On Value, Velocity and Monetary Theory.

A New Approach to Cryptoasset Valuations

Valuation methodologies have historically lagged behind the development of the assets they represent. While the Dutch East India Company became the first entity to sell stocks on a public exchange in the early 1600s, it was not until the 1930s that a comprehensive framework for deriving the fundamental value of equity securities was developed. What Graham and Dodd benefited from in 1934 that their predecessors perhaps lacked was a broadly-accepted philosophy of disclosure (eventually codified in the Securities Act of 1933) and, more importantly, a reliable accounting system with unified measurement standards and practices— a common language for discussing value. Without rules of disclosure and requisite accounting conventions, current attempts at studying cryptoasset fundamentals will descend into the Confusion of Confusions that described seventeenth century stock market investment advice.

In this piece, I propose an extension to the prevailing methodology for valuing cryptoassets — one that I hope will alleviate confusion by clarifying the vocabulary used in discussions of value. In the first part of the post, I survey current debates on cryptoasset fundamentals and investigate their core monetary assumptions. I find current valuation models to insufficiently capture the complexities of these conversations, motivating a new approach, which I outline in the second part of this post. The proposed method intends to disjoin demand for commodities and demand for money by placing each asset in a broader economy of return expectations and friction constraints. It is important to note, before continuing, that valuation theorists generally caution against valuation of non-cash-flow-generating assets. As such, the methodologies outlined below remain largely exploratory and imprecise. Nonetheless, I believe these discussions to be valuable in developing directional insights on cryptoasset value, which can be a key lever for projects in optimizing their incentive structures.

A Review of Prevailing Cryptoasset Valuation Frameworks

Valuation Frameworks
The prevailing approach to cryptoasset valuations is undoubtedly that most clearly articulated by Chris Burniske, which can be found in his book, as well as this bandwidth token model (for brevity, I refer to this as the “INET model” from here on out). Brett Winton’s social media token model is largely similar in its approach. The type of asset being modeled in the above takes on different names depending on who you ask — appcoin, medium-of-exchange token, cryptocommodity, proprietary-payment token, utility token. Though each of these terms captures some subtlety, you may consider them interchangeable for our purposes below. The overarching idea is that such an asset serves as the exclusive form of payment that the network will accept in exchange for an underlying scarce resource that it provides (bandwidth, storage, computation, and so forth).

The core thesis of current valuation frameworks is that utility value can be derived by (a) forecasting demand for the underlying resource that a network provisions (the network’s ‘GDP’) and (b) dividing this figure by the monetary base available for its fulfillment to obtain per-unit utility value. Present values can be derived from future expected utility values using conventional discounting. The theoretical framework that nearly all these valuation models employ is the equation of exchange, MV=PQ. While you will see this formula appear in nearly all discussions of cryptoasset value, it is often given little explanation and even less theoretical treatment. I attempt to offer some clarity on this in below, but for now let’s review the basic terms of the equation. M refers to tokens in circulation and V refers to their ‘velocity’ or the number of times each token changes hands in a given period (though we will expand this definition later on). On the right side, P refers to price and Q to quantity (or transaction value in real terms if we are using the so-called Fisher formulation, MV=PT). The right-hand side is the “real economy,” or ‘GDP,’ while the left is the “monetary economy.” The two operate in parallel to each other.

Returning to the models linked to above, both hard-code a constant velocity, project a money supply schedule, a price/quantity schedule, and use the aforementioned equality to derive value per coin. Of course, the output of the model is extremely sensitive to variations in the hard-coded values for both the discount rate and velocity, neither of which is explored in detail. This is not problematic per se as these models are intended to provide nothing more than directional insight. The problem has arisen as the discussion on value in the investment community has honed in on the “velocity” component, in what I will call the “velocity thesis.” The consequent lack of theoretical clarity in these discussions is a key motivator of this piece.

The Velocity Thesis

Valuation and 95 Crypto Theses for 2018 by Ryan Selkis; The Blockchain Token Velocity Problem by Kyle Samani; An (Institutional) Investor’s Take on Cryptoassets by John Pfeffer; On Medium-of-Exchange Token Valuations by Vitalik Buterin. I especially recommend the latter two as they form the inspiration for the approach detailed hereinafter.

(Note: I refer to these and other pieces under the “velocity thesis” for short-hand convenience. This is not to suggest that the people listed above do not have significant points of disagreement with each other with respect to the concept of value (they do). To the extent possible, I attempt to highlight these differences.)

of-value assets will generally suffer from high velocity at scale as users avoid holding the asset for meaningful periods of time, suppressing ultimate value. My claim here is that this thesis is directionally correct, but hard to operationalize. Much of the difficulty, in my view, derives from an inability to precisely define, measure, and project velocity over time. The first step to ameliorating this is to better understand the theoretical framework it derives from. Correspondingly, I find it instructive to take a step back and explain velocity more clearly before more formally restating the thesis.

