean(f2) -1.64 * cumstd(f2)))*f1; [f10] (2.7182818284590452353602874713527^(cummean(f2) -1.96 * cumstd(f2)))*f1; [f10] (2.7182818284590452353602874713527^(cummean(f2) -2.57 * cumstd(f2)))*f1

Figure 10 — AVIV confidence bands (shade)

Metrics: [m1] BTC: Liveliness; [m2] BTC: Circulating Supply; [m3] BTC: Investor Capitalization; [m4] BTC: Price

Formulae: [f1] m3/(m1*m2); [f2] log(subset(m1*m2*m4/m3, “2012”, “2099”)); [f3] m4*if(m4,”>”,((2.7182818284590452353602874713527^(cummean(f2) + 1.28 * cumstd(f2)))*f1),1,0); [f4] m4*if(m4,”>”,((2.7182818284590452353602874713527^(cummean(f2) + 1.64 * cumstd(f2)))*f1),1,0); [f5] m4*if(m4,”>”,((2.7182818284590452353602874713527^(cummean(f2) + 1.96 * cumstd(f2)))*f1),1,0); [f6] m4*if(m4,”>”,((2.7182818284590452353602874713527^(cummean(f2) + 2.57 * cumstd(f2)))*f1),1,0); [f7] m4*if(m4,”<”,((2.7182818284590452353602874713527^(cummean(f2) -1.28 * cumstd(f2)))*f1),1,0); [f8] m4*if(m4,”<”,((2.7182818284590452353602874713527^(cummean(f2) -1.64 * cumstd(f2)))*f1),1,0); [f9] m4*if(m4,”<”,((2.7182818284590452353602874713527^(cummean(f2) -1.96 * cumstd(f2)))*f1),1,0); [f10] m4*if(m4,”<”,((2.7182818284590452353602874713527^(cummean(f2) -2.57 * cumstd(f2)))*f1),1,0)

Figure 13 — MVCV confidence bands (indicator)

Metrics: [m1] BTC: Price; [m2] BTC: Coin Blocks Created (CBC); [m3] BTC: Coin Blocks Destroyed (CBD)

Formulae: [f1] m2-m3; [f2] cumsum(m1*m3); [f3] f8/f8; [f4] cummean(f8) + 0.84 * cumstd(f8); [f5] cummean(f8) + 1.28 * cumstd(f8); [f6] cummean(f8) + 1.65 * cumstd(f8); [f7] cummean(f8) + 2.33 * cumstd(f8); [f8] m1/subset(f2/cumsum(f1), “2012")

Figure 14 — MVCV confidence bands (price)

Metrics: [m1] BTC: Coin Blocks Created (CBC); [m2] Coin Blocks Destroyed (CBD); [m3] BTC: Price

Formulae: [f1] m1-m2; [f2] cumsum(m3*m2); [f3] f2/cumsum(f1); [f4] (cummean(f8) + 0.84 * cumstd(f8))*f3; [f5] (cummean(f8) + 1.28 * cumstd(f8))*f3; [f6] (cummean(f8) + 1.65 * cumstd(f8))*f3; [f7] (cummean(f8) + 2.33 * cumstd(f8))*f3; [f8] m3/subset(f2/cumsum(f1), “2012”)

Figure 15 — MVCV confidence bands (shade)

Metrics: Metrics: [m1] BTC: Coin Blocks Created (CBC); [m2] Coin Blocks Destroyed (CBD); [m3] BTC: Price

Formulae: [f1] m1-m2; [f2] cumsum(m3*m2); [f3] m3*if(m3,”>”,((cummean(f6) + 1.28 * cumstd(f6)))*(f2/cumsum(f1)),1,0); [f4] m3*if(m3,”>”,((cummean(f6) + 1.65 * cumstd(f6)))*(f2/cumsum(f1)),1,0); [f5] m3*if(m3,”>”,((cummean(f6) + 2.33 * cumstd(f6)))*(f2/cumsum(f1)),1,0); [f6] m3/subset(f2/cumsum(f1), “2012")

Defining money

After 12 years of adoption, the concept of Bitcoin as digital money is now widely known. Ironically, when learning about Bitcoin, many individuals are forced to (re)consider what money is. One example of a definition that they may run into is:

The most saleable good to transfer value across space and time

Bitcoin’s digital nature allows a seamless transfer of value across space. Its 21 million maximum supply makes it dilution-resistant and perfectly scarce, also allowing it to maintain purchasing power over time — assuming the future demand does not decline. So far, that hasn’t been the case.

Quite the opposite, actually. In a world that is choking on the side effects of endless money printing and ever-growing mountains of debt, Bitcoin’s hard money properties give it a gravitational pull from which it is difficult to detach. The resulting adoption improves its salability and market liquidity, repeatedly opening doors for even larger market participants to dip their toes in a pool that keeps expanding.

With Bitcoin currently being added to the balance sheets of publicly traded companies and even countries, an increasing number of people are trying to answer the question “what gives bitcoin value?” and thus what a fair price is.

Valuing Bitcoin

When Bitcoin was just 1 week old, Hal Finney became not only the first person besides Satoshi to mine bitcoin and receive the first transaction, but also the first to publicly speculate about its long-term value. By comparing its target market to a rough estimate of the worldwide household wealth, he envisioned a potential $100 trillion to $300 trillion market cap, which would give bitcoin a value of around $10 million per coin.

Since then, there have been many attempts at modeling both the short-term and long-term bitcoin price. Perhaps the most well-known models are the Stock-to-Flow (S2F) and S2F cross-asset (S2FX) models by PlanB, that predict a price for the current halving cycle (2020–2024) of around $100k and $288k, respectively. Although the statistical and methodological validity of either model can be debated, the models facilitated a narrative around scarcity as the central property that gives Bitcoin value.

Others have attempted to predict the bitcoin price via regression models that use time as an input variable. However, the predictions of time-based models tend to vary depending on the time period that is used as input for the model, providing unstable predictions based on methodologically invalid models.

Another approach is to extrapolate futures price via statistical regression, but to adaptively value it in comparison to a baseline for ‘fair value’ that adjusts as more information comes available. An example of such a dynamic model is the Bitcoin Price Temperature (BPT), that attributes a relative valuation to price in comparison to its 4-year average. Since the bitcoin price tends to move in ~4 year cycles (at least historically), comparing prices to their 4-year trend can help estimate how overheated or undercooled prices are. A downside of using just price is that it assumes that used trends are stable, which is not necessarily the case. However, changes in market participants’ behavior can completely reverse a previously strong trend, which such purely price-based valuation models are only sensitive with a lag.

An interesting aspect about Bitcoin is that its timechain is a public ledger of all transactions that were ever made. It provides a database of which legacy economists can only dream. In February 2017, Willy Woo first leveraged this by introducing the Network Value to Transactions (NVT) Ratio. In doing so, Woo pioneered the on-chain analysis field that has become very popular since then. The NVT Ratio compares the value of the bitcoin market to the value of all coins that are transacted weekly. Therefore, the models the bitcoin price based on one of the defining properties of money; the ability to transfer value.

Since the introduction of Woo’s NVT Ratio, the adoption of the Lightning Network adoption is changing Bitcoin’s on-chain footprint. An increasing amount of value is no longer being transacted directly on-chain but flows via channels on a layer on top of Bitcoin. As a result, the NVT ratio is gradually losing accuracy, creating a need to come up with alternative valuation methods.

HODLer behavior as a measurement stick

If scarcity is a key aspect that makes a money valuable by allowing it to transfer value across time, investigating the behavior of those that have provably experienced this use case may provide meaningful insights into it is valued by those that seem to understand it.

In March 2020, on-chain data intelligence company Glassnode made a first attempt at this. By analyzing the age of Bitcoin transactions, they found that at above cut-off point of around 155 days, unspent transaction output (UTXO) had a very low likelihood of moving on-chain again. Based on this, they created a metric they called Long-Tern Holder (LTH) supply, which is the total amount of bitcoin that fall into this basket. In November 2020, Glassnode improved upon the metric by no longer looking at individual UTXO’s, but instead utilizing (proprietary) algorithms and on-chain forensics to look at the average coin age of entities instead. They also applied a more fluid threshold for coins to age into this LTH supply.

A month later, in December 2020, Glassnode again iterated upon this concept by introducing a new metric called illiquid supply. Where the LTH supply looks at an entity’s average unspent bitcoin age, the illiquid supply looks at the entity’s spending history and classifies the entity as either illiquid, liquid or highly liquid. Figure 1 displays the circulating bitcoin supply (black), LTH supply (blue) and illiquid supply (red).

As can be seen in figure 1, Glassnode’s algorithm for the illiquid supply appears to apply a more liberal method when it comes to classifying an entity as unlikely to spend.

Knowing how much supply is in the hands of these long-term holders and illiquid entities, we can calculate the Long-term holder Value (LV) and Illiquid Value (IV), which represent the total value of the LTH and illiquid supply (LTH / Illiquid supply * price), respectively. Since the bitcoin price can be volatile, applying a moving average over the LV and IV is helpful to better grasp its long-term trends. Figure 2 visualizes the LV and IV with a 1-year moving average that accounts for seasonal effects (e.g., seasonal effects on Bitcoin mining, tax seasons, et cetera) on a yearly basis.

As can be seen in figure 2, the yearly average of the total value of the bitcoin supply that is in the hands of long-term holders and illiquid entities tends to be where the bitcoin price finds support during market downturns.

The reason for this can be attributed to a phenomenon called HODLing, which stems from a meme that finds its origin in a 2013 Bitcoin Forum post. Historically, bitcoin bear markets have proven to be tough, causing it to be declared dead 432 times at the time of writing. During bear markets, speculators that only bought bitcoin to try and get rich quick sell their coins. As a result, the market is flooded with excess supply that it may have difficulty absorbing after overly euphoric market conditions when the demand of these same speculators that drove up price falls away. Price then trends down until the low-conviction holders are all shaken from their positions and only ‘HODLers of last resort’ remain. By holding onto their coins no matter what, this group effectively sets the price floor that was visualized in figure 2. After all, thanks to the inelasticity of the bitcoin supply, price can only move up when there are no sellers left while there still is some demand.

Comparing market value to illiquid and LTH value

Similar to how David Puell and Murad Mahmudov created the Market-Value-to-Realized-Value (MVRV) Ratiothat Awe and Wonder then standardized into the MVRV Z-Score, it is possible to compare the bitcoin market value to the illiquid and LTH value.

This is done by first calculating the difference between the Market Value (MV) and the Long-term holder Value (LV) and Illiquid Value (IV), respectively. That number is then divided by the standard deviation the MV, creating the Market-Value-to-Long-term-holder-Value (MVLV) and Market-Value-to-Illiquid-Value (MVIV) metrics. The resulting MVLV and MVIV metrics therefore represent the number of standard deviations that the market value is (over)extended in comparison to the total value of the LTH and illiquid supply (figure 3).

Due to the similarity in the LV and IV metrics, both fundamentally and data-wise, the MVIV and MVLV are similar metrics, where the MVIV is the most expressive. The choice to use either should be based on the degree in which one feels that coin ageing should be considered to determine whether an entity is likely to sell their coins, since that aspect is more strongly reflected in the LV than in the IV.

