Long-Term Bitcoin Valuation: Stock-To-Flow Model Metcalfe’s Law and Crypto Asset Valuation

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Amsterdam Business School

Long-Term Bitcoin Valuation: Stock-To-Flow Model Metcalfe’s Law and Crypto Asset Valuation

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Bachelor Thesis

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Bachelor Economics and Business Economics Specialization Finance

Denis Oevermann

denis.oe@gmx.de

June 2021

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Statement of Originality

This document is written by Denis Oevermann who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

The thesis investigates long-term Bitcoin valuation with the Stock-to-Flow model and Metcalfe’s Law. The long-term explanatory power of the models on bitcoin’s price is tested through time-series regression analysis, using logarithmic regression models. The analysis is extended to 32 further crypto assets from all cryptocurrency sectors. The Stock-to-Flow model is highly significant and suited for predicting the long- term price of bitcoin. The model is extrapolated to project future confidence intervals for bitcoin’s price.

The Stock-to-Flow model estimates a tenfold in Bitcoin’s market valuation for every halving, caused by a doubling in the Stock-to-Flow ratio. Metcalfe’s Law is highly significant and suited to model Bitcoin’s long- term network valuation. Short- to medium-term prices of bitcoin deviate from long-term model prices.

Both models show that bitcoin at $36,000 is currently undervalued. The Stock-to-Flow model is not applicable to any type of crypto assets, including Bitcoin hard forks. Metcalfe’s Law is applicable to selective cryptocurrencies, with the majority being ecosystem, exchange, and payment crypto assets.

Decentralized finance digital assets and privacy tokens were not found to follow Metcalfe’s Law.

Keywords: Bitcoin, Cryptocurrency, Stock-to-Flow Model, Metcalfe’s Law, Bitcoin Valuation, Crypto Asset Valuation, Digital Asset Valuation, Cryptocurrency Valuation, Altcoin Valuation

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1 Introduction

“A purely peer-to-peer version of electronic cash”(Nakamoto, 2008) is how the anonymous Bitcoin inventor Satoshi Nakamoto describes the idea behind Bitcoin(BTC), the first digital cryptocurrency. Since then the cryptocurrency market was the center of a lot of hype and FOMO, fear of missing out. The most recent big and groundbreaking announcement is El Salvador making bitcoin legal tender on June 9, 2021(De, 2021). The first bitcoin transaction and ever recorded price of roughly $0.0008 per bitcoin occurred when two pizzas were bought by programmers on May 22, 2010, for a total of 10,000 bitcoins.

This became the famous “Bitcoin Pizza Day”, and the bitcoins spent are valued at a staggering $613 million as of March 2021(Tayeb, 2021). Such a tremendous growth requires proper valuation techniques, especially over the long-term, which will be investigated and analyzed throughout this thesis.

Over the course of the years, Bitcoin went through multiple cycles of boom and bust, and the classifications of Bitcoin range from asset, to currency to total rejection for any form of investment.

Famous economist Nouriel Roubini called Bitcoin the “mother of all scams”(Rooney, 2018), legendary value investor Warren Buffet is convinced that it is “rat poison”(Kim, 2018) and Charlie Munger says it is

“disgusting and contrary to the interest of civilization”(Li, 2021). On the other hand the world-renowned hedge fund manager and billionaire Ray Dalio owns “some Bitcoin”(Lewitinn, 2021), while the CEO of MicroStrategy, Michael Saylor decided to convert the majority of the corporate treasury into bitcoin for a total of over $1 billion(MicroStrategy, 2020). Despite strong polarization amongst those that believe in Bitcoin and those that cannot see any intrinsic value in it, the real problem to solve is how to determine the value of Bitcoin and other cryptocurrencies.

The importance of the need for proper valuation techniques to assess how much, if any, value can be assigned to cryptocurrencies is reinforced by looking at this new asset class in aggregate. While starting out small with an initial recorded market capitalization of $1.7 billion, with a Bitcoin market dominance of over 95%, in April 2013, the cryptocurrency market grew to over 10,000 different cryptocurrencies and digital assets as of May 2021 (coinmarketcap.com), valued at a total of $2 trillion. Nevertheless, despite this immense development in just barely a decade, when putting cryptocurrencies into perspective it is still a relatively small and undeveloped market. Bitcoin has a $1 trillion market cap, less than a tenth that of the entire gold market at $12.8 trillion. The global real estate market is valued at around $280 trillion, global equities and debt markets at $90 trillion and $130 trillion respectively(Desjardins, 2020).

While the primary focus and demand seem to head for the leading crypto asset, Bitcoin, a multitude of diverse and different crypto assets emerged, each bringing their individual set of functions

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and characteristics. Whereas Bitcoin is capped in supply at a total of 21 million bitcoin to be mined, second largest digital asset and smart contract ecosystem Ethereum does not have a finite supply. Traditional, Nobel-prize winning asset pricing models, such as the single-factor CAPM model(Sharpe, 1964) or the Fama and French three-factor model(Fama & French, 1993) and five-factor model(Fama & French, 2015), seem to not be applicable for the valuation of Bitcoin and digital assets.

It is widely acknowledged that traditional models are not suited and in fact “intrinsically and absurdly inaccurate”(Shiller, 2017) to value Bitcoin and cryptocurrencies or to assign fundamental value to them. Nevertheless, a wide spectrum of alternative approaches have been developed, such as a cost of production model(Hayes, 2017), measuring the electricity costs to mine bitcoin, or analysis of on-chain holding duration of bitcoin, including its network size and active addresses, constituting individuals holding the digital asset(Cipolaro & Stevens, 2020). The most interesting approach adopted from traditional assets, to model their scarcity, is the Stock-to-Flow model(S2F). Modelling Bitcoins’ value through scarcity(PlanB, 2020a), the model predicts an average price of $288,000 per bitcoin for the current halving cycle of 2020-2024.

Which models are most suited to value Bitcoin in the long-term, and potentially alternative digital assets as well, is the main goal for this thesis. Given the multitude of digital assets and their varying characteristics, the aim is to establish valuation models that work with Bitcoin and test whether they can be applied to further cryptocurrencies and digital assets with similar, and different attributes. The focus lies with the Stock-to-Flow model(PlanB, 2019), striving to confirm its validity and introducing it into an academic context first-time. The known characteristics of Bitcoin are used to project future price ranges.

The second method is the valuation of Bitcoin as a network, through Metcalfe’s Law(Peterson, 2017), similar to how certain technology and internet companies can be valued. Beyond that, Metcalfe’s Law is used to model future bitcoin price projections. The time frame for this analysis spans from 2010 until 2021, including over a decade of data. The Stock-to-Flow model and Metcalfe’s Law will be applied to 32 further crypto assets, including cryptocurrencies from all sectors and functionalities. This strives to evaluate the extent of the explanatory power of the two models and introduce possible valuation techniques for cryptocurrencies.