Most of the above articles define velocity as “the number of times money changes hands”, or formulaically as V=PQ/M, by reference to the equation of exchange. This, of course, leaves us none the wiser as to how to model velocity, as the equation of exchange is nothing more than an identity. MV=PQ just says that the money flow of expenditures is equal to the market value of what those expenditures buy, which is true by definition. The left and right sides are two ways of saying the same thing; it’s a form of double-entry accounting where each transaction is simultaneously recorded on both sides of the equation. Whether an effect should be recorded in M, V, P, or Q is, ultimately, arbitrary. To transform the identity into a tool with predictive potency, we need to make a series of assumptions about each of the variables. For example, monetarists assume M is determined exogenously, V is constant, and Q is independent of M and use the equation to demonstrate how increases in the money supply increase P (i.e. cause inflation). Initial M, Q, and P levels are usually separately estimated from different data sources, often leading to significant discrepancies. Meanwhile V is extremely hard to observe directly. As such, by convention, “[velocities] have generally been calculated as the numbers having the property that they render the equation correct. These calculated numbers therefore embody the whole of the counterpart to the statistical discrepancy.” (See Friedman).

a catch-all to make the two sides of the equation of exchange balance. It often simply captures the error in our estimation of the other variables in the model. Without further specification, saying that projects should minimize velocity is about as useful as saying that a business should attempt to maximize goodwill on its balance sheet. As velocity in its pure form is difficult to directly observe (the best attempt I am aware of is outlined in section 3.4 of the BlockSci paper), current (tautological) definitions of velocity as PQ/M need to be reformulated to allow us to estimate velocity separately from the other variables and project its fluctuations over time. Returning to our historical analogy, we need to develop better accounting definitions before we can truly operationalize velocity and related concepts (e.g. PE, RoA, PB would all be meaningless if we could not agree on how to define and measure them across businesses and over time).

2.) If token value is equal to PQ/VM, we can agree that the problem is not “high” vs “low” velocity, as some writing the topic seems to suggest (though that certainly matters, all things being equal). The real question is how changes in velocity correlate with changes in PQ. Strong positive correlations approaching 1 effectively decouple token value from network transaction growth (note that while this is a drag on the upside, it is protective of value on the downside). If the two are uncorrelated, then token utility value grows (and declines) linearly with demand for the underlying utility (this is what happens in the INET model). Negative correlations act as a lever, generating outsized price swings relative to growth or decline in PQ. Therefore, we need to compare the growth rates of velocity and PQ to formalize the velocity thesis: The thesis states that if velocity grows faster than PQ, token utility value declines. Vitalik and Pfeffer argue that this will likely happen given sufficiently low transaction friction and superior return/store-of-value alternatives. The validity (or invalidity) of this prediction is not something we can explore thoroughly in current models.

3.) Before continuing, I would note, as a practical matter, that I would caution against the suggestions of some proponents of the velocity thesis for projects to create artificial velocity suppression mechanisms. I view staking, mint-and-burn, and other “sinks” as useful only to the extent that they genuinely improve governance and user experience as opposed to acting as artificial price props. Furthermore, I believe velocity can only be practically useful if it is precisely defined and measurable. Let the finance folk argue about it for now, but until you can define and measure it, I would say you can safely ignore it and go back to building.

In sum, we can now concretely state that to support (or refute) the velocity thesis, we need to examine how velocity, PQ, and utility value relate to each other over time, requiring a way to operationalize velocity and project it over time. This, in turn, necessitates a slight departure from existing cryptoasset valuation methodology.

Now that we’ve examined the velocity thesis in some detail, we can articulate six challenges that it presents to the INET model from the standpoint of monetary theory:

1.) Demand for money and demand for commodities are conceptually distinct and should be accordingly decoupled in monetary valuation models. In the INET model, demand for INET and demand for bandwidth are practically one and the same. We need to model demand for money separately from demand for commodities.

2.) Cryptoassets are embedded in a broader asset universe. One way of looking at the INET model is as a single-good, single-asset economy. Utility tokens should instead be seen to compete with other assets for holders. As a corollary, expected returns of other assets should affect demand for the asset being modeled.

3.) Related to (2), transactional demand and speculative demand are conceptually distinct and have different drivers. In the INET model, speculative demand is captured in a supply reduction (HODLed coins are removed from circulation). If the asset is not a store of value, as per the velocity thesis, it may be more realistic to direct speculative demand to another asset and capture this store-of-value demand within the money demand curve.

4.) Blockchain economies are (currently) highly frictional. These frictions could be in the form of transaction costs/fees, cognitive costs, illiquidity, inconvenience, and others. We need to model these frictions, project their behavior over time, and trace their effects on demand for different assets.

5.) Velocity (a) varies over time and (b) should be measurable in a way that is (at least somewhat) distinct from the other variables. I.e. In the INET model, velocity and PQ have no correlation, while price and PQ have a perfect 1.0 correlation coefficient. We instead need to model endogenous velocity as time-varying and distinct from the money supply term to better study the effects of PQ movements on value accretion.

6.) Expanding on (5) payment patterns matter. In INET, patterns of payments don’t matter as long as they all sum to the same transactional volume. If users purchase one large token balance each year and spend it gradually over the year, the effects on value are different than if users made many small purchases to finance consumption as needed. We need a way of modeling different payment patterns and their effects on velocity and value.