Both metrics allow historical comparison of the overall market value in comparison to the value of the supply that is in the hands of entities that are unlikely to sell. As can be seen in figure 3, bear markets tend to bottom out at vales around 0 (which is the 1-year moving average of the IV and LV itself) and have historically topped out at values of about 8 and higher. Although the cyclicality in Bitcoin’s market valuation is mesmerizing and seduces many to assume that history will repeat, there are no guarantees that this (4-year) cyclicality will necessarily continue.

MVIV and MVLV Bands

Now that we have a metric that quantifies the relative valuation of the bitcoin market in comparison to the value of the LTH and illiquid supply, it is possible to map the bitcoin price at each respective MVIV/MVLV level on top of the price chart, allowing us to graph how much room for growth or decline there is for price to reach certain MVIV/MVLV levels again. This was done before with the BPT Bands and MVRV Bands that were discussed above.

This is done by adding a multiple of the standard deviation of MV to the IV or LV itself, where the multiple represents the MVIV/MVLV value that you want to visualize. The resulting numbers are then divided by the circulating bitcoin supply to get the valuations per bitcoin. When plotted on top of the price chart, these values represent the ‘Bands’ in the MVIV Bands and MVLV Bands concepts that are visualized in figures 4 and 5, respectively.

Comparing floor models

With the MVIV and MVLV Bands added to the mix, we now have four baseline bitcoin valuation models that each use different baselines to estimate its ‘fair value’. Figure 6 displays the baseline values of the MVIV, MVLV, MVRV and BPT Bands models.

As can be seen, the MVRV Bands baseline is the most responsive, since it is the only metric that does not include a one (MVIV & MVLV) or four-year (BPT) moving average component.

While relevant, that does not necessarily mean that it is the superior model to rely on. As can be seen in figure 6, the baselines of both the illiquid and LTH supply value are currently above that of the MVRV, which has historically only briefly occurred late 2014 and late 2018 during peak bear market conditions, and never during a market uptrend towards all-time highs as is currently the case.

An explanation may be that a shift in how the world sees Bitcoin may be happening. As can be seen in figure 7, the trends the percentage of the circulating bitcoin supply that is not on exchanges (blue) or that is labelled illiquid (green) have dramatically changed since roughly March 12th, 2020.

On that day, global financial market selloffs triggered a cascade of long liquidations that took the bitcoin price down over 50% in two days and cleared the market of all excess leverage. Since then, publicly traded companies and now even a country have adopted Bitcoin, while central banks have turned on their money printers heavily in their attempt to combat the economic downturn — creating a gigantic asset bubble instead.

In a time where Bitcoin is making strides to replace as the go-to hard money shelter against monetary inflation, an increased adoption of bitcoin as an asset to transfer value over time means that coins become less likely to move on-chain. That trend may be exacerbated by Lightning Network adoption, lowering the number necessity to transact on-chain even further. As a result, unspent transactions may take more time to ‘realize value’ via an on-chain footprint as is quantified in the MVRV metric. Simultaneously, their likelihood of being included in Glassnode’s illiquid or LTH supply increases.

If these trends continue, is possible that the MVRV baseline will start lagging and that the presented MVIV and MVLV metrics may provide a more reliable estimate for the bitcoin floor price. It is therefore nice that we now have multiple similar options to fall back on that utilize this valuation method from different angles. For the time being, these metrics are very similar — especially when the bitcoin market value deviates further away from the respective baselines (figure 8).

The similarity between the floor models that are depicted in figure 7 and the resulting metrics of figure 8 can also be seen as a form of confluence. The MVRV, MVLV and MVIV all incorporate the lifespan of the underlying coins. These metrics therefore reflect investor time preference and hold valuable information about the relative bitcoin valuation in comparison to the price floor that is set by HODLers.

A limitation of the MVLV and MVIV Bands metrics that we need to be cognizant of is that proprietary algorithms were used to construct the used illiquid and long-term holder supply metrics. It is likely that Glassnode keeps improving upon those algorithms to optimally service their clients, which would mean that both future and historic values may be subject to change over time. Charts representing MVIV and MVLV (Bands) metrics therefore should be seen as a snapshot in time that uses the most up-to-date method to quantify the supply that is in the hands of entities that are unlikely to spend it, and not be compared to prior visualizations of the same metric.

Live charts for these metrics are available via Glassnode Workbench:

Dilution-proof on Twitter: "1/3 We already had a live BPT chart but is now also possible to create @glassnode Workbench versions for the #bitcoin MVRV, MVLV & MVIV Bands 🥳MVLV: https://t.co/c9YQKOOnbsMVLV Bands: https://t.co/DAGD6oTWv1MVIV: https://t.co/hKFCDNeNb9MVIV Bands: https://t.co/AghJ1b0cca pic.twitter.com/ZI33gkJuXZ / Twitter"

1/3 We already had a live BPT chart but is now also possible to create @glassnode Workbench versions for the #bitcoin MVRV, MVLV & MVIV Bands 🥳MVLV: https://t.co/c9YQKOOnbsMVLV Bands: https://t.co/DAGD6oTWv1MVIV: https://t.co/hKFCDNeNb9MVIV Bands: https://t.co/AghJ1b0cca pic.twitter.com/ZI33gkJuXZ

Special thanks go out to @Anoi30604540, @_Checkmatey_ and @WClementeIII for providing feedback on the draft of the original article, which was published on Bitcoin Magazine on October 25th, 2021.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

Disclaimer: This article was written for educational, informational and entertainment purposes only and should not be taken as investment advice.

Realized Value

On September 23rd, 2018, at the Baltic Honeybadger conference in Riga, Nic Carter presented the concept of realized value (originally ‘realized cap’, but both terms are since then used interchangeably) that he had developed in collaboration with Antoine Le Calvez. By leveraging the Bitcoin timechain, which holds a public record of all Bitcoin transactions that were ever made, realized value looks quantifies the total United States Dollar (USD) value of all bitcoin that exist at the last time those coins were moved on-chain. Figure 1 displays this realized value (blue) alongside the total bitcoin market value (black), which is the total market value of all bitcoin that exist at any point in time.

Under the assumption that most on-chain transactions represent an actual transfer of value (e.g., buying or selling bitcoin against fiat money or using it to consume goods or services), realized value therefore represents the aggregated cost base of each bitcoin in existence. As can be seen in figure 1, this aggregated cost base appears to be well suited to estimate bottom prices during bear market conditions, as apparently most bitcoin holders are unlikely to realize losses on an asset that they feel has a lot of long-term upside.

Market-Value-to-Realized-Value (MVRV) Z-Score

This new concept of realized value was a breakthrough in the emerging field of on-chain analysis. On October 2nd, 2018, David Puell and Murad Mahmudov iterated on Carter and Calvez’s work by introducing the Market-Value-to-Realized-Value (MVRV) Ratio. The MVRV Ratio is calculated by dividing the total bitcoin Market Value (MV) by its Realized Value (RV). Therefore, the metric represents the extent in which the current bitcoin market valuation is overextended beyond (values >1) or actually at a discount (values <1) compared to the holders’ aggregated cost base.

A week later, on October 9th, 2018, Awe and Wonder further iterated upon the MVRV Ratio by creating a metric called the MVRV Z-Score. The MVRV Z-Score first calculates the difference between the total bitcoin market value and its realized value, and then divides that by the standard deviation of the market valuation — a common statistical procedure called ‘standardization’. The MVRV Z-Scores therefore represent the number of standard deviations that each bitcoin market valuation is increased or decreased against its realized value. Although the methodology behind this oscillator might be difficult to interpret for some, the visualization of this metric actually makes it much easier to compare how relative bitcoin market valuations compare to those of previous bitcoin market cycles.

Figure 2 displays the MVRV Z-Score over time. The colored horizontal lines represent MVRV Z-Scores of 0 (blue), 2 (green), 4 (yellow), 6 (orange), 8 (red) and 10 (brown).

MVRV Bands

Based on the same methodology that was used in creating the Bitcoin Price Temperature (BPT) Bands on December 15th, 2020, this article iterates upon the MVRV Z-Score by visualizing the price levels of the six colored MVRV Z-Scores that were highlighted in figure 2 on a regular (logarithmic) bitcoin price chart in figure 3. These ‘MVRV Bands’ represent the price that bitcoin would have if it reached were to reach those MVRV Z-Score levels.

Since the MVRV Z-Score divides the difference between the bitcoin market value and realized value by the (all-time) standard deviation of the market price, the metric is sensitive to changes in bitcoin price volatility. During times where the bitcoin market price rapidly increased, its all-time standard deviation also increases, causing the displayed bands to slope up, thus suggesting higher values are needed to reach those MVRV Z-Score levels, and vice versa during market downturns. This dynamic is better visible in figure 4, which zooms in on the last 5 years of data.

The metrics and visualizations that were introduced in this article are free to be replicated, used and expanded upon by others. At the time of writing there is no web-based version of the metric available yet, but the R code is available on GitHub.

This article was originally published on Bitcoin Magazine on October 12th, 2021.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

Disclaimer: This article was written for educational, informational and entertainment purposes only and should not be taken as investment advice.

Bitcoin’s difficulty adjustment mechanism is of its most important aspects, but learning how it works can be a daunting task. This article leverages on-chain data to visualize how this mechanism works and how it relates to hash rate, block intervals, transaction fees and the mempool. After reading this article, you will have a better understanding of why at certain times using Bitcoin may appear to be relatively slow and expensive, but also how Bitcoin fixes this and why this process is so essential to ensure Bitcoin’s monetary properties.

Bitcoin’s supply issuance schedule

If you’ve heard of Bitcoin, you have probably heard that its supply is hard capped at 21 million units (BTC), making it a perfectly scarce asset and thus the ultimate ‘hard money’.

When Bitcoin was created, miners received 50 BTC for each new block as a reward for their work. The software has a built-in rule that after every 210.000 blocks that are mined (~4 years if the block interval is 10 minutes), this ‘block subsidy’ is cut in half during an event called ‘the halving’. During this first ‘reward era’ that ended on November 28th, 2012, 10.5 million BTC were mined — half of its maximum supply. During the second reward era, half of that amount (10.5M / 2 = 5.25M) was issued, followed by half of that (5.25M / 2 = 2.625M) during the third reward era — and so forth. After 32 halvings, the block subsidy equals the smallest unit in Bitcoin (0.00000001 BTC = 1 sat) and cannot be split after, which means the block subsidy falls away completely after that (~2140 if block intervals were 10 minutes during its entire existence). The first 14 reward eras of Bitcoin’s issuance schedule are visualized in figure 1.

The careful reader will have noticed that in the previous paragraph, we mentioned twice that the actual calendar dates on which these halving events occur depend on the block intervals and that we assumed 10 minutes here. Why it is important that this supply issuance schedule is predictable in regular calendar-times in the first place?

The importance of relatively stable block intervals

Let’s consider what it would look like if Bitcoin didn’t have a built-in difficulty adjustment mechanism, but simply had a fixed mining difficulty.

If that fixed difficulty had been set relatively high, early mining would have been very expensive and blocks would have come in at a very slow pace early on. Clearly, that wouldn’t have been ideal to bootstrap a new network and could have meant that it never succeeded in the first place.

On the other extreme, if the difficulty would have been set relatively low to incentivize early network participants to join, block intervals would get smaller as more miners are joining the network and blocks would come in at an increasing pace. It would quickly run through its entire supply issuance schedule and likely wouldn’t have had enough time to develop a block space market that is needed to incentivize miners to keep mining blocks in order to process transactions and secure the network after the block subsidy runs out.

