The flood of bitcoinrelated articles in recent weeks threatens to overwhelm investors. Cutting through the noise, a Journal of Money, Credit and Banking paper published earlier this year provides a simple economic framework for assessing how many dollars per bitcoin we should be paying. The caveat: it is left to the reader to make any projections as to where the price of BTC will end up.
What Makes Valuing Bitcoin So Hard?
Bitcoin is the bestknown virtual currency and has two unique features. First, it is a scarce asset, which means its supply is fixed and predetermined. Second, its technology is designed to mint new bitcoin in exchange for clearing and settling transactions in a process that is disintermediated and ‘secure’ (for a primer, see Dwyer, 2015).
The advantages of the coin’s scarcity have warranted much attention in recent months. Since May, US M2 has been growing at a yearonyear rate above 20% (FRED), compared with an average of 5.9% since 1982. Bitcoin’s supply schedule, on the other hand, halves every four years and is independent of monetary authorities. So far, around 18.5mn bitcoin have been minted, and by around 2140 the full 21mn will have entered circulation. By one estimate, bitcoin could be scarcer than gold by 2024 (in terms of stocktoflow ratio).
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Summary
 The challenge of valuing bitcoin lies mainly in identifying how tokenholders will use the currency moving forward. With it being a scarce asset, its primary role could turn out to be as a store of value.
 A 2020 academic paper proposes using Fisher’s Quantity Theory of Money equation to value bitcoin. A decomposition of that equation can help to understand recent movements in BTC prices.
 The paper emphasises the need to distinguish between the total supply of bitcoin (21mn) and the current flow of bitcoin. A distinction between users and speculators should also be made.
Introduction
The flood of bitcoinrelated articles in recent weeks threatens to overwhelm investors. Cutting through the noise, a Journal of Money, Credit and Banking paper published earlier this year provides a simple economic framework for assessing how many dollars per bitcoin we should be paying. The caveat: it is left to the reader to make any projections as to where the price of BTC will end up.
What Makes Valuing Bitcoin So Hard?
Bitcoin is the bestknown virtual currency and has two unique features. First, it is a scarce asset, which means its supply is fixed and predetermined. Second, its technology is designed to mint new bitcoin in exchange for clearing and settling transactions in a process that is disintermediated and ‘secure’ (for a primer, see Dwyer, 2015).
The advantages of the coin’s scarcity have warranted much attention in recent months. Since May, US M2 has been growing at a yearonyear rate above 20% (FRED), compared with an average of 5.9% since 1982. Bitcoin’s supply schedule, on the other hand, halves every four years and is independent of monetary authorities. So far, around 18.5mn bitcoin have been minted, and by around 2140 the full 21mn will have entered circulation. By one estimate, bitcoin could be scarcer than gold by 2024 (in terms of stocktoflow ratio).
Source: FRED
The advantages of bitcoin’s technology are less clear. Although unregulated and disintermediated, as a means of payment it has become slow and commission is high. Also, while the Bitcoin blockchain is virtually immutable, its proofofwork consensus algorithm is computationally intensive. In addition, the recent move into bitcoin by institutions and wealthy individuals has not improved bitcoin’s resilience to regulatory news, nor have questions regarding its security been fully allayed.
It is clear that for an accurate, longterm projection of bitcoin prices, it is important to understand what uses (if any) the virtual currency will have moving forward. Yet, on this fundamental point, there remain several unknowns. Can it be used as a store of value or as an inflation hedge? Is it just a vehicle for transactions? Does its value lie only in its underlying blockchain? Perhaps even worse, according to Fidelity, ‘Bitcoin is many things to many people’. And therein lies the challenge of valuing it.
The Quantity Theory of Money Equation
The paper applies the wellknown transaction version of the quantity equation popularised by Irving Fisher (1911). Chris Burniske, the first buyside analyst to cover crypoassets and writer of Cryptoassets: The Innovative Investor’s Guide to Bitcoin And Beyond, has also promoted the method as a good way of valuing cryptocurrencies such as bitcoin.
In its simplest form, the equation looks like this:
Where, for the purpose of this paper, P_{t }, is a weightedaverage price within an economy; T_{t }is the quantity of goods and services purchased with a virtual currency; M_{t }is the monetary base; and V_{t} denotes the velocity of the virtual currency.
As an example, the LHS could represent a crude form of GDP (price x quantity). In the US, this figure is around $21tn. On the RHS, the US monetary base, M2, is $19tn, and velocity is estimated to be 1.1 (Chart 2). At any given point, the two sides of the equation should hold.