More broadly, I believe the community’s understanding of cryptoasset value drivers has outgrown the simple articulation of value in the INET model. And Chris seems to agree.

VOLT: A Two-Asset Model with Endogenous Velocity

In this section, I present an alternative cryptoasset valuation methodology that attempts to remedy the key problems identified in the last section. I model a fictitious utility token, VOLT, which can be exchanged by households to buy electricity at below-retail rates. Please note that while there are numerous projects targeting related use cases, this model in no way references these (it’s an entirely made-up example intended for illustrative purposes).

The token is embedded in an economy with one good (electricity) and two assets: VOLT and a store-of-value asset that has a given expected rate of annual return. This is a frictional economy wherein users start with a fixed dollar amount at the beginning of each year in the store-of-value asset and must transfer their deposits to VOLT in order to finance their consumption of electricity, incurring transaction costs with each transfer. Note: You can select the store-of-value asset to be your favorite SoV cryptoasset or fiat-denominated security. This choice is of little importance to the functioning of the model as presented, except to the extent that it impacts your forecasted transaction costs.

I model VOLT ‘money demand’ using the Baumol-Tobin “cash inventories” approach. Given that this method is slightly more involved than the INET approach, I pause to explain the key intuitions and underlying formulas before moving on to the actual model.

Total spending, Y, is the amount (in USD) that users plan to spend on VOLT each year. This can be thought of as the total GDP of the VOLT economy. Users spend Y uniformly throughout the year. R is the expected return on the store of value asset. C is the transaction cost of moving balances from the SoV asset to VOLT. N is the number of transfers that users of VOLT complete each year to ensure smooth consumption of electricity.

Users thus pay CN in transaction fees each year. The average money balance held in VOLT each year is Y/2N. The return that VOLT users forgo each year is RY/2N. Therefore, users select N, subject to Y, R, and C, in order to minimize their total cost function: RY/2N + CN. Taking the derivative of the total cost function with respect to N, we have:

Setting this equal to zero and solving for N we obtain the cost-minimizing N value of:

Finally, to get our money demand curve in terms of Y, C, and R, we plug the cost-minimizing N value back into the average money balance formula (Y/2N). We can now formulate our money demand function as:

value asset, and the cost per transaction.

Incidentally, we now have the tools at our disposal to formulate a definition of velocity without direct reference to the other monetary term in the equation of exchange, M. Velocity here is equal to the annual GDP, Y, of the VOLT economy over the demand for VOLT balances (the cost-minimizing average balance), or, equivalently, two times the optimal number of transfers, 2N. In other words, if a user transfers one large balance at the start of the year, each VOLT token turns over twice: Once when the user trades her SoV balance for VOLT and again when she exchanges it for electricity. If she buys in two times for half of the amount each time, each VOLT turns over four times, and so forth. Equipped with this definition, we can abandon the fixed-velocity approach of INET and instead project velocity endogenously alongside money demand as a function of Y, R, and C. Note this is equivalent to saying that ‘money demanded’ is equal to GDP over velocity, implying that our final result should still conform to MV=PT.

Step 1: VOLT Supply Schedule
Despite the departure on other points, we still need to project both supply for VOLT tokens and residential electricity facilitated by the VOLT economy. Thankfully, Chris’ shoulders are there for us to stand on and I follow a virtually identical approach. With respect to money supply, the only theoretical difference is that I explicitly assume VOLT will have no HODLers as they will instead opt to hold the store-of-value asset (i.e. VOLT users are risk-averse). What is interesting about this point is that, in the model, each of the three functions of money is performed by a different asset: We have a separate Store-of-Value asset, while VOLT is the medium of exchange and USD is the internal unit of account. Reality will, of course, be more complicated.

I model a supply of 100K VOLT, 10% of which is issued to founders, vesting at 25% annually starting after a one-year cliff. Another 10% is issued to the foundation, of which 20% is spent annually and returned to circulation. Unlike INET, I model VOLT supply as inflationary, growing at a 3% annual rate. This is arbitrary and included mainly for variety’s sake.

Total VOLT tokens in circulation are determined by the tokens already circulating, plus any tokens released by the founders or the VOLT foundation, plus new tokens created by the inflation mechanism each year.

make any sort of claim about electricity markets.

There are undoubtedly significant errors and oversimplifications in the assumptions.
First, I assume a retail electricity price of $0.12 per kWh. I project this to stay flat as retail electricity prices have been relatively stable in recent years. I assume VOLT users can purchase electricity at $0.035 per kWh, an average price across U.S. wholesale markets. Again, I forecast no growth or decline in this price through 2028. Average kWh consumption per U.S. household was 10,766 kWh per year in 2017. Again, I project no change in this going forward. There were approximately 126 million U.S. households in 2017, which I assume will grow at 1% annually through 2028. To simplify things, VOLT is assumed to only be available in the U.S and to be capable of addressing 10% of the U.S. residential electricity market at peak penetration. To avoid overestimating market penetration in earlier years (and underestimating in later years), I follow Chris in projecting an S-curve for adoption. This curve has VOLT entering ‘hypergrowth’ starting in 2023, with a deceleration in the rate of growth as VOLT approaches market saturation and maturity over time.