The thesis is structured in the following manner: Part 1.1 gives a brief overview and introduction of the cryptocurrency market, used terms, mechanisms, technology and important characteristics of Bitcoin itself; Part 2 reviews the current leading literature and scientific findings on the topic of Bitcoin and crypto asset valuation; the hypotheses and research question are presented in Part 3; Part 4 continues with the applied methodology and data used; the analysis and results will be explained in Part 5 for the

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Stock-to-Flow model, and Part 6 for Metcalfe’s Law, while Part 7 will extrapolate the valuation methods and models to other cryptocurrencies and digital assets; the discussion of the findings and results of the thesis is in Part 8; Part 9 is the thesis’ conclusion.

1.1 Introduction to Bitcoin and Cryptocurrency Market – Theoretical Background

To fully analyze Bitcoin and cryptocurrencies with the Stock-to-Flow model and Metcalfe’s Law, several clarifications must be made.

Cryptocurrency refers to all types of coins and tokens that exist on the blockchain in form of a distributed, decentralized ledger, with varying degrees of decentrality. Cryptocurrencies that are not Bitcoin are referred to as digital assets, crypto assets, and altcoins.

There is a multitude of diverse cryptocurrencies with their functionality ranging from payments and currencies; smart contracts, infrastructure and ecosystem; exchange and platform token;

interoperability and data querying; decentralized applications(dApps); decentralized finance(DeFi) for lending, borrowing, stablecoins, yieldfarming, swaps, derivatives, synthetic assets and wrapping of tokens; service cryptocurrencies; NFTs(non-fungible-token) for art and music; media and entertainment cryptocurrencies (coinmarketcap.com; investopedia.com; kraken.com).

Bitcoin with a capital “B” refers to the protocol and underlying blockchain technology, so the whole network, while bitcoin with a lowercase “b” is describing the currency itself, the actual coins.

Bitcoin is based on the blockchain technology that verifies electronic payments and transfers of bitcoin with cryptographic proof, without relying on a trusted third party(Nakamoto, 2008), usually centralized banks and financial institutions. All transactions occurring on the blockchain are timestamped and hashed into a continuous chain of hash-based proof-of-work. This implies that to change a transaction, all prior transactions must be redone through the proof-of-work mechanism.

The Bitcoin network itself is operated through decentralized nodes, which verify transactions and also confirm that bitcoin that are sent, have not been sent in earlier transactions, in order to avoid double- spending(Nakamoto, 2008). The proof-of-work (PoW) is a decentralized consensus mechanism based on the SHA-256 hashing algorithm. The participating nodes/miners in the network expend computing power, attempting to solve the algorithm and be the first the mine a new block. Each block consists of transactions that are validated and added to the existing blockchain. A different type of mining algorithm is proof-of- stake (PoS) where transactions on the blockchain get verified by participants, through staking their coins and tokens in the network to validate the blocks. The incentive for the exertion of tokens staked or computing power used is the block reward, in the case of Bitcoin a fixed amount of bitcoin. The initial

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block reward started at 50 Bitcoin. This reward is the same per block in each halving cycle and is cut in half during each Bitcoin halving event. The Bitcoin halving cycles are fixed at a length of 4 years, with the current fourth cycle, after the third halving taking place on May 18, 2020, yielding a reward of 6.25 bitcoin per newly mined block. The current average blocktime, the time needed to mine a new block, yielding the coinbase, is at around 9.5 to 10 minutes and differs due to differences in hashpower, the computing power used to solve the mining algorithm(blockchain.com). With Bitcoin cycles being fixed, and the block reward being cut in half during every halving, the last bitcoin ever to be mined is expected to be mined on May 7, 2140. Furthermore, in line with the immutability of the transactions, Bitcoin is capped at a total supply of 21 million coins. This implies a fixed total supply as well as a fixed issuance of new bitcoin in form of the mining block reward, called the coinbase. This might be described as a “monetary inflation” in terms of new coins being issued at fixed intervals. The total supply of bitcoin is constant, the newly available supply is constantly decreasing. These are two important economic traits, which will come into play during the later analysis. Chart 1.2 models Bitcoin’s monetary inflation.

Chart 1.2. Bitcoin Monetary Inflation: Total supply of bitcoin increases as monetary inflation, new bitcoin mined, is halved every halving cycle. [1] https://plot.ly/~BashCo/5.embed

In contrary to common belief in the usability of Bitcoin and crypto assets for criminal transactions and illegal activity, they are pseudo-anonymous, with the blockchain revealing all types of transactions, market behavior and the actual holdings of all participants. There are only a handful of truly anonymous untraceable cryptocurrencies. This is a useful property, as all data and market activities are transparent and publicly available, permissionless, via the blockchain, called on-chain data.

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If all miners agree to change the network and the underlying blockchain properties, such as the mining reward for example, this results in a soft fork. Once there is consensus on the agreed upon changes, the blockchain is continued, with the adoption of the new code and characteristics. If there is only a portion of the miners proposing a certain change, and they decide to continue only under the new rules proposed, this results in a hard fork. The hard fork implies, that the miners that voted for a change in the blockchain, continue their own blockchain afterward. The old blockchain continues in its usual way, while the split off blockchain, the hard fork, continues independently. An example for this would be the hard fork of Bitcoin Cash, which on the day the hard fork occurred got separated from Bitcoin, and became a new, independent blockchain(Investopedia, 2021).

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2 Literature Review

The current research on the valuation of cryptocurrencies and digital assets is limited and has been covered to a small extent, with the majority of in-depth and extensive analysis coming from industry participants themselves. Valuation methods are predominantly not unanimous in their approach since the characteristics of crypto assets vary. Nonetheless, the question of how to value non-physical assets has emerged with the rise of intangibles and internet companies already. A straightforward approach by Moro Visconti (2020) valued these intangible assets with respect to their reproduction cost and the value of the expected income generated, therefore depending on their total utility.

To value Bitcoin, several approaches have been undertaken. Though initially set up to become a currency, the recent investments and analysis supports the view that Bitcoin is rather an investable asset instead of a currency (Sunde & Gerasimova, 2019). Coming from classic asset and equity valuation a straightforward approach is to value bitcoin according to similar metrics, such as the equilibrium between miners, the sellers, and the buyers of bitcoin. Both rely and depend on the networks’ trustworthiness, while increased trust and confidence in Bitcoin increased its value(Pagnotta & Buraschi, 2018). The underlying idea is that miners would only mine bitcoin if they trust the network, while buyers are only willing to purchase bitcoin from the miners if they do the same, therefore resulting in an economic fixed point problem with the equilibrium being the current price of bitcoin.

Linking to the miner’s involvement in Bitcoin’s value, several models started at the beginning, the mining of bitcoin itself, considering a cost of production model which captures the no-arbitrage-price depending on the electricity and mining hardware costs(Hayes, 2017). Hayes (2017) found technological improvements that enable easier mining to reduce the price, whereas an increase in total hashing power increases Bitcoin’s mining difficulty and therefore the price. A Bitcoin halving and reduction of the mining reward, therefore an instant halving of profitability, counter this effect and in essence double mining costs. The cost of production model has further been supported by D’Onorio Demeo & Young (2017).

Overall, this model requires a lot of specific and detailed data, about what type of hardware was used, the specific amount of bitcoin mined in each region, while accounting for differences in electricity costs.