The paper applies this rule to virtual currencies, using the analogy that each cryptoasset supports their own native economy. Using simple algebra (Appendix), and defining S_{t }as the exchange rate (which is by convention the amount of the established currency one pays to obtain a single unit of virtual currency) and P_{t}^{E}as the weightedaverage price of the goods and services purchased with the virtual currency, they get:
This says that, to get a value of dollar per bitcoin (S_{t}), you need to divide the total amount of trade in goods and services with payments settled in bitcoin (T_{t}^{*} ) by the cryptocurrency’s velocity (V_{t}^{*}). The numerator is then divided by the monetary base (M_{t}) minus the number of bitcoin units being held as a store of value (Z_{t}).
Intuitively, the numerator reflects the value of virtual currency in terms of the established currency necessary to make payments. The asterisk above V_{t }emphasises that we should focus only on the proportion of bitcoin that actually changes hands on a regular basis. The denominator represents the number of tokens outstanding.
The Dynamics of Bitcoin’s Value
The equilibrium condition shows that four variables affect the dollar value of bitcoin. The ‘value’ of bitcoin increases when (i) the volume of the payments for goods and services in bitcoin increases (↑T_{t}^{*} ); (ii) less bitcoin changes hands (↓V_{t}^{*}); (iii) the total quantity of bitcoin decreases (↓M_{t}); and (iv) more people hold bitcoin as a speculative position^{[1]} (↑Z_{t}).
Practically, if we assume that the prices quoted in bitcoin are perfectly flexible with respect to changes in the exchange rate, then the recent rise may reflect two things. These are either a push towards using bitcoin more as a vehicle for transactions, or a rise in investors storing bitcoin. Velocity (total velocity, not velocity of used bitcoin), if anything, appears to have increased in recent months (Chart 3).
Source: Woobull
Challenges of the Fisher Equation
By component, T_{t}^{*} requires an accurate projection of the amount of trade in goods and services whose payments will be settled in bitcoin. Estimating this is perhaps the most challenging part of valuing bitcoin. It requires (i) an estimate of the total addressable market; (ii) an estimate of the subset bitcoin can realistically achieve within that market; and (iii) an estimate of bitcoin’s penetration within the target market.
For V_{t}^{*}, we need to determine what percentage of users use bitcoin for its store of value, and how many use it for clearing and settling transactions. From the proportion of those who actively trade bitcoin, we need to estimate the total velocity. In 2017, Chris Burniske estimated this to be around 15. Assuming Woobull’s estimate is correct, overall velocity has fallen fourfold since then. If the proportion of people holding bitcoin as a store of value or as a speculative position has remained at 60%, V_{t}^{*}could be around four.
Finally, M_{t }– Z_{t }requires an estimate of the total number of tokens outstanding. This gives the supply of tokens in the flow, which many estimates of the dollar bitcoin value appear to exclude. According to Chainanalysis, this could be as little as 3.5mn. The reader is left to determine the true value of T_{t}^{* }.
Bottom Line
With a barrage of crypto and bitcoinrelated numbers being thrown around, the aim of this piece is simply to provide an economic framework in which to form your own ideas. There are a couple of key points. First, the pandemic has peaked interest in bitcoin as a store of value, adding to the list of functions it may eventually serve. Second, valuing bitcoin requires a good estimate of (i) the ratio of users to speculators; (ii) the number of tokens outstanding, and (iii) bitcoin’s penetration within its addressable market.
Appendix
Fisher equation:
Multiply top and bottom by P_{t}^{E}:
Define:To get:
Notice that velocity can be divided into the amount of currency used and the amount of currency stored (which does not change hands and so has zero velocity):
Combining the two:
Click here to view paper.

By ‘speculation’, the paper means investors who hold a virtual currency with the intention that the future value will rise. When articles say the current rise in bitcoin is less to do with ‘speculation’, it is hard to know whether this is indeed correct. If the USP of bitcoin is as a digital store of value, then perhaps there is less speculation. If bitcoin’s primary use is for transactions, then more individuals holding onto bitcoin would reflect a rise in speculation. ↑
Sam van de Schootbrugge is a macro research economist taking a one year industrial break from his Ph.D. in Economics. He has 2 years of experience working in government and has an MPhil degree in Economic Research from the University of Cambridge. His research expertise are in international finance, macroeconomics and fiscal policy.
(The commentary contained in the above article does not constitute an offer or a solicitation, or a recommendation to implement or liquidate an investment or to carry out any other transaction. It should not be used as a basis for any investment decision or other decision. Any investment decision should be based on appropriate professional advice specific to your needs.)
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