Using the adoption curve, I estimate VOLT to capture a given percentage of kWh consumed by households in the US each year. This kWh share is multiplied by the wholesale electricity price to derive a value for annual spending on VOLT (i.e. VOLT’s ‘GDP’).

a separate S-curve for each market.
Step 3: Money Demand for VOLT Tokens
To create the VOLT demand curve, I assume an expected rate of return on the store-of-value asset, a given initial transaction cost, and a transaction cost decline schedule.
I assume a store-of-value asset with an expected return of 5% per year. Given that this essentially functions as a risk-free rate of return in our model, I would consider it quite an aggressive assumption (this just captures what I see as optimistic cryptoasset return expectations). You are obviously welcome (if not advised) to bring this value closer to a 3-month Treasury Bill (1.41% at the time of writing) or some other proxy of the risk-free rate (but remember to think about possible impacts on corresponding transaction cost assumptions). It may also be helpful to model some change in this value over time. However, ‘expectations’ are hard to project, so I just straight-line the value through 2028. I would love to see some debate on how to best handle this set of assumptions.
Transaction costs in the initial year are assumed to be $20 per transfer, which is arguably an underestimation. Remember that this number is a fully-loaded representation of friction in the VOLT economy. These costs could include (but are not limited to): network transaction fees (for example, average BTC transaction fees were at $30 and Ethereum’s average gas cost at $1.1 at the time of writing), exchange fees and spreads (e.g. Bittrex charges 0.25% commission on trades), other costs resulting from illiquidity, any instability (real or anticipated) motivating the holding of precautionary VOLT balances to safeguard smooth consumption, the extent to which any given transaction constitutes a taxable event in the jurisdiction in question, time waiting for confirmations, implicit costs relating to asset custody and counterparty risk, inconvenience and cognitive load. I expect the ‘mental’ friction component to be the most significant for an average user. The better we can estimate and forecast the transaction cost parameter, the more accurate our model will be, so I would appreciate suggestions and debate on this point as well.

As far as projecting how transaction costs will behave in the future, my main interest here is to numerically test the velocity thesis that states that utility token values will collapse alongside transaction costs in a frictionless future. To that aim, I find it most conceptually correct to model transaction cost declines in a similar manner to token adoption, using the familiar S-Curve. Here, friction could be said to decline for technological reasons (e.g. second-layer scaling solutions and cross-chain atomic swaps) as well as behavioral reasons (users become more comfortable with using cryptoassets in their daily lives). As such, transaction costs decline very slowly in initial years, but begin declining aggressively in 2023, the same year that VOLT enters hypergrowth (i.e. when mainstream users, not just early adopters, begin using the network as per the traditional S-curve “diffusion of innovation” theory). Ultimately, I assume a miniscule transaction cost in the final year, equal to $0.36 (essentially zero relative to the projected size of the average VOLT transfer of $270K in 2028).

number of transfers for that year. Similarly, the average VOLT held (VOLT demand function) is VOLT GDP over two times the number of transfers. This number times the expected rate of return on the SoV asset is the amount of return VOLT users forgo each year.
We calculate velocity directly as VOLT GDP over the annual VOLT money demand (average VOLT balance held). Remember that this can also be calculated as two times the number of transfers. Finally, utility value is calculated as Money Demanded/Money Supplied, or average VOLT balance held over the number of circulating VOLT tokens (MV=PQ solution). As such, we can restate the solution as VOLT GDP over the product of VOLT tokens in the float and velocity for that year.
Finally, we discount the future utility value in 2028 back to 2018. The discount rate here differs slightly from INET, as we need to incorporate the risk-free rate (very high at 5%). Note that the resulting present value of $0.0244 in 2018 is more than ten times lower than per-token utility value for VOLT in that year. In other words, VOLT would have to be trading at an over a 90% discount to utility value in 2018 to yield a positive expected return for an investor intending to hold through 2028.

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Alex Evans
Analyst at Lowe’s Ventures
Jan 18
On Value, Velocity and Monetary Theory
A New Approach to Cryptoasset Valuations

Valuation methodologies have historically lagged behind the development of the assets they represent. While the Dutch East India Company became the first entity to sell stocks on a public exchange in the early 1600s, it was not until the 1930s that a comprehensive framework for deriving the fundamental value of equity securities was developed. What Graham and Dodd benefited from in 1934 that their predecessors perhaps lacked was a broadly-accepted philosophy of disclosure (eventually codified in the Securities Act of 1933) and, more importantly, a reliable accounting system with unified measurement standards and practices— a common language for discussing value. Without rules of disclosure and requisite accounting conventions, current attempts at studying cryptoasset fundamentals will descend into the Confusion of Confusions that described seventeenth century stock market investment advice.