To summarize, relatively stable block intervals are needed to spread out Bitcoin’s supply issuance over time, which in turn is needed to incentivize miners to keep joining the network over a relatively long bootstrapping period, as well as to gradually develop a block space market that will be able to keep the lights on after the block subsidy runs out.

To guarantee that block intervals will remain relatively stable over a multi decade period, Bitcoin has a difficulty adjustment mechanism. As can be seen in figure 2, even with this built-in difficulty mechanism, its block intervals not very stable and on average much longer than 10 minutes per block during its first year of existence. The block intervals became more stable after Bitcoin set its first market price, and have been relatively stable at just under 10 minutes for roughly six years now — works like a charm.

Bitcoin’s difficulty adjustment mechanism

To mine bitcoin, miners use highly specialized computers to basically guess a certain number (slightly simplified). When a miner finds the number that the network is currently looking for, it earns the rights to create a new block on the Bitcoin blockchain, take its block subsidy, choose which transactions to include in that block and collect the fees of those transactions. At the time of writing, all miners that are active on the Bitcoin network are estimated have a total capacity (‘hash rate’) of 170 Exahashes per second (EH/s), which is 170,000,000,000,000,000,000 hashes per second.

In Bitcoin’s first year in existence (2009), it was still possibly to mine Bitcoin on the CPU (‘Central Processing Unit’; which is basically the central chip in a computer that takes care of lots of things) an average consumer computer, as the network’s hash rate was just a few million hashes per second. Over time, more computers joined the network and eventually chips that were better at heavy number crunching (GPU or ‘Graphics Processing Unit’; the chip in a computer that is applied for graphical tasks and linear algebra) or even hardware that is custom made for Bitcoin mining (an ASIC, or ‘Application Specific Integrated Circuit’) was used.

As you can imagine, as the network’s hash rate increased by a multi-trillion-fold from that first year until now, it was necessary to make it a lot harder to guess that certain number to ensure relatively stable block intervals.

In Bitcoin, ‘difficulty’ is the measure for how hard it is to find that number that the network is looking for. Every 2016 blocks (14 days if block intervals are 10 minutes), the Bitcoin software basically calculates the block intervals during that period and adjusts the difficulty so that at current capacity, the average block interval will be roughly 10 minutes again.

The interplay between Bitcoin’s difficulty, (the 14-day moving average of the) hash rate and block intervals over the last three months is visualized in figure 3. During the first visualized difficulty adjustment period (the red column on the left), the hash rate was declining (downtrend in black line). As network capacity decreased, block intervals increased (uptrend in blue line), making it necessary to decrease the difficulty (small drop in orange line after this period).

In three difficulty adjustment periods after (first green column in figure 3), the hashrate was increasing again, blocks came in faster than planned and difficulty adjusted upwards three times. Mid-April (right red column), there was a large power outage in China that caused a massive drop in Bitcoin’s hash rate, slowing down blocks a lot and making a huge downwards difficulty adjustment necessary after the period. After this happened (right green column), the power outage itself was solved and the downwards difficulty adjustment made it much easier for miners to create blocks again. As a result, some miners with less efficient hardware and/or more expensive energy could earn a profit mining again, actually overcompensating the previous loss of hash rate, actually sending it to new all-time highs.

This latest hash rate drop and recovery is a good example of why miners leaving the network does not have a cascading effect of miners leaving the network (sometimes called the ‘mining death spiral’ by critics), but the software simply increases the remaining miners’ profit margins, incentivizing other miners to (re)join the network.

Transaction fees

A side effect of this mechanism that we all feel is its impact on transaction fees. During times when the hash rate increases and blocks are coming in faster than planned (green columns in figure 4), transactions can relatively easily be included in blocks. Since this means that there are less transactions queued up in line (in Bitcoin called the ‘mempool’) to be included in upcoming blocks, transaction fees can be relatively low.

The opposite is true during periods where hash rate drops and block intervals increase (red column in figure 4). When blocks are coming in slowly, the queue of transactions waiting to get included gets crowded, and people need to bid up their transaction fees to basically jump the line. As such, transaction fees spike especially when the network capacity decreases (hash rate drops) and is waiting to be bailed out by the next difficulty adjustment.

In this paragraph, we discussed the fees of transactions that were included in blocks. For anyone that is looking to transact on the Bitcoin network, it is even more relevant to get a feel for what transactions that are still waiting in line to be included in future blocks are bidding for their needed block space.

Mempool

As briefly mentioned above, the Bitcoin mempool can be interpreted as the total of all transactions that were broadcasted on the network but are still waiting in line to be included in a future block. Technically, each of the thousands of Bitcoin nodes on the network has its own mempool, but since they are mostly well interconnected, visualizing them as a single waiting line is alright for didactive purposes.

Mempool.space is a popular and respected website that gives anyone not running their own node or simply looking to get a quick look at the mempool all the relevant data. Examples are the total size of the waiting line (mempool size), how many transactions are joining the queue (incoming transactions), if blocks are coming in faster or slower than expected (estimated difficulty adjustment) and estimations of how high the transaction fee of a new transaction needs to be to be included at low, medium or high priority.

Figure 5 visualizes the mempool of the last three months. As you would expect, the patterns described in figure 4 can also be seen here. Between late February and early April, when the amount of hash rate on the Bitcoin network increased and more blocks than planned were created, the mempool size (the size of the waiting line) decreased and transaction fees decreased. After the mid-April hash rate drop, the mempool quickly increased and transaction fees skyrocketed, but both declined extra fast after the April 30th difficulty adjustment and subsequent hash rate growth to all-time highs.

The future block space market

As briefly mentioned at an earlier point in this article, Bitcoin’s block subsidy is designed to decay over time, and the development of a healthy block space market where transaction fees become the primary source of revenue for miners is essential to incentivize miners to keep processing transactions and securing the network in the long-run.

This is possibly the most important test that awaits Bitcoin in the future, and is the subject of my previous Bitcoin Magazine article titled “An ode and forthcoming obituary to Bitcoin’s four-year cycle”, which is a recommended follow-up read. Finally, if you have any questions on the topics discussed in this article, feel free to send me a message on Twitter.

This article was originally published on Bitcoin Magazine on May 15th, 2021.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

Disclaimer: This article was written for educational, informational and entertainment purposes only and should not be taken as investment advice.

On January 3, 2009, Satoshi Nakamoto launched the Bitcoin network by mining the first block (the “genesis block”) in the Bitcoin blockchain. Today, a bit more than 12 years later, the network stores over $1 trillion in value and transfers more than $20 billion in on-chain volume on a daily basis. To get there, Bitcoin went through multiple boom and bust cycles in which it was praised to the moon and declared dead many times over — every time to resurrect from the death. This process kept repeating in a roughly four-year cycle that led many to believe that there is a certain predictability to long-term bitcoin prices, of which PlanB’s popular Stock-to-Flow (S2F) model is the most well-known attempt.

In this article, we’ll first take an in-depth look at why the bitcoin price moves in a four-year cycle related to its halving schedule. We then dive into how this market cycle influences more fundamental properties of the Bitcoin network itself that are related to the behavior of miners and users. Finally, I introduce a hypothesis for how the maturation of the Bitcoin network itself will eventually extinguish its four-year cycle, and explain why this would be a good thing for the network and its users.

Bitcoin’s fixed supply issuance schedule

When Satoshi Nakamoto launched the Bitcoin network, there was a need to (1) bring the bitcoin units into circulation and (2) incentivize early users to actually participate in the network by running their own mining nodes to secure the network. By doing so, the chances of a single entity attacking the network via a majority attack (or 51% attack) were decreased.

To do this, Satoshi Nakamoto decided on a coin issuance schedule where Bitcoin network participants would receive a 50-bitcoin mining reward (also called “coinbase,” not to be confused with the eponymous exchange) per created block. Every 210,000 blocks (~4 year, assuming 10-minute block-intervals), this reward halves. After the first halving (November 28, 2012), miners received 25 bitcoin; after the second halving (July 9, 2016), 12.5; since the last halving (May 11, 2020), they received 6.25, and so forth.

By combining this coin issuance schedule with Adam Back’s ingenious proof-of-work mechanism, Bitcoin’s monetary policy regarding its supply (figure 1, blue line) and monetary inflation (figure 1, orange line) became set in stone on a per-block basis as soon as the network launched — unlike its central bank predecessors.

Impact of the halving on supply, demand and price

Intended or not, the roughly four-year halving that has occurred three times in Bitcoin’s existence so far appears to have been a consistent trigger in pushing up the price every time. As can be seen in figure 2, after every halving event (white striped vertical lines), the bitcoin price (white line) has moved up dramatically in the year after those events. The average bitcoin price during a four-year moving window (black line) has been positive during its complete lifespan as a result.

Before each halving event, the bitcoin price is a dynamic equilibrium between

1. the supply of newly mined bitcoin that enters the market;
2. the demand for bitcoin by new market participants and recurring purchases;
3. the degree in which that new demand comes from long-term HODLers that take the respective bitcoin off the market; and
4. the degree in which increased market prices or other triggers entice existing long-term HODLers to increase the supply available on the market by selling bitcoin.

After the halving, the supply of newly mined bitcoin that enters the market is cut in half. If the demand for bitcoin remains unchanged, this means that a supply shortage is gradually formed. Since Bitcoin’s supply is perfectly inelastic, this supply shortage cannot be solved by creating more bitcoin. As a result, the only way for the market to unlock supply to satisfy the demand for bitcoin is to entice current holders to sell their bitcoin — which means that the market price has to move up.

Due to bitcoin’s status as a Veblen good, this rising price tends to attract even more demand, exacerbating the already existing supply shortage and driving up the price much faster than it organically would. Those price developments resulted in a temporary bubble each time that ended with a market crash and subsequent multi-month to multi-year bear market that was necessary for supply and demand to find a new equilibrium — each time at a (much) higher level than during the previous cycle.

This mechanism was brilliantly visualized by Croesus_BTC in this tweet thread and is compiled in figure 3.

Although the post-halving price increases in the bitcoin price charts are already pretty distinct and the causal mechanism for such a cycle to exist is quite self-evident; it is nice to get more robust evidence for the notion that the bitcoin price indeed moves in a four-year cycle. In this published article on April 15, 2021, btconometrics performed a Fourier analysis to prove that this is indeed the case. Although the statistical methods used are relatively complicated and explaining them is beyond the scope of this article, the graphical representation of the results is actually straightforward to interpret. As can be seen in figure 4, the highest values are reached very close to the red line that represents the four-year cycle, illustrating that the cyclicality in bitcoin is indeed very close to that.

The Bitcoin Price Temperature (BPT)

Now that we have insight into the mechanism that is driving bitcoin’s four-year cycles, we can take a more in-depth look at what this price cyclicality looks like. To do so, I have created a metric called the Bitcoin Price Temperature (BPT), which was introduced in this article.

In short, the BPT is calculated by subtracting every daily closing price by the average bitcoin price during the previous four years, and then dividing that number by the price’s standard deviation during that time span. The result is a metric that reflects to what extent any historic bitcoin price deviates from its four-year moving average while taking its volatility into account, and, thus, how “hot” or “cold” the price is — hence the name, Bitcoin Price Temperature. By utilizing the bitcoin price’s standard deviation into the metric, the BPT metric adjusts for price volatility, unlike otherwise similar indicators like the Mayer Multiple.