The approach of including the trust aspect in the valuation of Bitcoin as a decentralized financial network(Pagnotta & Buraschi, 2018) is similar to the Framework for Token Confidence(Hargrave et al., 2018), which measures how value is created out of “thin air”(Hargrave et al., 2018) due to users confidence in the underlying network. This value was measured through known factors that affect traditional equity valuations, such as the team, concept, user and market adoption as well as familiarity

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of a given token, all yielding to the halo effect, referring to the token’s popularity in this case, based on positive impressions. This market sentiment in Bitcoin valuation has been captured through the conditional beta model (Khanh, 2020), which allows the beta of the valuation model for a cryptocurrency to change due to uncertainty.

One of the most proposed and successful approaches to assign a value to Bitcoin has been its valuation as a network, through Metcalfe’s Law, which states that a network’s value is proportional to the square of its users(Alabi, 2017). This approach fits the actual price of bitcoin at a given time well and was used for the identification of temporary bubbles and overvaluations, captured by deviations from the suggested network valuation(Alabi, 2017). This valuation approach was extended by a Log-Periodic Power Law Singularity – LPPLS – Model which generalized Metcalfe’s law further based on actual network properties and captured the disconnects from Metcalfe’s network price, which were subject to super- exponential, unsustainable growth in price(Wheatley et al., 2018). Furthermore the LPPLS model captured positive feedback phenomena that caused the bitcoin price to increase, while being able to recognize price bubbles. Peterson (2017) was able to exactly measure the disconnect in price during these active overvaluations and bubble phases and prove that this was statistically unlikely to not be caused by active price manipulation.

Gandal et al. (2018) have similar findings and proved that these overvaluations were in fact subject to market manipulation which was enabled due to low market capitalization and low trading volumes but tended to diminish with market maturation and growth. Generally valuing Bitcoin as a network with Metcalfe’s Law and the extension of the LPPLS-Model would make the determination of its price easier than for equities, which rely on a multitude of valuation metrics, such as P/E-Ratio, P/B-Ratio, price-to-cash-flow etc.(Wheatley et al., 2018). García-Monleón et al. (2021) used Metcalfe’s Law only for the valuation of single-layer cryptocurrencies, such as Bitcoin, that function solely to transfer value, as well as multi-information layer cryptocurrencies which have added characteristics and utilities attached to the token. Those cryptocurrencies that are used solely to receive funding via an ICO(initial exchange offering), have intrinsic value equal to the rights and utility accessed.

Moving beyond Bitcoin valuation, there is general consensus, that different types of crypto assets require different valuation approaches, as they each have different characteristics and traits (García- Monleón et al., 2021; Gore, 2020; Pfeffer, 2017). While noting a general price driver to be psychological FOMO(Fear of Missing Out) on potential appreciation gains, Gore (2020) found that each digital asset requires its own dynamic valuation method that fits the specific characteristics of the respective cryptocurrencies. A simple yet common valuation method for all cryptocurrencies is to evaluate the total

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market cap that can be achieved, given the underlying functions and utility, and derive the future price from there. This method was also used by Pfeffer (2017), after splitting crypto assets into three broad categories, separating network and ecosystem token, decentralized applications(dApps) and money, payments and monetary store of value tokens. The potential increase in current market valuation was considered, assuming one of these crypto assets was to replace and dominate a certain market, together with the total risk exposure. Pfeffer (2017) also considered the potential increase in market capitalization for Bitcoin, if it was to replace gold, to be at least 20x-60x, together with any assumed chance of success, a small non-negative percentage. Taking a minor position in bitcoin, the resulting total risk exposure is low, and the investment’s expected payoff would always have a favorable risk-reward ratio. This method and general valuation is only feasible over the long-term(Pfeffer, 2017). Another measure is the NVT- ratio(Network-Value-to-Transaction-value), which is a variation of the P/E ratio from equity valuation, where the value of the blockchain’s network is divided by the value of the transactions taking place at a given time, yielding comparisons and long-term fair-valuation averages(Gore, 2020).

The largest benefit with assessing the value of Bitcoin is the transparency of on-chain data, as the blockchain is transparent and reveals all transactions, participants, and holdings at any point in time. The usage of this data is, however, mostly limited to industry participants when assessing Bitcoin’s fundamentals and potential valuation, whereas the previous examples of valuation attempts were mostly from academic nature. Nevertheless, on-chain data constitutes a strong fundamental valuation method for bitcoin, capturing its price dynamics well (Kristoufek, 2019). Using the on-chain data, it is possible to evaluate the long-term growth and development, and therefore the price change over time in relation to changes in fundamentals of the Bitcoin network. It can be seen, that most bitcoin are held long-term with increasing holding duration, implying owners which are reluctant to sell, as well as large holders accumulating further bitcoin, during periods of price appreciation(Cipolaro & Stevens, 2020).

Furthermore, detecting larger transaction volumes, increases in institutional and high net worth individual’s interest can be captured, while the on-chain data reveals growing address counts and increasing mining fees, all fueling and causing bitcoin’s price to further increase(Cipolaro & Stevens, 2020).

One of the most accurate and reliable models in the past to capture the price of bitcoin over the long-term was developed by PlanB (2019), who took the Stock-to-Flow model from traditional, scarce, commodity valuation and was first to establish it for Bitcoin valuation. The Stock-to-Flow model puts the supply of a given asset in proportion to the new supply created, measuring the time it would take to reproduce all existing supply. The logarithm of the Stock-to-Flow ratio was applied to the logarithm of Bitcoin’s market valuation, yielding a highly significant correlation between the two. This model was later

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extended to a cross-asset model, including gold, silver, diamonds and bitcoin, showing that all prices follow similar patterns, for the respective Stock-to-Flow ratios, modelling their scarcity(PlanB, 2020a).

Given this highly significant correlation, the model might still be relevant for the future in evaluating bitcoin’s price and it remains relevant to examine, whether the model will hold. As the characteristics of the newly mined coins in the future is known today already, it gives rise to the question whether according to the efficient market hypothesis (EMH), the price has to appreciate immediately to the suggested future price(PlanB, 2020b). This, however, is not the case, as bitcoin is subject to remaining risks and uncertainties which are not captured by the model, therefore the future price suggested by the Stock-to- Flow model does not have to match the EMH price today(PlanB, 2020b).

Overall, the valuation methods have been diverse in their approaches and results, although those that applied the same techniques and crypto assets had consensus for the greater part about their application and implications. The usage of on-chain data in assessing value and trends is limited to institutional industry research and involvement in cryptocurrencies, whereas the academic side of research focusses on connections to known valuation techniques from equities, intangibles, and sentiment analysis. Also, previous research focused mainly on Bitcoin. Therefore, the existing literature on crypto asset or digital asset valuation including other cryptocurrencies is not excessively comprehensive.

The thesis will add to the current findings, by valuing bitcoin via the Stock-to-Flow model, attempting to verify its significance and relevance in measuring bitcoin’s price over the long-term. It will be the first to take the Stock-to-Flow model into an academic research context. At this state a lot of significant and accurate cryptocurrency valuation methods are developed and used outside of scientific research. The thesis introduces a new valuation model for Bitcoin into academia, whereas past crypto asset valuation approaches focused predominantly on traditional asset valuation methods. Next to analyzing the Stock-to-Flow model and Metcalfe’s Law, these methods will be applied to further crypto assets from a broad variety of sectors, being first to attempt and promote valuation methods.