In this piece, I propose an extension to the prevailing methodology for valuing cryptoassets — one that I hope will alleviate confusion by clarifying the vocabulary used in discussions of value. In the first part of the post, I survey current debates on cryptoasset fundamentals and investigate their core monetary assumptions. I find current valuation models to insufficiently capture the complexities of these conversations, motivating a new approach, which I outline in the second part of this post. The proposed method intends to disjoin demand for commodities and demand for money by placing each asset in a broader economy of return expectations and friction constraints. It is important to note, before continuing, that valuation theorists generally caution against valuation of non-cash-flow-generating assets. As such, the methodologies outlined below remain largely exploratory and imprecise. Nonetheless, I believe these discussions to be valuable in developing directional insights on cryptoasset value, which can be a key lever for projects in optimizing their incentive structures (I write in more detail about this process of ‘mechanism design’ here).

A Review of Prevailing Cryptoasset Valuation Frameworks
The prevailing approach to cryptoasset valuations is undoubtedly that most clearly articulated by Chris Burniske, which can be found in his book, as well as this bandwidth token model (for brevity, I refer to this as the “INET model” from here on out). Brett Winton’s social media token model is largely similar in its approach. The type of asset being modeled in the above takes on different names depending on who you ask — appcoin, medium-of-exchange token, cryptocommodity, proprietary-payment token, utility token. Though each of these terms captures some subtlety, you may consider them interchangeable for our purposes below. The overarching idea is that such an asset serves as the exclusive form of payment that the network will accept in exchange for an underlying scarce resource that it provides (bandwidth, storage, computation, and so forth).

The core thesis of current valuation frameworks is that utility value can be derived by (a) forecasting demand for the underlying resource that a network provisions (the network’s ‘GDP’) and (b) dividing this figure by the monetary base available for its fulfillment to obtain per-unit utility value. Present values can be derived from future expected utility values using conventional discounting. The theoretical framework that nearly all these valuation models employ is the equation of exchange, MV=PQ. While you will see this formula appear in nearly all discussions of cryptoasset value, it is often given little explanation and even less theoretical treatment. I attempt to offer some clarity on this in below, but for now let’s review the basic terms of the equation. M refers to tokens in circulation and V refers to their ‘velocity’ or the number of times each token changes hands in a given period (though we will expand this definition later on). On the right side, P refers to price and Q to quantity (or transaction value in real terms if we are using the so-called Fisher formulation, MV=PT). The right-hand side is the “real economy,” or ‘GDP,’ while the left is the “monetary economy.” The two operate in parallel to each other.

Returning to the models linked to above, both hard-code a constant velocity, project a money supply schedule, a price/quantity schedule, and use the aforementioned equality to derive value per coin. Of course, the output of the model is extremely sensitive to variations in the hard-coded values for both the discount rate and velocity, neither of which is explored in detail. This is not problematic per se as these models are intended to provide nothing more than directional insight. The problem has arisen as the discussion on value in the investment community has honed in on the “velocity” component, in what I will call the “velocity thesis.” The consequent lack of theoretical clarity in these discussions is a key motivator of this piece.

The Velocity Thesis

To understand the current debates on velocity and value, I suggest reading the following if you have not already: Crypto Valuation and 95 Crypto Theses for 2018 by Ryan Selkis; The Blockchain Token Velocity Problem by Kyle Samani; An (Institutional) Investor’s Take on Cryptoassets by John Pfeffer; On Medium-of-Exchange Token Valuations by Vitalik Buterin. I especially recommend the latter two as they form the inspiration for the approach detailed hereinafter.

(Note: I refer to these and other pieces under the “velocity thesis” for short-hand convenience. This is not to suggest that the people listed above do not have significant points of disagreement with each other with respect to the concept of value (they do). To the extent possible, I attempt to highlight these differences.)

The uniting argument in the above articles is that tokens that are not store-of-value assets will generally suffer from high velocity at scale as users avoid holding the asset for meaningful periods of time, suppressing ultimate value. My claim here is that this thesis is directionally correct, but hard to operationalize. Much of the difficulty, in my view, derives from an inability to precisely define, measure, and project velocity over time. The first step to ameliorating this is to better understand the theoretical framework it derives from. Correspondingly, I find it instructive to take a step back and explain velocity more clearly before more formally restating the thesis.

Most of the above articles define velocity as “the number of times money changes hands”, or formulaically as V=PQ/M, by reference to the equation of exchange. This, of course, leaves us none the wiser as to how to model velocity, as the equation of exchange is nothing more than an identity. MV=PQ just says that the money flow of expenditures is equal to the market value of what those expenditures buy, which is true by definition. The left and right sides are two ways of saying the same thing; it’s a form of double-entry accounting where each transaction is simultaneously recorded on both sides of the equation. Whether an effect should be recorded in M, V, P, or Q is, ultimately, arbitrary. To transform the identity into a tool with predictive potency, we need to make a series of assumptions about each of the variables. For example, monetarists assume M is determined exogenously, V is constant, and Q is independent of M and use the equation to demonstrate how increases in the money supply increase P (i.e. cause inflation). Initial M, Q, and P levels are usually separately estimated from different data sources, often leading to significant discrepancies. Meanwhile V is extremely hard to observe directly. As such, by convention, “[velocities] have generally been calculated as the numbers having the property that they render the equation correct. These calculated numbers therefore embody the whole of the counterpart to the statistical discrepancy.” (See Friedman).