The left chart in figure 5 illustrates the BPT. As shown, the bitcoin price has actually rarely been below its four-year moving average (the blue horizontal line at zero), and it has historically reached its four-year cycle tops at a price temperature of eight or higher. On a smaller time frame, the bitcoin price has also changed its bullish or bearish trajectory several times at temperatures of around two and six. While these levels have been determined based on a limited sample and thus need to be taken with a grain of salt, they are interesting price levels to monitor during bitcoin’s current and future four-year cycles — assuming those will continue to be similar to the past cycles, which will be discussed later in this article.

Another way to look at the cyclicality of the BPT and bitcoin price itself, is to “reset the clock” at every halving, creating a chart where the BPT and/or bitcoin price itself per cycle are overlaid, making them easier to compare. As can be seen in the left chart in figure 6, the price temperature gradually moves up after the halving at an increasing pace, historically creating a blow-off top circa 12 to 18 months after the halving, taking the remainder of the four-year cycle to cool off again and find an equilibrium somewhere near its four-year moving average.

The right chart in figure 6 illustrates the actual bitcoin price in United States Dollars (USD) per halving cycle with an overlay of the BPT and BPT Bands. Every time the price temperature reaches the cooldown period of its four-year cycle, the bitcoin price has found an equilibrium at a price level that is (at least) an order of magnitude higher than the previous cycle.

This is also why dollar-cost averaging (DCA) into bitcoin and HODLing it for the long haul (or at least four years) has historically been such an effective strategy. It doesn’t matter if you have bought the top or the bottom; as long as you have held onto your bitcoin for at least four years, you’ve historically done very well — without the additional costs of time, anxiety and in some countries (like the United States) tax burdens that come with active trading.

Impact of the market cycle on Bitcoin’s hash rate and coin issuance

In anticipation of each Bitcoin halving, articles spreading fear, uncertainty and doubt (FUD) about something called ‘the mining death spiral’ start appearing. The mining death spiral FUD suggests that since the block subsidy is split in half, miners are faced with a 50% cut in their profitability, which will cause (some of) them to stop mining. In turn, this would make the network less secure, making it less valuable, making the price go down, further decreasing miner profitability, making them turn off more miners and so forth.

While it is true that in the short-term some miners are turning off hardware that is less efficient or running on more expensive energy, that dip is barely visible on long-term charts and ensures that the remaining mining activity on the network is actually very efficient and healthy. More importantly, that temporary dip is actually completely undone by the positive side effects of the halving-induced price increase that was described earlier.

As a result of the increasing bitcoin price following the halving-induced supply shortage, mining profitability increases again, incentivizing miners to (re)join the network. As a result, the network’s hash rate actually increases, making the network more secure and thus more valuable. This means that on a multiyear horizon, we are actually seeing the complete opposite of what the mining death spiral FUD suggests will happen — all thanks to Bitcoin’s four-year cycle.

In figure 7, the almost continuously increasing hash rate of the Bitcoin network is illustrated. As can be seen, the hash rate barely drops after each halving (white striped vertical lines), and as the bitcoin price and thus the BPT measure that we introduced in the previous paragraph increases, hash rate growth accelerates. During the second half of the cycle, when price is cooling down, hash rate growth stagnates a bit — until the next halving occurs and a new market cycle incentivizes more rapid growth of this network characteristic that is so important for its overall security, actually making the network itself more valuable.

To ensure that new blocks are created every ~10 minutes (which is necessary to make the network relatively stable to transact on and that the supply issuance is actually spread out over time), the network has a built-in difficulty adjustment mechanism. Every 2,016 blocks, which is every ~14 days, the network makes it a bit easier to mine if the hash rate on the network is relatively low, or a bit more difficult to mine if the hash rate on the network is relatively high.

This means that during these periods of the cycle where the hash rate keeps going up, more new bitcoins are created than would be expected based on the original supply issuance schedule that assumes 10-minute block times. This inspired David Puell to explore the ratio of the daily coin issuance and the average daily coin issuance over the past year, which resulted in the Puell Multiple.

The Puell Multiple is displayed in figure 8, along with several levels that appear interesting based on visual inspection (which is subjective and should thus be taken with a grain of salt). As can be seen, the daily coin issuance takes an abrupt decline on the day of each halving, which is due to the halving of the block subsidy. In the months after, as price increases, mining becomes more profitable, a new hash rate floods onto the network, and the daily coin issuance ramps up again. When the bitcoin price growth stops and the market cycle finishes with a blow-off top that is followed by a cooldown period, mining profitability decreases, causing the daily coin issuance to go down again. The Puell Multiple is, therefore, regularly seen as an interesting indicator to monitor Bitcoin’s cyclicality from an on-chain perspective.

Besides the hash rate growth and resulting temporary increase in daily coin issuance that are particularly indicative of cyclical miner behavior, the Bitcoin blockchain holds valuable information regarding another important group of market participants; those that use bitcoin to transact on-chain.

Influence of the market cycle on the mempool and transaction Fees

Intuitively, the first thing that you might think of to visualize the behavior of that group might be to create a chart of the number of daily transactions. If we were to do so, we would indeed see an overall trend that, as time passes, more transactions are made on a daily basis, but as the Bitcoin network matures, that growth stagnates. That stagnation can be easily explained; a Bitcoin block can only include a certain amount of transactions, so the metric wouldn’t be an ideal proxy for how crowded it actually is on the network. What happens when most or all of the newly created blocks are full, is that the number of transactions that are cued up increases. In Bitcoin, this cue is called a “mempool,” which is visualized in figure 9. As is evident based on that figure, the number of transactions that are waiting to be included in the blockchain have increased rapidly after breaking the all-time high price of ~$20,000 in December 2020.

The mempool is currently in a state where it hasn’t cleared in approximately five months, which means that, when any miner created a new block during that time span, they had plenty of unconfirmed transactions to include in the block. A logical conclusion is that miners are financially incentivized to include the unconfirmed transactions that are offering the highest transaction fee to reward the miner for including their transaction, which is indeed how most of the current miners operate.

As a result, unconfirmed transactions with a high transaction fee are included in new blocks first, while transactions with a low fee remain stuck in the mempool longer. This is visible in figure 9, where the mempool is currently particularly filled with unconfirmed transactions that pay a fee of 1–5 satoshis per vByte, while the mempool is regularly cleared from transactions of a higher fee rate.

An implication of this mechanism is that, during busy times on the network, anyone that is looking to make an on-chain transaction on the network needs to bid up their transaction fee to get their tiny share of block space on the Bitcoin blockchain that is needed to get their transaction confirmed. As such, a block space market (sometimes called “fee market”; which is technically incorrect because the block space on the Bitcoin blockchain is being bid on) develops.

Since the value of the transaction fees that are included in Bitcoin blocks essentially represents the magnitude of this developing block space market, it is a better proxy for network activity than simply looking at transaction counts. Figure 10 visualizes the average bitcoin transaction fees in USD over time, overlaid by the BPT metric that we introduced before. In anticipation of each halving, the average transaction fee is already gradually increasing, but its growth particularly accelerates when the bitcoin price increases after each halving. After the market cycle reaches a blow-off top and prices start to cool down again, network activity decreases again and finds a new equilibrium when the overall bitcoin market cycle bottoms out.

Besides the cyclicality, a clear, increasing trend in the average bitcoin transaction fees can be observed in figure 10. While this may seem like a bad thing (don’t we all prefer to pay less for transacting?), this is actually of the utmost importance for Bitcoin’s long-term existence. After all, if the block subsidy declines every four years and at some point in the future disappears altogether, miners still need an incentive to keep mining and process transactions.

The contribution of transaction fees to the block reward

Figure 11 visualizes the percentage in which transaction fees (red) and the block subsidy (blue) account for the overall block reward that miners receive when creating a block. When first glancing at these percentages on a continuous scale (left figure), it seems like transaction fees are relatively irrelevant, as the block subsidy has accounted for the vast majority of the block reward during all of Bitcoin’s history. While this is true, when these percentages are displayed on a logarithmic scale (right figure), it becomes more apparent that over time, there is actually a clear upward trend in the degree to which transaction fees play a role in the block reward. On a cycle-by-cycle basis, you can even see that the percentage increases by roughly an order of magnitude, underlining how large this growth actually is.

It is difficult to predict exactly when the point will be reached where transaction fees will (consistently) account for the majority of the block reward (based on eyeballing the charts above; perhaps after one to three more cycles?). However, as long as there is at least some activity on the Bitcoin network, it is a given that this point will be reached at some point in the future because the block subsidy trends toward zero by design.

When this point is reached, there is one more incredibly important question that we’ll get an answer on: will the hash rate on the network stay relatively stable at a level that is sufficient to guarantee the network’s overall security? If the answer to that question is “yes,” Bitcoin will have passed the biggest test in its existence and have passed the final exam toward its full maturity. Perhaps it could even be the point where the Bitcoin Core software versioning is upgraded toward 1.0 and above. While we cannot establish with absolute certainty that the question above can ultimately be answered with “yes,” a case can be made to be optimistic about the outcome, as was done by Dan Held in this May 2019 article.

This brings us to the final part of this article, where we’ll hypothesize how that perspective would impact the four-year cycle, and what that future for Bitcoin would look like.

How a healthy block space market will kill the four-year cycle

The subtitle of this article already gave away the direction of my take on this: when Bitcoin gets to the “full maturity” mentioned above and a healthy block space market exists that is able to sufficiently incentivize miners to structurally keep the lights on, I expect the four-year cycles as we know them today to fade into oblivion.

The easiest way to substantiate this claim is to fast-forward all the way to the late 2130s, when Bitcoin’s block subsidy is estimated to run out. In the absence of a block subsidy, 100% of the new demand for bitcoin will have to be satisfied by purchasing bitcoin from existing holders (and to some extent miners that sell some of their fee revenue to pay for expenses, which will likely be just a fraction of the total supply that is available for sale on the market). This creates a perfectly inelastic situation where price changes become a perfect reflection of changes in demand for bitcoin. To visualize this end state, Croesus_BTC’s visualization of the demand/supply mechanic has been adjusted to this new situation in figure 12.

Now that we have established that the halving cycles will, by design, end at some point during the next ~118 years, it is helpful to rewind to the present and assess what the short-term path toward that end state will look like in the near future.

To understand those implications, it is important to grok that the relative impact of each halving on the block subsidy is the same (block subsidy divided by two), but the absolute impact of each halving on the block subsidy decreases over time. For example, the fourth-annual inflation rate dropped by -50% in 2012, but then by -33.3% in 2016, -9.6% in 2020 and will drop by just -3.8% in 2024, -1.7% in 2028 and -0.8% in 2032. More simply put, the larger the percentage of bitcoin’s finite supply has already been issued, the smaller the impact of a change in the remaining issuance rate on the supply that is already circulating on the market.

Now that we have established that the block subsidy is literally designed to decay into oblivion over time, the final step is to understand when the halving of the block subsidy will indeed start to lose its relevance.

The way I see it, this probably won’t be attributable to a single point in time, but it will be a gradual process that will happen when transaction fees overtake the block subsidy as the primary source of miner revenue (figure 13). After all, the smaller the contribution of the block subsidy to the portion of the miner revenue becomes, the smaller the impact of halvings will be on the supply that is available for sale on the market.

How the death of the four-year cycle will impact Bitcoin’s future

When the earlier described process has progressed to a point where transaction fees have become the primary source of miner revenue and the four-year cycle has indeed decayed into irrelevance, it will impact Bitcoin’s future in several ways.