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3 Hypothesis & Research Question

The thesis’ research question is:

How much of bitcoin’s price variation is explained through the Stock-to-Flow model and Metcalfe’s Law?

While also testing whether these methods are applicable to other crypto assets.

All hypotheses are meant to test the explanatory power and significance of the coefficients towards the price of bitcoin.

Stock-to-flow Model:

The first hypothesis is that an increase in Bitcoins’ Stock-to-Flow ratio increases the bitcoin price:

𝐻₀: 𝛽₁= 0 vs. 𝐻₁: 𝛽₁> 0

Network Valuation and Metcalfe’s Law:

The second hypothesis is that an increase in the squared active Bitcoin network address count, increases the bitcoin price:

𝐻₀: 𝛽₁= 0 vs. 𝐻₁: 𝛽₁> 0

4 Methodology

The thesis’ research is focused on testing the explanatory power of the Stock-to-Flow model, as proposed by PlanB (2019) and Metcalfe’s Law, as used in (Alabi, 2017; Peterson, 2017; Wheatley et al., 2018), for the price of bitcoin. In addition, the Stock-to-Flow model and Metcalfe’s Law will be used to make future price projections, based on the known properties of Bitcoin’s future mining output and supply.

Afterwards, the methodology will be applied in identical form to 32 further crypto assets.

In order to determine the explanatory power of the models and test the hypotheses whether the effect in each model is positive, time series regression analysis will be performed. The 𝛽₁-coefficient of each model is tested on its significance and whether the respective null hypotheses will be rejected in favor of the alternative hypothesis.

Data

The Data for analyzing bitcoin and other cryptocurrencies is easily and transparently visible and accessible, as it is running on a public blockchain, and can at any point in time be fully accessed and copied by

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participating in the network, through running a node for example. For this research, the data has been accessed from CoinMetrics’ open source blockchain data base. The data spans from July 2010 until June 2021 and includes over a decade of price and blockchain data. Though Bitcoin is operating since January 2009, the first traceable and reliable price data has not been tracked prior to July 18, 2010.

For the analysis, the following, daily data was collected: the BTC/USD denominated closing price, which is calculated among multiple markets; BTC/Current Supply in native units which is the sum of all native units ever created that are visible on the ledger, so therefore already issued, at the end of that interval; the BTC/Annual Inflation Rate, which is the percentage of new native units that are, continuously, issued over that interval, extrapolated to one year, divided by the current supply of native tokens; the Active Address Count, which is the sum count of unique addresses that were active in the network in that interval(individual addresses are not double-counted in case they were previously active, active implies the address was either a recipient or originator of a ledger change, so a transaction occurring); the BTC/Coinbase Issuance of native tokens, which is the sum of new native units issued that interval, and only includes protocol mandated continuous emissions on schedule, this means, though unlikely, if one were to hack the Bitcoin network and issue bitcoin manually by force, these wouldn’t be included in the count.

All the above mentioned data is retrieved in identical form, with varying time horizons, all starting with their inception and proceeding until June 2021, for the following crypto assets: Bitcoin Cash(BCH), Bitcoin SV(BSV), Bitcoin Gold(BTG), Ethereum(ETH), Litecoin(LTC), XRP(XRP), Chainlink(LINK), Stellar Lumen(XLM), Cardano(ADA), Polkadot(DOT), Binance(BNB), Voyager(ETHOS/VGX), NEO(NEO), REN(REN), Waves(WAVES), Monero(XMR), Verge(XVG), Dash(DASH), New Economy Movement(XEM), OMG Network(OMG), Nexus Mutual(NXM), DOGE(DOGE), DigiByte(DGB), 1inch(1INCH), Aave(AAVE), Compound(COMP), Synthetix(SNX), Uniswap(UNI), Sushiswap(SUSHI), Yearn.Finance(YFI).

Models

Stock-to-Flow-Model

The Stock-to-Flow model measures the scarcity, in terms of reproduction time, of an asset, in this case bitcoin. The stock measures the number of all outstanding bitcoin at a certain point in time, this does not include those bitcoins that are to be mined in the future. This is analogous to gold, where the supply is only including those amounts, that are already in existing circulation and not the outstanding underground supply that can be mined. The flow measures the annual new production of the asset, so newly mined bitcoin during that period, which can also be considered as the inflation rate. Dividing the stock by the

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flow, we achieve a score that is equal to the years of production, at the current inflation rate of new production, it takes to produce the full supply and stock of current, total bitcoin outstanding.

The stock 𝑆 is the simple measure of the total current supply of native units outstanding at the end of the interval 𝑡:

𝑆_𝑡 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑡𝑜𝑡𝑎𝑙 𝑠𝑢𝑝𝑝𝑙𝑦 𝑜𝑓 𝑏𝑖𝑡𝑐𝑜𝑖𝑛 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑡 𝑒𝑛𝑑 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 𝑡

The flow is derived either straightforward by taking the coinbase issuance of native units, so the total bitcoin reward of all blocks on a given day, or alternatively by multiplying the continuously annualized inflation rate of a certain day with the current supply of native tokens and dividing by 365 days.

The flow 𝐹 is the coinbase issuance of native units over the interval 𝑡:

𝐹𝑡 = 𝑐𝑜𝑖𝑛𝑏𝑎𝑠𝑒 𝑖𝑠𝑠𝑢𝑎𝑛𝑐𝑒 𝑜𝑣𝑒𝑟 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 𝑡 The Stock-to-Flow score is therefore:

𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡 = 𝑆_𝑡 𝐹𝑡

(1)

The Market Capitalization/Market Value 𝑀𝑉 of Bitcoin is measured as the price of bitcoin at interval 𝑡 multiplied by the total supply outstanding bitcoin at the end of interval 𝑡:

𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 = 𝑃_{𝑏𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 ∗ 𝑆_𝑡 (2) Since the total range of recorded bitcoin prices expand over a total magnitude of 𝑃_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛} ∗ 10⁸, for the data used 10⁶, the model is applied in log-log form, using the natural logarithm—ln. The dependent variable is the market capitalization of Bitcoin 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛, the independent variable is the log of the Stock-to-Flow ratio. The final regression model is the following:

ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) = 𝛼 + 𝛽₁ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡) + 𝜀_𝑡 (3) Because it is a log-log model, it will reveal the change in the market capitalization caused by a change in the S2F ratio. So 𝛽₁ gives the elasticity of 𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛} with respect to the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜. Therefore, 𝛽₁ is the estimated percentage change in 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛 for a 1% change in the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜. The 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜 is the explanatory variable of interest.

Metcalfe’s Law—Bitcoin Network Valuation

Metcalfe’s Law states that a networks’ value is equal to the squared amount of its users, so the network value 𝑉, with 𝑛 being the number of users:

𝑉_𝑡 = 𝑛_𝑡² (4)

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Applying this Bitcoin, the number of the active address count (𝐴𝐴𝐶) of the Bitcoin network are squared, to receive the market capitalization of Bitcoin. The active address count is described as the sum count of unique addresses that were active in the network during that interval. Individual addresses are not double counted in case they were previously active, where active implies the address was either a recipient or originator of a ledger change, so a transaction occurring.