Based on this understanding, we can now make three observations about the velocity thesis:

1.) The first practical problem with velocity is that it’s frequently employed as a catch-all to make the two sides of the equation of exchange balance. It often simply captures the error in our estimation of the other variables in the model. Without further specification, saying that projects should minimize velocity is about as useful as saying that a business should attempt to maximize goodwill on its balance sheet. As velocity in its pure form is difficult to directly observe (the best attempt I am aware of is outlined in section 3.4 of the BlockSci paper), current (tautological) definitions of velocity as PQ/M need to be reformulated to allow us to estimate velocity separately from the other variables and project its fluctuations over time. Returning to our historical analogy, we need to develop better accounting definitions before we can truly operationalize velocity and related concepts (e.g. PE, RoA, PB would all be meaningless if we could not agree on how to define and measure them across businesses and over time).

2.) If token value is equal to PQ/VM, we can agree that the problem is not “high” vs “low” velocity, as some writing the topic seems to suggest (though that certainly matters, all things being equal). The real question is how changes in velocity correlate with changes in PQ. Strong positive correlations approaching 1 effectively decouple token value from network transaction growth (note that while this is a drag on the upside, it is protective of value on the downside). If the two are uncorrelated, then token utility value grows (and declines) linearly with demand for the underlying utility (this is what happens in the INET model). Negative correlations act as a lever, generating outsized price swings relative to growth or decline in PQ. Therefore, we need to compare the growth rates of velocity and PQ to formalize the velocity thesis: The thesis states that if velocity grows faster than PQ, token utility value declines. Vitalik and Pfeffer argue that this will likely happen given sufficiently low transaction friction and superior return/store-of-value alternatives. The validity (or invalidity) of this prediction is not something we can explore thoroughly in current models.

3.) Before continuing, I would note, as a practical matter, that I would caution against the suggestions of some proponents of the velocity thesis for projects to create artificial velocity suppression mechanisms. I view staking, mint-and-burn, and other “sinks” as useful only to the extent that they genuinely improve governance and user experience as opposed to acting as artificial price props. Furthermore, I believe velocity can only be practically useful if it is precisely defined and measurable. Let the finance folk argue about it for now, but until you can define and measure it, I would say you can safely ignore it and go back to building.

In sum, we can now concretely state that to support (or refute) the velocity thesis, we need to examine how velocity, PQ, and utility value relate to each other over time, requiring a way to operationalize velocity and project it over time. This, in turn, necessitates a slight departure from existing cryptoasset valuation methodology.

A Monetary Critique of the INET Model

Now that we’ve examined the velocity thesis in some detail, we can articulate six challenges that it presents to the INET model from the standpoint of monetary theory:

1.) Demand for money and demand for commodities are conceptually distinct and should be accordingly decoupled in monetary valuation models. In the INET model, demand for INET and demand for bandwidth are practically one and the same. We need to model demand for money separately from demand for commodities.

2.) Cryptoassets are embedded in a broader asset universe. One way of looking at the INET model is as a single-good, single-asset economy. Utility tokens should instead be seen to compete with other assets for holders. As a corollary, expected returns of other assets should affect demand for the asset being modeled.

3.) Related to (2), transactional demand and speculative demand are conceptually distinct and have different drivers. In the INET model, speculative demand is captured in a supply reduction (HODLed coins are removed from circulation). If the asset is not a store of value, as per the velocity thesis, it may be more realistic to direct speculative demand to another asset and capture this store-of-value demand within the money demand curve.

4.) Blockchain economies are (currently) highly frictional. These frictions could be in the form of transaction costs/fees, cognitive costs, illiquidity, inconvenience, and others. We need to model these frictions, project their behavior over time, and trace their effects on demand for different assets.

5.) Velocity (a) varies over time and (b) should be measurable in a way that is (at least somewhat) distinct from the other variables. I.e. In the INET model, velocity and PQ have no correlation, while price and PQ have a perfect 1.0 correlation coefficient. We instead need to model endogenous velocity as time-varying and distinct from the money supply term to better study the effects of PQ movements on value accretion.

6.) Expanding on (5) payment patterns matter. In INET, patterns of payments don’t matter as long as they all sum to the same transactional volume. If users purchase one large token balance each year and spend it gradually over the year, the effects on value are different than if users made many small purchases to finance consumption as needed. We need a way of modeling different payment patterns and their effects on velocity and value.

More broadly, I believe the community’s understanding of cryptoasset value drivers has outgrown the simple articulation of value in the INET model. And Chris seems to agree.

VOLT: A Two-Asset Model with Endogenous Velocity

In this section, I present an alternative cryptoasset valuation methodology that attempts to remedy the key problems identified in the last section. I model a fictitious utility token, VOLT, which can be exchanged by households to buy electricity at below-retail rates. Please note that while there are numerous projects targeting related use cases, this model in no way references these (it’s an entirely made-up example intended for illustrative purposes).