First, the decay of the four-year cycle would mean that pricing models that depend on the assumption of a halving-related market cycle being present will lose accuracy and, at some point, break. This would apply to the Bitcoin Price Temperature (BPT) and BPT Bands that were discussed earlier but also for the popular S2F and S2FX models. The big question regarding the latter; would those models break to the downside (e.g., via diminishing returns as long-term volatility declines) or to the upside (e.g., via a steepening adoption curve and/or hyper-inflation-like event)?

Second, as the percentage of bitcoin’s finite supply that has already been issued increases, the bitcoin price becomes an increasingly pure reflection of the market demand for bitcoin. This means that in a long-term post-halving-cycle future, cyclicality in Bitcoin will likely be more closely related to the actual economic activity of its market participants and thus their economic cycle (sometimes also called “business cycle”).

Third, if the bitcoin price increasingly becomes a pure reflection of the market demand for bitcoin, the likelihood of a dramatic exponential price rise past what we have seen so far increases. After all, due to the ever-decreasing supply issuance rate, demand for bitcoin has an increasingly direct influence on its price. With gold, large increases in demand can be answered by increasing the supply rate via additional mining, but this is not possible in bitcoin — making it the ultimate hard money. If Bitcoin were to reach mass adoption and follow a similar technology adoption curve to what we’ve seen in the use of the internet or mobile phones (figure 14), the likelihood of a “supercycle” happening in the bitcoin price increases (or a mixture between that and its traditional four-year cycle as a more fluid transformation). Something similar to this has also been described by Croesus_BTC in a June 2020 Twitter thread.

Fourth, another consequence of the absence of a four-year cycle as we know it could mean that the bitcoin price eventually becomes less volatile. As was recently pointed out in a note by JP Morgan, that development would be a positive for institutional interest in the asset, which would further validate it as a macro store of value.

Finally, if a healthy block space market will indeed kill bitcoin’s four-year cycle, it means that transacting on the Bitcoin blockchain will likely have become quite expensive. This means that in the future, most of us won’t be transacting via the Bitcoin base layer on a regular basis. More likely, the block space fee pressure will incentivize more effective batching of transactions (or, as Nic Carter put it during Baltic Honeybadger 2018, “container ships, not parcels,”) and broader adoption of layers (e.g., the Lightning Network) that have been built on top of Bitcoin’s base layer. In the future, most of us will probably primarily use the latter to interact with Bitcoin, aside from occasional lightning channel opens or closes or large transactions.

This article was originally posted on Bitcoin Magazine.

Special thanks go out to GeertJancap for the useful feedback on the draft of this article.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

Disclaimer: This article was written for informational purposes only and should not be taken as investment advice.

This article follows up on a previous one in which a metric was introduced that is being rebranded and expanded upon as the Bitcoin Price Temperature (BPT). The BPT metric will first be described in a more detailed manner, including the rationale behind the proposed causal mechanism of its 4-year market cycles, the interpretation of the BPT metric and its limitations. Thereafter, the BPT Bands concept is introduced and supported by several charts in which the indicator and its potential application are visualized.

Bitcoin’s 4-year cycle

When Bitcoin was launched, early network participants were rewarded 50 BTC for each new block that was created. Every 210.000 blocks, this ‘block reward’ is halved, gradually slowing down the supply issuance. Due to this built-in disinflationary monetary policy, Bitcoin has a strictly controlled and finite supply. After 33 halvings (~2140), the block reward will become lower than the smallest unit in the system (1 satoshi or ‘sat’, which is 0.00000001 BTC), topping off Bitcoin’s supply at a total of 20,999,999.97690000 BTC.

To ensure that blocks are created roughly every 10 minutes so that Bitcoin’s transaction capacity and supply issuance are relatively stable, a difficulty adjustment mechanism was built in. Every 2016 blocks (~2 weeks), the Bitcoin software checks to what extent new blocks have been created every ~10 minutes. If the average block time is lower, it increases the complexity of the random number that miners are trying to guess in order to win the rights to create the next block. Likewise, if the average block time is more than 10 minutes, the difficulty is adjusted downwards, making it easier for miners to create new blocks. If blocks are mined exactly every 10 minutes, the duration of one halving cycle is 4 years (210.000 blocks *10 minutes per block = 2.100.000 minutes, 2.100.000/60/24/7/52 = 4.00641 years). In practice, the average halving cycle duration was 3.8 years (1381 days) so far, as a result of the continuously growing network capacity (‘hash rate’).

A side effect of these halvings is that once every ~4 years, a supply shock is introduced to the market, abruptly lowering the amount of new supply that becomes available via mining. If the net demand for Bitcoin stays the same (e.g., people periodically buying Bitcoin as a savings vehicle or investment), this abrupt decrease in newly minted Bitcoin means that the only other way to acquire Bitcoin is by buying them from current holders. Since holding Bitcoin as a long-term store of value (also known as ‘hodling’) is such a popular theme under market participants, those Bitcoin may only become available at increased prices. The price increase on its turn leads to increased awareness that is typically accompanied with an increase in demand, throwing oil on the fire and creating manic market circumstances that lead to overheated prices (a feedback-loop known as ‘reflexivity’), often followed by a rapid decline and cool-down period. These mechanics have been eloquently and graphically described by @Croesus_BTC in this Twitter thread.

The chart of the Bitcoin price over the past ~10 years (figure 1) shows how the halvings so far were indeed always followed-up by exponential price growth and a subsequent cool-down period. The white line illustrates the daily price, whereas the black line depicts its moving average (using the to-date-available data the first four years), which is the mean price during a 4-year window. The 4-year moving average price is continuously going up, showing that on a four year time-frame, dollar cost averaging into Bitcoin has historically been beneficial at any time.

It is impossible to formally conclude that the halvings caused these overheated market conditions based on a sample of just 2 observations. However, the combination of the clear rationale for the potential causal mechanism and the matching price action make a compelling case that there might be more truth to this hypothesis than can currently be proven.

The most well-known attempt to more formally test the hypothesis that Bitcoin’s market value can be modeled based on its halving-induced scarcity is the Stock-to-Flow (S2F) model. In a previous article, I summarized all developments in the S2F and later introduced S2F cross-asset (S2FX) models, as well as their most prominent critiques. The models provide an interesting outlook for Bitcoin’s future price if the hypothesis that Bitcoin’s exponential growth is indeed a function of its gradually increasing scarcity. However, problems with the assumptions made by the statistical tests that were used in the S2F model analyses and the small sample size of the S2FX model prevented the emergence of broad consensus about the outcomes.

In the absence of such irrefutable proof, the predictions of these models are accompanied with a relatively broad uncertainty (margins). Therefore, there is still a need for indicators that more flexibly reflect to what extent current Bitcoin market prices are (ab)normal in the context of its own price history and volatility, particularly related to the 4-year market cycles. The Bitcoin Price Temperature (BPT) metric does exactly this.

Bitcoin Price Temperature (BPT)

The Bitcoin Price Temperature (BPT) is a measure for the distance between the current Bitcoin price and its 4-year moving average. The BPT is calculated by first calculating the difference between the daily price and its 4-year moving average, and then dividing that number by the standard deviation of that 4-year window (using the to-date-available data during the first four years). In R, the BPT can therefore calculated using the following formula:

btp[i] = (price[i] — mean(price[ifelse(i<1460, 0, (i-1460)):i]) / sd(price[ifelse(i<1460, 0, (i-1460)):i]

The BPT metric therefore reflects the number of standard deviations that a point deviates from the mean, which can technically be called a ‘Z-Score’ and is a common standardization method in multiple scientific disciplines.

Since the 4-year moving average represents the ‘normal’ price during a four year window, the BPT metric therefore reflects how (ab)normal the current price is in the context of its own 4-year price history. The BPT metric can therefore be seen as a temperature-check, where higher values represent potentially (over)heated price levels, and lower or even negative values suggest that those prices are relatively low based on a 4-year window. Figure 2 illustrates the BPT over time.

In figure 2, the blue (BPT=0) line represents the 4-year moving average. As is evident after comparing figures 1 and 2, the BPT makes it much easier to compare to what extent the different market cycles were similar than on the regular price chart. One of the more interesting findings is that the four most prominent market cycle tops (2011, 2x 2013 and 2017) peaked out soon after the Bitcoin price hit a temperature of 8 (red line), temporarily overshooting to temperatures of up to 12 before starting their steep descend back to ‘cool down’ all the way back to 0–1 . The orange (BPT=6) and green (BPT=2) lines also represent key price temperatures where the price trend changed its course on multiple occasions. It is good to note that there are no statistical reasons why these levels were highlighted in the figure above, but these were identified based on technical analysis, which has its limitations.

The similarity between the relative price action of the cycles becomes even more apparent in figure 3. The first period of Bitcoin’s existence (blue line) was special because the existing supply was relatively heavily diluted on a daily basis and Bitcoin didn’t have a formal market price in the used data (by Coinmetrics) during the first 561 days. Nonetheless, this period had its own manic market cycle and blow-off period right after Bitcoin received a market price, a pattern that so far has been repeating during each halving cycle.

It is important to note that the BPT is solely a backwards-looking metric and does not hold predictive powers. The visual representation of (the similarity of) the 4-year market cycles may make a compelling case that we are witnessing cyclically repeating market cycles here. However, there are no guarantees that these cycles will repeat, nor that they will be exactly similar to the previous cycles if the cyclicality itself does continue and future market tops reach similar relative price levels. Particularly the degree of euphoria during the manic part of the market psychology cycle is hard (if not impossible) to predict, since there are many more variables at play other than the time and halvings that are depicted here.

A fundamental argument against the hypothesis that these cycles are to repeat over-and-over again in the future, can be based on the notion that while the relative impact of each halving is the same (block reward / 2), the absolute impact of each halving on the block reward is decreasing (4-annual inflation rate dropping by -50%, -33.3%, -9.6%, -3.8%, -1.7%, -0.8%, etc.). Therefore, the impact of future halvings on the described supply-side liquidity shocks may gradually decrease. It is still possible that other factors (e.g., policy changes related to elections or cycles in traditional financial markets) may cyclically influence Bitcoin’s market cycle, but that those cycles don’t necessarily follow the same 4-year periods that we saw before.

However, the relative price action of the current 220-day old halving cycle (2020~2024) again shows remarkable similarities to the previous one (2016–2020). Figure 4 depicts the correlation between the BPT of these two cycles over time, where the color-overlay represents the statistical significance (green = statistically significant at p<0.05, red = not). Using the to-date-available data of the current and previous cycle, there is a high (r=0.77) correlation between the relative price movements of these two cycles.

It is impossible to proof that history will indeed repeat itself. Nonetheless, many Bitcoin market participants appear to have built some conviction in the assumption that the repetitive nature of these market cycles will continue in the foreseeable future. Therefore, using the BPT to monitor these relative price movements, as well as the expected price levels if the BPT were indeed to reach the key BPT levels of prior cycles again, may be useful. This brings us to the new concept of BPT Bands.

Bitcoin Price Temperature (BPT) Bands

Since the BPT values reflect the ‘temperature’ of the Bitcoin price, the metric can be useful as a color-overlay on the regular Bitcoin price chart. Additionally, it is possible to display the key levels that were identified above (or any other BPT level) on that same price chart, by simply multiplying the standard deviation by the BPT level (so 2*SD for BPT=2, 6*SD for BPT=6, etc.) and adding this to the 4-year moving average. The result is displayed in figure 5.