Metcalfe’s Law states, that the Market Valuation of Bitcoin, 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛, is equal to the active address count(𝐴𝐴𝐶) of Bitcoin, squared:

𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 = 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡² (5)

Since the total range of recorded bitcoin prices expand over a total magnitude of 𝑃𝐵𝑖𝑡𝑐𝑜𝑖𝑛 ∗ 10⁸, for the data used 10⁶, the model is applied in log-log form, using the natural logarithm—𝑙𝑛. The market capitalization 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛 is the dependent variable, and the active address count squared 𝐴𝐴𝐶² being the independent variable. The final regression model is the following:

ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) = 𝛼 + 𝛽₁ln(𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡²) + 𝜀_𝑡 (6)

Because it is a log-log model, it will reveal the change in the market capitalization caused by a change in the 𝐴𝐴𝐶². So 𝛽1 gives the elasticity of 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛 with respect to the 𝐴𝐴𝐶² Therefore, 𝛽1 is the estimated percentage change in 𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛} for a 1% change in the 𝐴𝐴𝐶². The 𝐴𝐴𝐶 is the explanatory variable of interest.

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5 Analysis and Results Stock-to-Flow Model

The regression output of ln(𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡) on ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡) is presented as log-log-model in Chart 5.1.

The scatterplot and the performed OLS regression reveal a clear linear relation between Bitcoins’ market capitalization and the corresponding S2F-ratio on a logarithmic scale. The groupings of datapoints distinguish individual halving cycles, with a clear division.

Chart 5.1. Bitcoin Stock-to-Flow – Modeled as Log-Log: Each group of datapoints constitute bitcoins market capitalization and the respective S2F-ratio in a single halving cycle.

A simple linear regression was calculated to predict ln(𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡) based on ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡). Table 5.1 gives the regression results.

Table 5.1. Regression result of ln(MV-Bitcoin) on ln(S2F-ratio)

Predictor b b 95% CI [LL, UL] ß t p

(Intercept) 14.1578***

(0.0443) [14.0709, 14.2447] 319.4864 <0.001

ln(S2F) 3.3209***

(0.0166) [3.2883, 3.3535] 0.9536 199.6616 <0.001 standard error in parentheses; * p<0.05, ** p<0.01, *** p<0.001

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A highly significant relationship was found, 𝐹(1, 3974) = 39864.74, 𝑝 < .001, with an 𝑅² of . 90935.

The natural logarithm of Bitcoins’ predicted Market Capitalization is equal to:

ln(𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡) = 14.1578 + 3.3209ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡)$

when ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡) is measured as a number. 𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 increases by 3.3209% for each 1% increase in the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡. The correlation coefficient 𝑟 = 0,9535. Given the high significance and an 𝑅² of . 90935, the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡 explaining 90.935% of the variation in 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡, the model explains the bitcoin price well. This indicates that an increase in the Stock-to-Flow ratio is consistent with an increase in 𝑃𝑏𝑖𝑡𝑐𝑜𝑖𝑛_𝑡. This change in Bitcoins’ valuation following a change in the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡 is statistically highly significant at 𝑝 < 0.001. The probability that the found result is due to chance, ceteris paribus, is less than 0.1%. Therefore, the null hypothesis 𝐻₀: 𝛽₁= 0, that Stock-to-Flow ratio has no effect on the bitcoin price, is rejected.

5.1 Power Law Function determining Bitcoins’ Market Value

The regression line equation can be solved for the market cap of Bitcoin, to derive the absolute effect of a change in the Stock-to-Flow ratio on the market valuation of Bitcoin:

ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) = 14.1578 + 3.3209ln(𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡)$ (7) The resulting power law function:

𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 = 𝑒^14.1578 ∗ 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜_𝑡^3.3209$ (8) Combining the power law function with the observations and properties of the halving cycles it follows that the doubling of the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡 during a halving results in a tenfold of 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡. This can be directly verified from the power law function (8), as the 𝑆2𝐹 − 𝑅𝑎𝑡𝑖𝑜𝑡 gets exponentiated by a factor of 3.3209, a doubling yields a tenfold increase. The current halving cycles’ S2F ratio so far has an average score of 57, and the power law function (8), for Bitcoin’s market valuation yields a 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_2020−2024 = 𝑒^14.1578 ∗ 572020−20243.3209

$= $954,419,000,000 = $51,000 per bitcoin, using the current amount of bitcoin outstanding at 18.7 million. The actual average price of bitcoin over the past 3 months, March 2021 until June 2021, is $52.112 per bitcoin. The actual average bitcoin price during this halving cycle, May 2020 until June 2021 is $26.700. According to the Stock-to-Flow model, bitcoin, at an average monthly price of $38.000 mid-May until June 2021, is currently undervalued.

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Chart 5.2 visualizes bitcoins’ price as well as the corresponding S2F-ratio and its half-year moving average over time, on a logarithmic scale.

Chart 5.2. Bitcoin Stock-to-Flow over Time: The Stock-to-Flow Ratio doubles after every halving cycle, the bitcoin price increases tenfold. The 180-day moving average models this progression closely over time.

Chart 5.2 shows, that the S2F-ratio moves up gradually, step by step, which is due to the property of the flow being cut in half every four years during the halving and causes an instant doubling in the Stock-to- Flow ratio. In between the halving cycles, the S2F increases steadily, as the flow remains constant during a halving cycle, while the stock grows due to the coinbase issued and added to the stock. It is noteworthy, that the S2F does not exactly dictate the price of bitcoin but can rather be described as an average value, and therefore average price, during the current halving cycle. The swings in the S2F-ratio are due to the coinbase not being exactly constant. While on average yielding the same block reward, the daily mined bitcoin differs due to differences in hashpower and therefore average mining time per block. Another observation is that the price of bitcoin does not instantly jump during the shock of a doubling in the S2F ratio but increases with a delay of roughly a year.

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5.2 Extrapolation of the Stock-to-Flow Model to the Future

Given the known stock and the known flow in the future, these properties can be used to plot the forthcoming S2F ratios of bitcoin, to project the future progression and predicted price ranges of bitcoin.

The standard error (SE) is calculated to add a confidence interval to the Stock-to-Flow model. The bandwidths applied to the Stock-to-Flow model in Chart 5.3 are the one, and two standard error deviation from the mean, all plotted on a half-year per moving average basis. These bandwidths were a broader and more accurate price range for bitcoin in the past, during its swings around the Stock-to-Flow ratio.

Chart 5.3. Bitcoin Stock-to-Flow over Time – Extrapolation to Future: Added are the bitcoin price trendline, the 1x and 2x Standard Error (SE) on a 180-day moving average, constituting the bandwidth and confidence interval for the bitcoin price. Blue blur added for better visualization.

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Since the future standard error cannot be exactly forecasted, the standard error is assumed to double in every new cycle, as this is consistent with previous changes in the SE due to a halving. Because the future flow is known, the respective stock of outstanding bitcoin can be determined, and the Stock-to-Flow ratio is derived. The forecast of the Stock-to-Flow model, including the confidence interval is modelled by Chart 5.4 on a log-log scale.