The token is embedded in an economy with one good (electricity) and two assets: VOLT and a store-of-value asset that has a given expected rate of annual return. This is a frictional economy wherein users start with a fixed dollar amount at the beginning of each year in the store-of-value asset and must transfer their deposits to VOLT in order to finance their consumption of electricity, incurring transaction costs with each transfer. Note: You can select the store-of-value asset to be your favorite SoV cryptoasset or fiat-denominated security. This choice is of little importance to the functioning of the model as presented, except to the extent that it impacts your forecasted transaction costs.

I model VOLT ‘money demand’ using the Baumol-Tobin “cash inventories” approach. Given that this method is slightly more involved than the INET approach, I pause to explain the key intuitions and underlying formulas before moving on to the actual model.

Total spending, Y, is the amount (in USD) that users plan to spend on VOLT each year. This can be thought of as the total GDP of the VOLT economy. Users spend Y uniformly throughout the year. R is the expected return on the store of value asset. C is the transaction cost of moving balances from the SoV asset to VOLT. N is the number of transfers that users of VOLT complete each year to ensure smooth consumption of electricity.

Users thus pay CN in transaction fees each year. The average money balance held in VOLT each year is Y/2N. The return that VOLT users forgo each year is RY/2N. Therefore, users select N, subject to Y, R, and C, in order to minimize their total cost function: RY/2N + CN. Taking the derivative of the total cost function with respect to N, we have:

Setting this equal to zero and solving for N we obtain the cost-minimizing N value of:

Finally, to get our money demand curve in terms of Y, C, and R, we plug the cost-minimizing N value back into the average money balance formula (Y/2N). We can now formulate our money demand function as:

We can thus say that VOLT ‘money demanded’ is equal to the cost-minimizing VOLT balance that users hold each year, which is a function of the GDP that the VOLT economy facilitates, the expected rate of return on the store-of-value asset, and the cost per transaction.

Incidentally, we now have the tools at our disposal to formulate a definition of velocity without direct reference to the other monetary term in the equation of exchange, M. Velocity here is equal to the annual GDP, Y, of the VOLT economy over the demand for VOLT balances (the cost-minimizing average balance), or, equivalently, two times the optimal number of transfers, 2N. In other words, if a user transfers one large balance at the start of the year, each VOLT token turns over twice: Once when the user trades her SoV balance for VOLT and again when she exchanges it for electricity. If she buys in two times for half of the amount each time, each VOLT turns over four times, and so forth. Equipped with this definition, we can abandon the fixed-velocity approach of INET and instead project velocity endogenously alongside money demand as a function of Y, R, and C. Note this is equivalent to saying that ‘money demanded’ is equal to GDP over velocity, implying that our final result should still conform to MV=PT.
The model I use in the next section can be found here: https://docs.google.com/spreadsheets/d/1a1SzF2H1Y3twTvqAlGAwm8Q2jG-CPnP1Q-7qopN-4LE/edit#gid=428912142
I would appreciate reporting of any issues you find with the model (especially mechanical problems/bugs), so I can update the sheet to work for everyone else.

Step 1: VOLT Supply Schedule
Despite the departure on other points, we still need to project both supply for VOLT tokens and residential electricity facilitated by the VOLT economy. Thankfully, Chris’ shoulders are there for us to stand on and I follow a virtually identical approach. With respect to money supply, the only theoretical difference is that I explicitly assume VOLT will have no HODLers as they will instead opt to hold the store-of-value asset (i.e. VOLT users are risk-averse). What is interesting about this point is that, in the model, each of the three functions of money is performed by a different asset: We have a separate Store-of-Value asset, while VOLT is the medium of exchange and USD is the internal unit of account. Reality will, of course, be more complicated.

I model a supply of 100K VOLT, 10% of which is issued to founders, vesting at 25% annually starting after a one-year cliff. Another 10% is issued to the foundation, of which 20% is spent annually and returned to circulation. Unlike INET, I model VOLT supply as inflationary, growing at a 3% annual rate. This is arbitrary and included mainly for variety’s sake.

Total VOLT tokens in circulation are determined by the tokens already circulating, plus any tokens released by the founders or the VOLT foundation, plus new tokens created by the inflation mechanism each year.
Step 2: The VOLT Electricity Demand
Note: For the electricity market, please open the notes in the assumption cells (highlighted on the top right of each cell) to see citations and additional notes. My aim here is to arrive at a value for GDP for the rest of the model to work, not to make any sort of claim about electricity markets. There are undoubtedly significant errors and oversimplifications in the assumptions.
First, I assume a retail electricity price of $0.12 per kWh. I project this to stay flat as retail electricity prices have been relatively stable in recent years. I assume VOLT users can purchase electricity at $0.035 per kWh, an average price across U.S. wholesale markets. Again, I forecast no growth or decline in this price through 2028. Average kWh consumption per U.S. household was 10,766 kWh per year in 2017. Again, I project no change in this going forward. There were approximately 126 million U.S. households in 2017, which I assume will grow at 1% annually through 2028. To simplify things, VOLT is assumed to only be available in the U.S and to be capable of addressing 10% of the U.S. residential electricity market at peak penetration. To avoid overestimating market penetration in earlier years (and underestimating in later years), I follow Chris in projecting an S-curve for adoption. This curve has VOLT entering ‘hypergrowth’ starting in 2023, with a deceleration in the rate of growth as VOLT approaches market saturation and maturity over time.