This BPT Bands visualization allows for several interesting observations:

• While the regular BPT chart was convenient for identifying potential price support and/or resistance levels (the key levels identified as the colored horizontal lines in figure 2), displaying them on the price chart (figure 5) emphasizes that if these BPT levels are reached again in a later cycle, it is done at a higher price due to the long-term upwards trend.
• As a result of the previous point, the chart illustrates that when a certain price level is reached again at a later point, the ‘temperature’ of that price tends to have cooled down significantly. For instance, when the Bitcoin price reached a near $20,000 price for the first time late 2017, its BPT was ~8. When it recently did so again in late 2020, the BPT was ‘just’ ~3, suggesting that the ~$20,000 all time high price level is much less abnormal at the time of writing than it was during the 2017 cycle top.
• The BPT Bands are similar to Bollinger Bands, the differences being that the BPT bands use a much larger (4 years) time window than is usually done with Bollinger Bands (20 days), as well as range up to a much larger number of standard deviations (up to 12 vs. 1–2) that is used. Furthermore, due to the combination of the large time-frame and the high volatility over that time period, the Bitcoin price is rarely in the negative BPT range, making the negative BPT bands of negligible use, unlike Bollinger Bands. Nonetheless like Bollinger Bands, the BPT Bands widen during periods with high volatility (e.g., a bull market) and contract during periods with low volatility.

This responsiveness to volatility is also one of the key differences between the BPT Bands and the Mayer Multiple bands, the 2-year MA Multiplier, the Golden Ratio Multiplier and similar moving average-based bands that are calculated by multiplying a certain moving average. The prices related to those bands gradually move up at a pace that is equal to the slope of the moving average itself. The slopes of the BPT Bands move up more steeply if the 4-year volatility increases, suggesting higher prices during volatile market conditions that may be more appropriate in that context.

Update September 20th, 2021: Thanks to Glassnode’s workbench feature, it is now possible to access live versions of the BPT and BPT Bands charts (figure 6) for free.

Update October 21st, 2021: The BPT & BPT Bands are now also featured on Glassnode Workbench itself.

Special thanks go out to Twitter user @Anoi30604540 for providing feedback on the developed charts, as well as for reviewing the draft of this article.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

The indicators that were introduced in this article are free to be replicated, used and expanded opon by others, as long as the author of and/or the link to this article is referred to. Future work could go out to developing a TradingView indicator for the BPT Bands (e.g., in a wider range from -2 to 12 so that the bands are more visible on more smaller time-frames) and/or a Python implementation of the R code that is available on Github, which can be used for more flexibly visualizing the BPT Bands on online chart platforms.

Disclaimer: This article was written for entertainment purposes only and should not be taken as investment advice.

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Bitcoin Price Temperature (Bands) was originally published in Coinmonks on Medium, where people are continuing the conversation by highlighting and responding to this story.

This article first addresses the Market-Value-to-Realized-Value (MVRV) Z-Score, an existing Bitcoin price metric that inspired the author to develop the new indicator that is introduced in this article. After briefly describing an alternative version of the MVRV Z-Score, the new Bitcoin Price Z-Score is introduced. The Bitcoin Price Z-Score is a relatively simple indicator that can be used to visually assess to what extent the current-day Bitcoin price is (ab)normal in comparison to its own price history. Additionally, the indicator is used to visually compare Bitcoin’s price development since this year’s halving event with those of the previous 4-year halving cycles.

Update 15–12–2020: This indicator has been rebranded as ‘Bitcoin Price Temperature (BPT)’ and expanded upon by using it as a color-overlay on the regular price chart, making it an ideal ‘thermometer’ to visually assess to what extent current prices are (over)heated or (under)cooled based on a 4-year time window. Additonally, the concept of BPT Bands was added. The more detailed follow-up article is available here.

Market-Value-to-Realized-Value (MVRV) Z-Score

The Market-Value-to-Realized-Value (MVRV) ratio was introduced by David Puell and Murad Mahmudov in late 2018. The MVRV ratio compares Bitcoin’s current market value (the number of coins in existence times the price per coin) with its realized value, which is the value of all existing unspent transaction outputs (UTXO’s) at the time when they were last moved. A week later, Awe & Wonder proposed the MVRV Z-Score, an alternative version where the MVRV ratio was divided by the standard deviation of the realized value. As a result, the MVRV Z-Score is even more expressive than the original MVRV ratio, clearly exposing historical market tops and bottoms. A live version of the MVRV Z-Score is publicly available on lookintobitcoin.com by Philip Swift and on woobull.com by Willy Woo.

While Awe & Wonder’s MVRV Z-Score is calculated using the appropriate formula, one can argue that it is not actually a Z-Score according to its formal definition. Traditionally, a Z-Score is calculated by subtracting the value of a variable with the population mean of that variable and then dividing that by the population standard deviation [z = (x — μ) / σ]. Awe & Wonder’s MVRV Z-Score uses the realized value as the population mean (μ) of the market value and its standard deviation as that of the population (σ). However, unlike for instance social or medical sciences that study large groups of humans, we don’t need to estimate the population mean and standard deviation, since we know Bitcoin’s actual full price and supply history and thus all of its past MVRV ratio values.

Therefore, an alternative way to calculate the MVRV Z-Score is to subtract the mean MVRV ratio of all previous values from each MVRV ratio in time, and then dividing it by the standard deviation of those historic values. The figure below illustrates the MVRV Z-Score version by Awe & Wonder (left figure) and the proposed alternative MVRV Z-Score version (right figure).

The original MVRV Z-Score by Awe & Wonder (left figure) describes how many standard deviations the market value differs from the realized value for any point in time. Since Bitcoin’s market value is almost always higher than its realized value, the original MVRV Z-Score is rarely negative. The proposed alternative (right figure) describes how many standard deviations each MVRV ratio value lies away from its own historical mean. As a result, the proposed alternative varies more between positive and negative values, and has a slightly different distribution than the original MVRV Z-Score.

However, is the proposed alternative also a more useful metric?

It would be if the actual MVRV ratio itself was the variable that the observer is interested in. However, that is not necessarily the case. For instance, the MVRV ratio at the time of writing is 0.09 standard deviations above its historical mean. This means that the difference between the current MVRV ratio and its own historical mean is slightly larger than is usually the case. While this clearly holds some potentially useful information about market behavior, it is arguably more useful to know to what extent the current market value is overheated or not — which is what the original MVRV Z-Score represented.

However, the relevance of the proposed alternative method to calculate the Z-Scores would be much more relevant if the actual Bitcoin price was used as the variable of interest — which is what the Bitcoin Price Z-Score is all about.

Bitcoin Price Z-Score

The Bitcoin Price Z-Score can be calculated for each point in time (“i”) by subtracting the mean Bitcoin price up to that time (“mean(price[0:i])”) from the respective price (“price[i]”), and then dividing it by the standard deviation of the Bitcoin price up to that time (sd(price[0:i]).

z[i] = (price[i] — mean(price[0:i])) / sd(price[0:i])

The Bitcon Price Z-Scores therefore represent the number of standard deviations that the price of any time point differs from its own historical mean. Perhaps a more simplistic way to think about this is to consider the mean price to be a moving average. A moving average is the mean value over the previous time period (e.g., 7 days, 200 days, 1 year, etc.), that changes as the time period that is used to calculate the mean (the ‘moving window’) changes. Since we’re using Bitcoin’s entire price history in this calculation, this version of the Bitcoin Price Z-Score essentially looks at the relative difference between a Bitcoin price and its ‘infinite moving average’.

The Bitcoin Price Z-Score therefore can be useful as an indicator to determine how (ab)normal the Bitcoin price is in comparison to its own price history. The further away from the mean (a Z-Score of 0) a value is, the more abnormal it is based on its price history. The figure below shows a time series plot of this ‘infinite moving average’ version of the Bitcoin Price Z-Score. The striped green (Z-Score 1), orange (6) and red (11) lines were placed by the author because they visually appear to be interesting from a technical analysis perspective, and are thus arbitrary.

Thanks to the applied Z-Scores, the relative price changes during the past market cycles have become quite comparable. The first cycle was a bit different to the later cycles due to Bitcoin’s immaturity and short price history, but the 2013 double tops and the late 2017 market top have very similar Z-Scores of 11 to 12. Based on this chart, the abnormality of the Bitcoin price increase at the 2017 top was similar to that of the first 2013 top.

At the same time, the current November 2020 price rush to the near all time high (ATH) prices of that same late 2017 top yielded a much lower (~4) Z-Score than during that actual 2017 top (~12). This chart therefore illustrates that the current near-ATH prices are much less abnormal now than those same prices were in late 2017. You can therefore argue that the chart also implicitly visualizes a Lindy effect in the Bitcoin price; the more time price spends at an increased price level, the more normal it becomes.

However, the gradually increasing bottoms are less ideal when you would also like to use this indicator to identify possible market bottoms. After December 22nd, 2011, the Bitcoin Price Z-Score actually never drops below 0 again, and the market bottoms of 2015 and 2018–2019 become slightly higher than the previous cycle every time so far.

Luckily, there’s a logical explanation and possible solution for this. Since we’re using all of Bitcoin’s previous price history as a comparison, that price history becomes longer at every time point, giving the previous values with lower prices more and more weight in the equation that we’re using here. As can be seen in the logarithmic price chart below, Bitcoin’s price also tends to move away from the ‘infinite moving average’ (red line) that we’re using here.

Unfortunately, this chart did spoil the solution to our problem; using a 4-year moving average window might be more appropriate. The Bitcoin software programmatically halves the new coin issuance that is given to miners as a reward for their efforts when a new blocks is found every 210.000 blocks (the striped vertical lines), which happens roughly every four years (210.000 blocks *10 minutes per block = 2.100.000 minutes, 2.100.000/60/24/7/52 = 4.00641 years). As a result, a periodically repeating supply shock is introduced, which has been followed up by a parabolic price increase every time so far.

Although it is tricky to conclude that that the halvings indeed caused these ~4-year cycles based on such a small sample (n=2.125), a good case can be made that it is more appropriate to use the 4-year moving average when calculating the Bitcoin Price Z-Score. The figure below therefore uses the same method as before to calculate the Z-Scores, but with a tweak: it uses the to-date-available data the first four years, and only uses the 4-year moving window data after that. The code that was used for this calculation (as well as all other analyses described in this article) are available on GitHub.

As expected, the market bottoms are now more comparable, with each cycle bottoming out around the 4-year moving average (a Z-Score of 0; the green line). The last time this version of the Bitcoin Price Z-Score was below zero was on March 16th, 2020, which was the day after the Covid19 global market panic, where Bitcoin’s price crashed by ~50% in two days. The 2017 market top is now slightly less abnormal in comparison to the 2013 double tops, but the 2011 market top is more similar to the others. Intuitively, these proportions seem to be more appropriate than those in the initial version.

As mentioned before, the colored lines in the chart were arbitrarily chosen because they appear to be related to previous market cycle tops. This chart and method have no predictive powers and there are no guarantees that the Bitcoin Price Z-Scores will necessarily reach any level again in the future. However, if you assume that the 4-year cycles will repeat, it is possible to calculate what current-day prices would be needed to reach those Z-Scores:

• Yellow line (Z-Score 6): $38.220,88
• Orange line (Z-Score 8): $50.961,17
• Red line (Z-Score 11): $70.071,60

However, it is unrealistic to expect the Bitcoin price to move towards those levels overnight. If the Bitcoin price is indeed to reach those levels, a more likely scenario is that it gradually increases towards those levels, possibly with a parabolic rise to reach the actual market top like it did during the previous cycles. In such a scenario, these predicted price levels will also gradually increase over time and need to be recalculated using that future data.