Chart 5.4. Bitcoin Stock-to-Flow over Time – Extrapolation to Future: The Stock-to-Flow Ratio doubles after every halving cycle, the bitcoin price increases tenfold. The 180-day moving average models this progression closely over time. This characteristic is extrapolated to the future. Added are the 1x and 2x Standard Error (SE) on a 180-day moving average, constituting the bandwidth and confidence interval for the bitcoin price. Blue blur added for better visualization.

The future projection of the S2F-ratio runs until December 31^st, 2029, which is the 6^th Bitcoin halving cycle.

The characteristic of the bitcoin price approximately ten-folding, for every doubling in the S2F-ratio, can be observed for the future halving cycles. The current, 4^th cycle, 2020-2024, projects a price of around

$100,000 per bitcoin towards the end of the cycle, the 5^th, 2024-2028, and 6^th, 2028-2032, averaging at approximately $1 million and $10 million per bitcoin respectively. These prices are derived using the known halving cycle’s S2F-ratios.

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6 Analysis and Results Metcalfe’s Law

The regression of ln(𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡) on ln(𝐴𝐴𝐶𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡2

) is presented in Chart 6.1. The scatterplot and the performed OLS regression reveal a clear linear relation between the market capitalization of Bitcoin and the corresponding active address count squared, once presented on a logarithmic scale. Chart 6.1 shows deviations of the network valuation around the long-term trend. Also, the trendline is slightly flatter than Metcalfe’s Law, with a 1:1 Metcalfe’s Law network valuation vs. Bitcoin Market Valuation, suggests.

Chart 6.1. Bitcoin Metcalfe’s Law -Modeled as Log-Log: The chart shows a clear long-term trend of Bitcoin’s Market Capitalization and Metcalfe’s network valuation. In the short-term Bitcoin deviates from the long- term trendline.

A simple linear regression was calculated to predict ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) based on ln(𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡²). Table 6.1 gives the regression results.

Table 6.1. Regression result of ln(MV-Bitcoin) on ln(AAC^2)

Predictor b b 95% CI [LL, UL] ß t p

(Intercept) -0.1215 (0.0978) [-0-3133, 0-0703] -12.419 0.2144

ln(AAC^2) 0.9280***

(0.0040) [0.92013, 0.9358] 0.9650 231,9296 <0.001 standard error in parentheses; * p<0.05, ** p<0.01, *** p<0.001

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A highly significant relationship was found, 𝐹(1, 3974) = 53791.35, 𝑝 < .001, with an 𝑅²of . 93120.

The logarithm of Bitcoin’s predicted Market Capitalization is equal to:

ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) = −0.1215 + 0.9279ln(𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡²)$ (9) when 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡² is measured as a number. 𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 increases by 0.9279% for each 1% increase in the 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡². This does not refer to the increase in the 𝐴𝐴𝐶𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡 itself because an increase in 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 gets exponentiated and is therefore not a linear increase since it gets squared. The effect is positive but not constant. The correlation coefficient 𝑟 = 0,9650. Given the high significance and the 𝑅²of . 93120, the 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡² explaining 93.12% of the variation in 𝑀𝑉𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡, the model explains the bitcoin price well. This indicates an increase in the price of bitcoin, following a growing number of active network addresses. This change in Bitcoins’ valuation following a change in the squared active network address count of Bitcoin is statistically highly significant at 𝑝 < 0.001. The probability that the found result is due to chance, ceteris paribus, is less than 0.1%. Therefore, the null hypothesis, that the squared active network address count has no effect on the bitcoin price, is rejected.

6.1 Power Law Function determining Bitcoins’ Market Value

The regression line equation can be solved for the market cap of Bitcoin, to derive the absolute effect of a change in the squared active address count on the market valuation of Bitcoin:

ln(𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡) = −0.1215 + 0.9279ln(𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡²)$ (9) The resulting power law function:

𝑀𝑉_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡 = 𝑒^−0.1215 ∗ (𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡²)^0.9279$ (10) Using the current outstanding bitcoin supply of 18.7 million, the price of bitcoin according to Metcalfe’s Law, with a 3-months average, March 2021 until June 2021, 𝐴𝐴𝐶𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡2

of 1.2 trillion, is $64,171. The actual 3 months average, March 2021 until June 2021, bitcoin price is $52.000. Metcalfe’s Law predicts an average bitcoin price of $57,058, with 1.067 trillion average 𝐴𝐴𝐶_{𝐵𝑖𝑡𝑐𝑜𝑖𝑛}_𝑡² for this halving cycle so far, May 2020 until June 2021. The actual average bitcoin price during this halving cycle so far is $26.700. According to Metcalfe’s Law, bitcoin, at an average monthly price of $38.000 mid-May until mid-June 2021, is currently undervalued.

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Chart 6.2 models Metcalfe’s Law and Bitcoin’s Market Capitalization over time and shows that the projected Metcalfe network valuation follows a logarithmic curve, when presented on a log-log scale, with a diminishing magnitude in growth over time. This observation is consistent with super exponential growth, in network valuation as well as Bitcoins’ valuation, in the early market phases, spreading over multiple orders of magnitude. The more recent years showed less exponential growth during market maturation in the later phases. Furthermore, Bitcoin’s market capitalization tracks Metcalfe’s Law’s network valuation with a delay and does not exceed it at any point in time. The regression equation (9) confirms the second observation, as a one percentage increase in the 𝐴𝐴𝐶𝐵𝑖𝑡𝑐𝑜𝑖𝑛_𝑡2

only leads to a 0.9279 percentage increase in Bitcoin’s market capitalization.

Chart 6.2. Bitcoin Metcalfe’s Law – Network Value over Time: Bitcoin’s Market Capitalization tracks Metcalfe’s Law accurately in the long-term, but never exceeds Metcalfe’s network valuation.

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26 6.2 Extrapolation of Metcalfe’s Law to the Future

The implementation of the known properties is modelled in Chart 6.3. Power trendlines are used as they capture the growth in Metcalfe’s network valuation and Bitcoin’s market valuation. The power trendlines indicate an increasing gap between the Bitcoin market capitalization and the network valuation of Metcalfe’s Law.

Chart 6.3. Bitcoin: Metcalfe’s Law – Network Value over Time – Power Trendline: The progression of Metcalfe’s Law’s network valuation and the bitcoin price are modelled over time. The power trendlines show an increasing gap between predicted model price and actual price.

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Using the current power functions, Metcalfe’s network valuation, together with the bitcoin price, will be forecasted until December 31^st, 2029. Chart 6.4 presents this. The fit of the power trendline, measured by the 𝑅² is slightly higher for Metcalfe’s network valuation, than for the actual bitcoin price. Given the power function, the gap increases to almost one order of magnitude by the end of 2029. The projected average price, according to Metcalfe’s Law during the 2020-2024 halving cycle is $97,000 per bitcoin, using an average outstanding supply of 18.96 million bitcoin. For the 2024-2028 halving cycle the average Metcalfe’s Law price, with an average supply of 19.97 million bitcoin outstanding, is $276,000 per bitcoin.

The projected bitcoin price at the end of 2029 is $49,452 according to the bitcoin price power trendline.