Using the adoption curve, I estimate VOLT to capture a given percentage of kWh consumed by households in the US each year. This kWh share is multiplied by the wholesale electricity price to derive a value for annual spending on VOLT (i.e. VOLT’s ‘GDP’).

Again, the numbers are exclusively illustrative. If we needed to be more precise, for example, we might project adoption on a state-by-state or county-by-county basis (real-world electricity markets are highly localized) and specify a separate S-curve for each market.
Step 3: Money Demand for VOLT Tokens
To create the VOLT demand curve, I assume an expected rate of return on the store-of-value asset, a given initial transaction cost, and a transaction cost decline schedule.
I assume a store-of-value asset with an expected return of 5% per year. Given that this essentially functions as a risk-free rate of return in our model, I would consider it quite an aggressive assumption (this just captures what I see as optimistic cryptoasset return expectations). You are obviously welcome (if not advised) to bring this value closer to a 3-month Treasury Bill (1.41% at the time of writing) or some other proxy of the risk-free rate (but remember to think about possible impacts on corresponding transaction cost assumptions). It may also be helpful to model some change in this value over time. However, ‘expectations’ are hard to project, so I just straight-line the value through 2028. I would love to see some debate on how to best handle this set of assumptions.
Transaction costs in the initial year are assumed to be $20 per transfer, which is arguably an underestimation. Remember that this number is a fully-loaded representation of friction in the VOLT economy. These costs could include (but are not limited to): network transaction fees (for example, average BTC transaction fees were at $30 and Ethereum’s average gas cost at $1.1 at the time of writing), exchange fees and spreads (e.g. Bittrex charges 0.25% commission on trades), other costs resulting from illiquidity, any instability (real or anticipated) motivating the holding of precautionary VOLT balances to safeguard smooth consumption, the extent to which any given transaction constitutes a taxable event in the jurisdiction in question, time waiting for confirmations, implicit costs relating to asset custody and counterparty risk, inconvenience and cognitive load. I expect the ‘mental’ friction component to be the most significant for an average user. The better we can estimate and forecast the transaction cost parameter, the more accurate our model will be, so I would appreciate suggestions and debate on this point as well.

As far as projecting how transaction costs will behave in the future, my main interest here is to numerically test the velocity thesis that states that utility token values will collapse alongside transaction costs in a frictionless future. To that aim, I find it most conceptually correct to model transaction cost declines in a similar manner to token adoption, using the familiar S-Curve. Here, friction could be said to decline for technological reasons (e.g. second-layer scaling solutions and cross-chain atomic swaps) as well as behavioral reasons (users become more comfortable with using cryptoassets in their daily lives). As such, transaction costs decline very slowly in initial years, but begin declining aggressively in 2023, the same year that VOLT enters hypergrowth (i.e. when mainstream users, not just early adopters, begin using the network as per the traditional S-curve “diffusion of innovation” theory). Ultimately, I assume a miniscule transaction cost in the final year, equal to $0.36 (essentially zero relative to the projected size of the average VOLT transfer of $270K in 2028).

Based on the formulas previously laid out, I calculate the optimal number of transfers per year as a function of VOLT GDP, the expected rate of return on the SoV asset, and the transaction cost. The amount transferred each time is the total spending in VOLT (VOLT GDP) over the number of transfers for that year. Similarly, the average VOLT held (VOLT demand function) is VOLT GDP over two times the number of transfers. This number times the expected rate of return on the SoV asset is the amount of return VOLT users forgo each year.
We calculate velocity directly as VOLT GDP over the annual VOLT money demand (average VOLT balance held). Remember that this can also be calculated as two times the number of transfers. Finally, utility value is calculated as Money Demanded/Money Supplied, or average VOLT balance held over the number of circulating VOLT tokens (MV=PQ solution). As such, we can restate the solution as VOLT GDP over the product of VOLT tokens in the float and velocity for that year.
Finally, we discount the future utility value in 2028 back to 2018. The discount rate here differs slightly from INET, as we need to incorporate the risk-free rate (very high at 5%). Note that the resulting present value of $0.0244 in 2018 is more than ten times lower than per-token utility value for VOLT in that year. In other words, VOLT would have to be trading at an over a 90% discount to utility value in 2018 to yield a positive expected return for an investor intending to hold through 2028.

Step 4: Revisiting the Velocity Thesis
Plotting VOLT’s utility value over time, we see the velocity thesis’ core prediction in action as utility value peaks in 2025 and declines through 2028. Viewed through the prism of the INET model, this would appear strange as between 2025 and 2028 VOLT GDP grows nearly 100%, yet utility value per token declines.

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