Since the use of Z-Scores improves the comparability between the cycles and we assume that those 4-year cycles are related to the halving events, it might be interesting to assess to what extent the price developments of those cycles are indeed similar. To do so, the figure below overlays the price developments of the Bitcoin Price Z-Scores of each halving epoch.

The first epoch was clearly quite different from the others. Since Bitcoin’s inception on January 3rd, 2009, it took over 1.5 years before the first US dollar price was captured — at least in the freely available Coinmetrics Community data that was used here. Aside from the obvious fact that the newly-born Bitcoin network needed a bit of time to mature and develop an actual market, the lack of price history in those early days itself also provides a clear statistical reason why it was relatively hard to get high Z-Scores there. After four years (~1.5 years into the 2nd epoch), this is no longer an issue, since a 4-year moving window was used after that. Therefore, particularly the third and this fourth epoch will be optimally comparable.

The second, third, and so far this start of the fourth epoch are actually relatively similar. As can be seen in the chart, the current Z-Score (right end of the purple line) is really close to the Z-Scores of the 203 day post-halving Z-Scores of the previous two cycles. Bitcoin’s current price developments therefore appear to be in line with those of the previous cycles so far.

Update 15–12–2020: This indicator has been rebranded as ‘Bitcoin Price Temperature (BPT)’ and expanded upon by using it as a color-overlay on the regular price chart, making it an ideal ‘thermometer’ to visually assess to what extent current prices are (over)heated or (under)cooled based on a 4-year time window. Additonally, the concept of BPT Bands was added. The more detailed follow-up article is available here.

Follow Dilution-proof on Medium or Twitter to be notified of future updates.

Disclaimer: This article was written for entertainment purposes only and should not be taken as investment advice.

The indicators that were introduced in this article are free to be replicated, used and expanded opon by others, as long as the author of and/or the link to this article is referred to. The code used for the charts and analyses in this article are publicly available on GitHub.

Introducing the Bitcoin Price Z-Score was originally published in The Startup on Medium, where people are continuing the conversation by highlighting and responding to this story.

A little more than one year ago, a Dutch investor that chose to publish his Bitcoin-related work under the pseudonym PlanB published an article in which he introduced the Bitoin Stock-to-Flow (S2F) model. Since then, the model became very popular and a lot has happened. After several independent reviews that provided additional evidence, the relationship between Bitcoin’s value and scarcity was considered provably non-spurious. Recently, those conclusions were shown to be flawed, and a new model that overcomes these flaws was introduced. This article attempts to provide an overview of these developments and breaks down the complex econometric nuances in an easy to understand fashion.

Scarcity

When you ask someone what makes Bitcoin valuable, “there will never be more than 21 million bitcoin” or “you can’t print more of them” are common answers — particularly in times where central bank’s are printing unlimited money. According to certain Austrian Economic theories, scarcity is one of the monetary properties (along with divisibility, durability, portability and recognizability) that gives money value. As Robert Breedlove argues in “The Number Zero and Bitcoin”, Bitcoin even achieves absolute scarcity, a property that is only feasible in the digital domain.

Although the idea of scarcity being a key aspect in Bitcoin’s value proposition has been there since the whitepaper was published, finding an appropriate quantifiable proxy to measure scarcity was less obvious. Inspired by a segment of the book “The Bitcoin Standard”, where author Saifedean Ammous described the scarcity of gold in terms of Stock-to-Flow (S2F) ratio, Plan B decided to explore if a S2F ratio of Bitcoin could be used to model its price.

Stock-to-Flow (S2F) ratio

The S2F ratio is calculated by dividing the stock (the total supply) by the flow (the new production) of an asset. In Plan B’s article, he described gold’s stock to be 185.000 tons, and its flow to be 3.000 tons per year. Hence, gold’s S2F ratio at that time was 185.000 / 3.000 = 61.67, or 62 when rounded up.

However, the S2F ratio of gold fluctuates over time (figure 1). When the gold price is relatively high, gold mining is more viable, incentivizing miners to do so. As a result, the flow increases and S2F ratio decreases. When the gold price is low, mining is less viable, especially in less efficient mines with a high production cost. If these close down or reduce their production, gold’s flow decreases, increasing its S2F ratio again.

Unforgeable costliness

The idea that an asset like gold is difficult to obtain or forge is known as unforgeable costliness, a term that became related to Bitcoin thanks to Nick Szabo, the creator of Bit Gold (a Bitcoin-predecessor). Besides gold (S2F ~62) and silver (S2F ~22), there are few monetary assets that can reliably be expressed in terms of S2F ratio and are considered to be unforgeably costly.

Other metals like palladium (S2F 1.1) and platinum (S2F 0.4) are also relatively rare and difficult to obtain, but are mostly used in industrial production. Their worldwide supply is relatively low in comparison to their yearly production, which means that its producers can have a large influence on the market price by in- or decreasing production, making these assets less optimal to use as a monetary asset.

Bitcoin’s predictable supply issuance

In Bitcoin, the threshold to start mining Bitcoin is very low. Anyone with spare computational power and a power-plug can join the rat-race to be next in line to create a new block and be rewarded in newly minted coins and transaction fees. Due to the competition that has built up over the years it is very difficult to do so profitably, but in essence the network is open for anyone to join.

However, if anyone can just create their own printing-press and start mining Bitcoin, why isn’t its S2F ratio blown to smithereens?

We need to thank Adam Back for this. In 1997, Back introduced the concept of Proof-of-Work (PoW) with Hashcash, a system designed to limit e-mail spam and denial-of-service attacks. Due to a built-in mechanism called ‘difficulty adjustment’, a PoW system periodically adjusts the difficulty of the random number that miners need to guess by adding or removing one or more digits.

In Bitcoin, this difficulty adjustment happens every 2016 blocks, which is about 2 weeks (assuming 10 minute block-intervals). When too much computational power is added to the network and new blocks are found faster than intended (1 block per 10 minutes), the difficulty increases. Miners then need to spend more resources to earn the same reward, incentivizing less-efficient miners to leave the network. Conversely, when miners leave the network and blocks are created slower than expected, the difficulty decreases, giving miners leeway to resume their activities. Thanks to this nifty difficulty adjustment system, Bitcoin’s stock and flow are quite predictable over time.

Bitcoin’s predictable stock and flow

When Bitcoin was launched on January 3rd, 2009, miners received 50 bitcoin mining reward (also called ‘coinbase’; not to be confused with the eponymous exchange) per created block. Every 210.000 blocks (~4 year, assuming 10 minute block-intervals), this reward halves. After the first halving (November 28th, 2012) miners received 25 bitcoin, after the second halving (July 9th, 2016) 12.5 and since the last halving (May 11th, 2020) they receive 6.25.

While we don’t know exactly when blocks are mined, Bitcoin’s stock and flow are completely predictable on a per-block basis (figure 2).

As a logical result, Bitcoin’s S2F ratio can be calculated at any point in time. According to Clark Moody’s dashboard, Bitcoin currently has a S2F ratio of 55, making it almost as scarce as gold. After the 2024 halving, it will surpass that of gold, making it the most scarce monetary asset in the world in S2F ratio terms.

If you have understood this explanation so far, you’ve grasped Bitcoin’s most prominent value proposition (censorship-resistance being another) — with or without the S2F model.

Nonetheless, Plan B tried to take it one step further by attempting to prove that the first-principles based hypothesis that Bitcoin’s price increase can be attributed to it’s ever-increasing relative scarcity is correct by using mathematical models — and thus predict its future price.

The Bitcoin Stock-to-Flow (S2F) model

On March 22nd, 2019, PlanB published “Modeling Bitcoin Value with Scarcity”. To visually assess if bitcoin scarcity, measured in S2F ratio, is indeed related to price, Plan B plotted both on a logarithmic scale. On a logarithmic scale, the distance between 1 and 10 is the same as between 10 and 100, between 100 and 1000, etcetera, making it useful to determine relative price changes.

When S2F increases, so does its market value, as all dots line up in a diagonal line (left graph in figure 3). This is called a ‘linear relationship’ and can be tested using statistical techniques (e.g., based on ‘ordinary least squares’, or OLS). Like the graph suggested, the relationship between Bitcoin’s S2F ratio and market value was indeed significant. According to this model, 94.7% of the historical bitcoin price can be explained by its S2F ratio. Plan B used the S2F ratio and market value of silver (grey dot) and gold (yellow dot) to cross validate the model. The fact that both lined up well with the modeled price was an early sign that this relationship might apply across assets as well.

Since the S2F ratio of Bitcoin can be estimated in in the future, the bitcoin S2F ratio and price can be plotted on a time chart (right graph in figure 3). Despite Plan B rounding down the parameters of the model, it predicted a $55.000 per bitcoin price after the 2020 halving. When Plan B published his article, the bitcoin price was $4.000 and was just recovering from a big price drop.

Over the next few months, several other versions of the S2F became available. These models used slightly different data (e.g., daily instead of monthly, or a different time window) and thus predicted different future prices. The version of the S2F model that became widely popular predicted a bitcoin price of around $100.000 after the May 2020 halving (figure 4).

Although many Bitcoin proponents were ecstatic about the model’s optimistic price predictions, there also were critiques.

It is ‘priced in’

One of the recurring critiques about the S2F model is that since Bitcoin’s supply schedule has been publicly known since its launch, it must be ‘priced in’, as the Efficient Market Hypothesis suggests. According to PlanB, markets are indeed fairly efficient because easy arbitrage opportunities are no longer available. Nonetheless, he thinks markets are structurally overestimating risk, leaving room for the S2F model to be useful as a valuation tool in investing.

Demand is missing

Another recurring comment is that price is a function of supply and demand — and that demand is missing from the S2F model. While this statement is technically correct, it misses the point that statistical models are by definition a simplification of reality and are never 100% accurate, but can still be useful if they are accurate enough. As statistician George Box once put it:

“All models are wrong, but some are useful.” — George Box

Despite demand not being included in the S2F model, the fact that it accounts for almost 95% of the variance in the bitcoin price suggests that it is accurate enough to be useful…. or is it?

Spurious correlations

High correlations like the one we saw in the S2F model are more common than you might expect. Particularly in time series that are both trending in the same direction, finding a high correlation between two variables that have absolutely nothing to do with each other can happen (e.g., see figure 5).

The possibility of the S2F model’s results possibly being spurious was also addressed in a July 2019 review article by a Dutch econometrician called Marcel Burger. In the article, Burger replicated the S2F model and tested whether the model met the needed statistical requirements needed to use those techniques. Burger found flaws related to the model’s underlying assumptions, and suggested that the model should be improved upon.

The rise of cointegration

In an August 11th 2019 publication, phraudsta, an Australian statistician, picked up where Burger left off. phraudsta’s work improved upon the original S2F model by applying a different statistical technique (a Vector Error Correction Model) to overcome the statistical limitations that were identified by Burger. More importantly, phraudsta found that Bitcoin’s S2F ratio and price are ‘cointegrated’, which means that the identified long-term relationship between the two is actually not spurious.

To explain what cointegration entails, phraudsta used an analogy about a drunk walking his dog. Imagine them strolling around, both occasionally going in different directions but remaining in close proximity due to the leash that connects them. Here, the drunk and his dog are ‘cointegrated’; they are connected and will both end up in the same place — wherever that may be.