The projected bitcoin price according to Metcalfe’s Law’s network valuation power trendline, at the end of 2029 with a 20.45 million bitcoin supply, is $473,00.

Chart 6.4. Bitcoin: Metcalfe’s Law – Network Value over Time – Power Trendline Extrapolation to Future:

The progression of Metcalfe’s Law’s network valuation and the bitcoin price are modelled over time. The power trendlines show an increasing gap between predicted model price and actual price. The power functions are used to project Metcalfe’s network valuation and the bitcoin price to the future.

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7 Extrapolation to Crypto Assets and Cryptocurrencies

This section focusses on the application and extrapolation of the Stock-to-Flow model and Metcalfe’s Law to other crypto assets. To evaluate a large variety of different digital assets for their suitability, cryptocurrencies from all sectors and functionalities are selected, such as bitcoin hard forks; currencies and digital payment networks; interoperability and decentralized oracle; exchange and brokerage;

ecosystems and smart contract platforms; privacy tokens, decentralized finance (DeFi) including lending and borrowing, swaps, automated market maker (AMM); and decentralized exchange (DEX) aggregators.

All data is derived from CoinMetrics, the infographics are collected from coinmarketcap.com, coinario.com and Investopedia.com. The analysis performed is identical with the methodology described in section four. All procedures and methods were fully replicated, and Bitcoin is included for reference.

The respective results are modelled as follows:

A summary table for each model is given at the beginning, elaborating on the crypto assets’

functionality, type of asset and their respective sector; whether the models were applicable, if so the variance explained is given, otherwise the reason for non-applicability; and whether the model is suited to measure the crypto asset’s price. Following the elaboration is the visualization of the model output.

The output and results of the Stock-to-Flow models is given in Table 7.1 and Table 7.2. Charts 7.1 and 7.2 model the Stock-to-Flow for Bitcoin(BTC), Bitcoin Cash(BCH), Bitcoin SV(BSV), Bitcoin Gold(BTG), Ethereum(ETH), Litecoin(LTC), Monero(XMR), Verge(XVG), Dash(DASH), Doge(DOGE), DigiByte(DGB). The S2F-models are displayed on a log-log scale over time. Each crypto asset is modelled from its inception onwards. Since not all cryptocurrencies are mined through a proof-of-work (PoW) algorithm, or have different issuance protocols, the S2F model is restricted to the aforementioned cryptocurrencies.

The output and results of Metcalfe’s Law are given in Table 7.3 and Table 7.4. Charts 7.3 and 7.4 model Metcalfe’s Law for Bitcoin(BTC), Bitcoin Cash(BCH), Bitcoin SV(BSV), Bitcoin Gold(BTG), Ethereum(ETH), Litecoin(LTC), XRP(XRP), Chainlink(LINK), Stellar Lumen(XLM), Cardano(ADA), Polkadot(DOT), Binance(BNB), Voyager(ETHOS/VGX), NEO(NEO), REN(REN), Waves(WAVES), Verge(XVG), Dash(DASH), New Economy Movement(XEM), OMG Network(OMG), Nexus Mutual(NXM), DOGE(DOGE), DigiByte(DGB), 1inch(1INCH), Aave(AAVE), Compound(COMP), Synthetix(SNX), Uniswap(UNI), Sushiswap(SUSHI), Yearn.Finance(YFI). The respective power trendlines are added as well as the 𝑅². Each crypto asset is modelled on a log-log scale including all data since their respective inception. Metcalfe’s Law is not applicable to Monero since it is a private blockchain, and therefore does not have data on its participants.

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Table 7.1. Stock-to-Flow Summary for Crypto Assets 1/2: Crypto assets categorized by sector and functionality. The table indicates whether the model is applicable and suitable for a specific crypto asset

Stock-to-Flow Summary Table 1/2

Acronym Name Type & Function S2F Applicable Suitable

BTC Bitcoin BTC 𝑅^2 = .90935 ✓

BCH Bitcoin Cash BTC Hardfork 𝑅^2 = 0.01482 x

BSV Bitcoin SV BTC Hardfork 𝑅^2 = 0.32601 x

BTG Bitcoin Gold BTC Hardfork 𝑅^2 = 0.07413 x

ETH Ethereum Decentralized Ecosystem / Platform / Smart Contracts

PoS-mining

𝑅^2 = 0.59207 x LTC Litecoin Currency / Digital Payment 𝑅^2 = 0.58463 x

XRP XRP Currency / Digital Payment no issuance x

LINK Chainlink

Decentralized Oracle Network / Data / Smart Contracts

no issuance x

XLM Stellar

Lumen Open Monetary Network SCP-mining x

ADA Cardano Decentralized Ecosystem /

Platform / Smart Contracts PoS-mining x DOT Polkadot

Multichain Protocol / Cross-Chain

Interoperability

no max supply x

BNB Binance Exchange / Ecosystem PoS-mining x

ETHOS

(VGX) Voyager Crypto Brokerage Service reward system x

NEO NEO Ecosystem / Payments no mining x

REN REN DeFi Interoperability /

Liquidity premined x

WAVES Waves Decentralized Applications

(Dapps) / Smart Contracts LPoS-mining x XMR Monero Private / Anonymous

Transactions 𝑅^2 = 0,79321 ?

XVG Verge Privacy / Anonymous

Payments Network 𝑅^2 = 0,00019 x

DASH Dash Payments Network with

Privacy Focus 𝑅^2 = 0.59972 X

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Table 7.2. Stock-to-Flow Summary for Crypto Assets 2/2 Crypto assets categorized by sector and functionality. The table indicates whether the model is applicable and suitable for a specific crypto asset

Stock-to-Flow Summary Table 2/2

Acronym Name Type & Function S2F Applicable Suitable

XEM

New Economy Movement

Ecosystem no issuance x

OMG OMG

Network

Layer-2 Scaling Solution on

Ethereum PoS-mining x

NXM Nexus Mutual Decentralized Insurance Protocol

active token

sale x

DOGE DOGE Digital Currency / Tipping no max supply x DGB DigiByte Asset Creation Platform /

Dapps / Smart Contracts 𝑅^2 = 0.79944 ? 1INCH 1inch Decentralized Exchange

(DEX) Aggregator / Swaps

Liquidity

Mining x

AAVE Aave DeFi Lending / Borrowing PoC-mining x COMP Compound DeFi Lending / Borrowing delayed PoW x

SNX Synthetix DeFi Synthetic Assets PoC-mining x

UNI Uniswap DeFi Automated Market Maker / Trading / Swaps

Liquidity

Mining x

SUSHI Sushiswap DeFi Automated Market Maker / Trading

Liquidity

Mining x

YFI Yearn.Finance DeFi Aggregator / Yield

Farming Liquidity

Mining x

The Stock-to-Flow model only exhibits explanatory power and suitability for Bitcoin itself, as shown by Chart 7.1 and Chart 7.2. Monero(𝑅² = 0.79321), DASH(𝑅² = 0.75399) and DigiByte(𝑅² = 0.79944) have a substantially higher market value than the S2F ratio suggests and show some long-term correlation, but don’t follow the model as accurately as Bitcoin. For all other crypto assets, including hard forks of Bitcoin, the actual market valuation and the S2F-ratio suggested market valuation deviate by multiple orders of magnitude and show no coherent trend. Except for Verge, the Bitcoin hardforks Bitcoin Cash, Bitcoin SV and Bitcoin Gold, showed the lowest correlation out of all the crypto assets analyzed. Ethereum, despite PoS mining, shows a weak trend of tracking the Stock-to-Flow model, but also has overvaluation of multiple orders of magnitude. Doge has a prolonged period where S2F model and the actual price

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Chart 7.1 Stock-to-Flow Model: Bitcoin, Bitcoin Cash, Bitcoin SV, Bitcoin Gold, Ethereum, Litecoin, Monero, Verge

match, seemingly incidental, as it has no maximum supply and therefore no scarcity. Alltogether, no cryptocurrency shows a consistent trend of tracking the S2F-model in a significant way.