The opposite would be true if a drunk is on his way home, and a stray dog crosses his path. Both stroll around together for a bit, but this relationship proves to be meaningless if a car drives by and scares the dog away.

In his conclusion, phraudsta suggests that this analogy needs to be changed to apply to the Bitcoin S2F model. Since the S2F ratio variable is actually rather constant, unlike the drunk or his dog, it would be more appropriate to consider Bitcoin’s price to be the drunk and S2F ratio to be the road home.

Shortly after, in September 2019, Marcel Burger replicated phraudsta’s findings. Later that month, a German senior analyst at BayernLB, Manuel Andersch, did the same. After these confirmations, the S2F model was broadly considered to be statistically valid and became even more popular.

Structural breaks

In March 2020, Bitcoin Elf suggested phraudsta to explore if the Bitcoin halvings should be seen as ‘structural breaks’ in the S2F ratio time series. Around the same time, Marcel Burger published an article in which he referred to an academic publication that also covered this topic.

According to that article, a structural break “is a sudden jump or fall in an economic time series which occurs due to the change in regime, policy direction, and external shocks, among others”. Figure 6 illustrates some examples of structural breaks. If these images didn’t already remind you of the increases in S2F ratio after the Bitcoin halvings, they should.

In the article “Stock-to-Flow Influences on Bitcoin Price”, phraudsta applied statistical tests to conclude that the halving events should indeed be seen as structural breaks and need to be accounted for. However, when the effect of the halving events is removed, the S2F variable loses much of its trend. Temporary fluctuations in coin issuance that are corrected for on a two-weekly basis via the difficulty adjustments are then the only remaining source of variance in the S2F variable (figure 7).

phraudsta continued by testing if the S2F variable is ‘stationary’ (without trend) or ‘non-stationary’ (with trend). After removing the effect of the halving events from the S2F variable, it no longer has a long-term trend and becomes ‘stationary’, unlike the bitcoin price that is clearly ‘non-stationary’. In a stationary process, the values can go up and down over time, but stay around a mean (figure 8, top graph). In a non-stationary process, the values also go up and down, but don’t revert back to the mean (figure 8, bottom graph).

While this may seem like a small and overly detailed statistical discussion, its domino effect is rather large: the finding that Bitcoin’s S2F ratio is stationary and price is not means that the cointegration test should not have been applied. Subsequently, this means that it is no longer proven that the relationship between S2F ratio is not spurious. While this doesn’t statistically invalidate the S2F model itself and also doesn’t mean that the relationship between S2F ratio and price is spurious, it re-introduces uncertainty. After all, if the relationship possibly is spurious, it means that there’s no reason why the bitcoin price couldn’t deviate from the S2F ratio trend at any time.

After phraudsta’s article, there was a lot of discussion on this topic. Bitcoin’s S2F ratio was used in the model as a measure of scarcity and the halving events clearly were designed to be the heart and soul of Bitcoin’s long-term scarcity. If you remove the S2F variable’s most important scarcity-component, it seems like you might be missing the plot if you use its remains to test if ‘scarcity drives price’. Is this really necessary?

The bitcoin price as a random walk

A presentation at the Value of Bitcoin conference on May 12th by Sebastian Kripfganz, an assistant professor at the University of Exeter that is an expert in econometric time series analysis, threw fuel on the fire.

In his presentation, Kripfganz described that the effect of the halving events on the S2F ratio’s time series indeed needs to be accounted for, but with a different explanation: because it is deterministic. Kripfganz didn’t explain this with much detail. For him it seemed a fact of life; you simply cannot use a deterministic variable in these time series analyses. The implications are the same as we saw in phraudsta’s analysis: after accounting for the halvings, Bitcoin’s S2F ratio is stationary, making cointegration analysis impossible.

Kripfganz continued by using a different statistical technique (an Autoregressive Distributed Lag or ARDL model) to test if the long-term bitcoin price can be modeled nonetheless. Kripfganz concluded that neither Bitcoin’s S2F ratio or the halving effects explained the long-term bitcoin price, and that it could be best described as a ‘random walk with drift’ from a statistical perspective. This means that while Bitcoin’s price trends upwards so far, it is essentially a ‘random walk’, which means that it could go anywhere.

While Kripfganz’s analysis was highly respected, the necessity of needing to remove the effect of the halving events in the S2F ratio variable because it is deterministic wasn’t immediately well understood. Doesn’t this again take out the essence of what made S2F ratio an interesting proxy for scarcity in the first place, causing us to throw out the baby with the bath water?

The fall of cointegration

An article published on May 20th by Marcel Burger provided clarity on the ‘determinism-debate’ started by Kripfganz. Burger dove deep into academic literature on time series analysis dating back to 1938 and concluded that Kripfganz was right. The cointegration analysis that was performed can only be applied on time series without a deterministic component.

Why you cannot use a time series with a deterministic component is an even deeper and more complex rabbit-hole in statistics. The implications are rather simple though: if you play a game, you have to adhere to its rules. In this case, you cannot use a statistical method to prove something that it cannot test.

Like phraudsta did before him, Burger concluded that in hindsight, the methods of his prior cointegration analysis were improperly applied, invalidating his prior conclusion that Bitcoin’s S2F ratio and price are cointegrated. Burger emphasized that this doesn’t mean that the relationship between between Bitcoin’s S2F ratio and price is spurious and that the S2F model is useless, just that we are now less certain that they aren’t.

After his presentation, Kripfganz mentioned that scarcity could still play a role in the upwards trend (the drift) that he identified in his model, but that it would be impossible to prove that it does from a statistical perspective. This suggests that we have reached the limits of what is statistically possible to prove with the time series analysis methods that are available today.

However, phraudsta disagrees that it would be impossible to prove that S2F ratio and market value are related altogether and implies that using cross asset information could be a way to overcome the limitations of time series analysis (figure 9).

The Bitcoin Stock-to-Flow Cross Asset (S2FX) model

On April 27th, a few weeks before the discussion on cointegration peaked, PlanB already introduced the Bitcoin Stock-to-Flow Cross Asset (S2FX) model that phraudsta hinted at. Like the title suggests, the model is based on data from multiple assets by introducing data from silver and gold to the equation. By doing so, the new model is no longer a time series, since the used datapoints are no longer lined up in a time-ordered fashion.

Deterministic or not, Bitcoin’s S2F ratio as originally defined by Plan B clearly increases over time. To create a cross asset model, which time-point do you use as the datapoint for Bitcoin? Could it be that the monetary properties of Bitcoin changed over time, as Bitcoin gradually became adopted?

Phase transitions

Plan B explored this from the viewpoint of phase transitions. A classical example is that of water, which transitions from a solid form to liquid, gas and eventually ionized when its temperature increases. Plan B went on to describe that you can argue that the dollar also underwent phase transitions. The dollar originally was a gold coin, then transitioned into a silver coin, a gold-backed piece of paper and since 1971 a piece of paper backed by nothing.

In July 2018 Nic Carter and Hasu published “Visions of Bitcoin — How major Bitcoin narratives changed over time”, in which they describe how the way Bitcoin is being described has changed over time (figure 10).

According to Plan B, these can be merged in four overarching phases:

1. Proof of concept: immediately after the launch of the network.
2. Payments: after bitcoin reached USD parity (1 BTC = $1).
3. E-Gold: after the first halving, when bitcoin approached gold parity (1 BTC = 1 ounce of gold).
4. Financial asset: after the second halving, when bitcoin reached the $1 billion transaction volume per day milestone.

Bitcoin clusters

Based on these four phases, Plan B applied an algorithm to identify four clusters of monthly bitcoin datapoints. The centers of these clusters (the yellow, orange and red dots in figure 11) represent the datapoints that will be used in the statistical modeling. These datapoints are complemented by two more datapoints for silver (the grey dot) and gold (the gold-colored dot).

Using the same method as for the original S2F model, Plan B found that the model explained 99.7% of the variance in the six cross asset datapoints. Compared to the S2F model, the S2FX model has a higher explained variance and is even more optimistic about the future price, as it predicts a price of around $288.000 per bitcoin in the current halving period (2020–2024)

Is six datapoints enough?

The S2FX model was well received, but received critical notes as well. The most-heard discussion was about whether or not creating a model based on just six datapoints would be robust enough. Due to the low number of datapoints, the model’s parameters and thus predictions could change when more datapoints are added.

For Plan B the results based on these 6 datapoints were indeed enough to convince him that there indeed is a relationship between S2F ratio and market value. As a counterargument against the critique, he calculated the probability of finding 99.7% explained variance with just 6 random datapoints, and that chance is indeed very low (figure 12).

Estimating the ‘Phase 5’ bitcoin price

In phraudsta’s May 7th article “S2FX — Phase 5 Estimations”, he reproduces the S2FX model and calculates margins of uncertainty around the predicted price. With his version of the S2FX model, phraudsta finds a predicted price that is a bit higher ($350.000) than Plan B’s predicted price. While S2F ratio is statistically a very significant predictor of price, the margins of uncertainty around the predicted price are rather large due to the small sample size. According to phraudsta’s calculations, the predicted price for Phase 5 could be anywhere between $83.000 and $1.480.000 (figure 13), while the actual price could further deviate from that predicted price as well.

Other critical notes

One can also question if it is indeed appropriate to split the Bitcoin data up into four different assets and assume those to be independent datapoints. After all, the bitcoin clusters are being formed in a time-contingent manner — otherwise, predicting the fifth phase wouldn’t be possible.

Finally, if you do consider this clustering method to be appropriate, you can still wonder if four is indeed the right number of clusters. Due to the clearly upwards trending price in relation to the S2F ratio an adjustment of the latter will likely still lead to the conclusion that there is a significant relation between the two, but the model’s predicted price could change as a result.

Like Plan B noted in his article, the model ideally needs to be expanded by adding more assets. The theory would be strengthened if it can be proven that there is a relationship between S2F ratio and market value of monetary assets without using Bitcoin data to create the model, and only use Bitcoin as a benchmark. While this sounds nice in theory, it is much harder to apply it in practice, as appropriate assets to use are actually quite scarce.

Does the S2FX model also work for the housing market?

On May 2nd Peter Harrigan, CEO of Grey Swan Digital and former trader at CME, did a first attempt at to extend the cross asset model. In his article “Bitcoin Stock-to-Flow Cross Asset Model Works Well on Housing”, he explores adding another asset class (housing) to the S2FX model. Like the title of his article suggests, this addition appears to rhyme well with the S2FX model.

Based on a detailed calculation, Harrigan determined the S2F ratio and market value of the American housing market in the context of ‘square footage’ and ‘value added’. These two new datapoints appear to align well with the predicted market value estimated by the S2FX model (Figure 14).

Plan B is currently looking into doing a similar analysis to add diamonds and European housing market data to the S2FX model, and has already shared an early indication that at least the latter seems to agree with the model as well.

Final note

Adding more assets to the S2FX model and validating the accuracy of the used data sources should be a main focus in future research. While doing so would likely strengthen the robustness of the model, it could also cause the model’s predicted valuations to change. It is therefore important to realize that one should be cautious in accepting the exact valuations that are predicted by the discussed models and approach this work more as a growing body of evidence that tests the fundamental value proposition that scarcity drives value.

Special thanks go out to Manuel Andersch, Plan B and Guy Swann, who provided feedback during the writing process.

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Disclaimer: This article was written for entertainment purposes only and should not be taken as investment advice.

Modeling Value Based on Scarcity was originally published in The Startup on Medium, where people are continuing the conversation by highlighting and responding to this story.