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32 Chart 7.2. Stock-to-Flow Model: Dash, DOGE, DigiByte

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Table 7.3. Metcalfe’s Law Summary 1/2: Crypto assets categorized by sector and functionality. The table indicates whether the model is applicable and suitable for a specific crypto asset

Metcalfe’s Law Summary Table 1/2

Acronym Name Type & Function Metcalfe Applicable Suitable

BTC Bitcoin BTC 𝑅^2 = 0,93120 ✓

BCH Bitcoin Cash BTC Hardfork 𝑅^2 = 0,23755 x

BSV Bitcoin SV BTC Hardfork 𝑅^2 = 0,34780 x

BTG Bitcoin Gold BTC Hardfork 𝑅^2 = 0,38990 x

ETH Ethereum Decentralized Ecosystem /

Platform / Smart Contracts 𝑅^2 = 0,88395 ✓ LTC Litecoin Currency / Digital Payment 𝑅^2 = 0,89416 ✓

XRP XRP Currency / Digital Payment 𝑅^2 = 0,72427 ✓

LINK Chainlink

Decentralized Oracle Network / Data / Smart Contracts

𝑅^2 = 0,89165 ✓

XLM Stellar

Lumen Open Monetary Network 𝑅^2 = 0,76227 ✓

ADA Cardano Decentralized Ecosystem /

Platform / Smart Contracts 𝑅^2 = 0,53954 x DOT Polkadot

Multichain Protocol / Cross-Chain

Interoperability

𝑅^2 = 0,82494 ✓

BNB Binance Exchange / Ecosystem 𝑅^2 = 0,67839 ✓

ETHOS

(VGX) Voyager Crypto Brokerage Service 𝑅^2 = 0,54488 x

NEO NEO Ecosystem / Payments 𝑅^2 = 0,62327 x

REN REN DeFi Interoperability /

Liquidity 𝑅^2 = 0,86817 x

WAVES Waves Decentralized Applications

(Dapps) / Smart Contracts 𝑅^2 = 0,17570 x XMR Monero Private / Anonymous

Transactions private blockchain x

XVG Verge Privacy / Anonymous

Payments Network 𝑅^2 = 0,44226 x

DASH Dash Payments Network with

Privacy Focus 𝑅^2 = 0,75399 ✓

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Table 7.4. Metcalfe’s Law Summary 2/2: Crypto assets categorized by sector and functionality.

The table indicates whether the model is applicable and suitable for a specific crypto asset Metcalfe’s Law Summary Table 2/2

Acronym Name Type & Function Metcalfe Applicable Suitable

XEM

New Economy Movement

Ecosystem 𝑅^2 = 0,76510 ✓

OMG OMG

Network

Layer-2 Scaling Solution on

Ethereum 𝑅^2 = 0,59303 x

NXM Nexus Mutual Decentralized Insurance

Protocol 𝑅^2 = 0,04080 x

DOGE DOGE Digital Currency / Tipping 𝑅^2 = 0,40867 x DGB DigiByte Asset Creation Platform /

Dapps / Smart Contracts 𝑅^2 = 0,36846 ✓ 1INCH 1inch Decentralized Exchange

(DEX) Aggregator / Swaps 𝑅^2 = 0,00610 x AAVE Aave DeFi Lending / Borrowing 𝑅^2 = 0,61053 x COMP Compound DeFi Lending / Borrowing 𝑅^2 = 0,10179 x

SNX Synthetix DeFi Synthetic Assets 𝑅^2 = 0,82268 x

UNI Uniswap DeFi Automated Market

Maker / Trading / Swaps 𝑅^2 = 0,02637 x SUSHI Sushiswap DeFi Automated Market

Maker / Trading 𝑅^2 = 0,17932 x

YFI Yearn.Finance DeFi Aggregator / Yield

Farming 𝑅^2 = 0,00525 x

Metcalfe’s Law shows varying degrees of explanatory power for the price of the underlying crypto assets, as depicted by Chart 7.3 and Chart 7.4. It is applicable for Bitcoin, but not its hardforks. Litecoin(LTC), DigiByte(DGB) and DASH(DASH) appear to track Metcalfe’s Law perfectly on average, deviating from Metcalfe’s network valuation at times. Ethereum(ETH), XRP(XRP) and Chainlink(LINK) have a high correlation with Metcalfe’s Law, but show severe overvaluations compared to the suggested Metcalfe network valuation. Exchange and brokerage cryptocurrencies Binance and Voyager have high overvaluations with respect to Metcalfe’s Law, and reveal a weak correlation with Metcalfe’s network valuation. Equally, New Economy Movement, NEO, REN, Waves, and Verge showed significant overvaluations to Metcalfe’s Law, with no discernible trend towards their network valuation, except for REN(REN). Decentralized Finance protocols 1inch, Aave, Compound, Uniswap, Sushiswap and

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Chart 7.3 Metcalfe’s Law: Bitcoin, Bitcoin Cash, Bitcoin SV, Bitcoin Gold, Ethereum, Litecoin, XRP, Chainlink, Stellar Lumen, Cardano, Polkadot, Binance, Voyager, NEO, REN, Waves, Verge, Dash

Yearn.Finance(YFI) showed no correlation with Metcalfe’s Law. Synthetix(SNX) has a high correlation with Metcalfe’s Law, but shows high overvaluation and a weak trend. REN and SNX are the only DeFi digital assets that have a high correlation with Metcalfe’s network valuation.

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Chart 7.4 Metcalfe’s Law: New Economy Movement, OMG Network, Nexus Mutual, DOGE, DigiByte, 1inch, Aave, Compound, Synthetix, Uniswap, Sushiswap, Yearn.Finance

9 Discussion

The explanatory power of Metcalfe’s Law and the Stock-to-Flow model on Bitcoins valuation were examined. Both models were found to be highly significant and explain almost the entire price variation of bitcoin. The models were highly accurate in modelling the long-term price for bitcoin, while deviating in the short- to mid-term from the projected model price. The thesis’ research found similar, almost identical current bitcoin prices, as predicted by PlanB (2019) with the Stock-to-Flow model. This does, however, not imply that they are capturing all the underlying reasons for price movements. While the S2F model perfectly captures and measures the scarcity on the supply side of Bitcoin, it assumes constant

Long-Term Bitcoin Valuation: Stock-To-Flow Model Metcalfe’s Law and Crypto Asset Valuation

Amsterdam Business School