Cryptoasset Valuation: Introducing Beta of Velocity | by Johnny Antos | Blockchain Advisory Group

Johnny Antos

Note: This article is complementary to “Considerations regarding “On Value, Velocity and Monetary Theory.” The two pieces are best understood when read together.

Written by Johnny Antos and Justin Shin

Blockchain Advisory Group (BAG) provides technical and principled strategic advisory services to high-quality crypto core teams and traditional private and public corporate management teams.

Since the inception of bitcoin ~10 years ago, many have considered cryptoassets as a form of money. The most popular formulations of “cryptoassets-as-money” use the Equation of Exchange or variations of it.

When limiting the scope of analysis strictly to the cryptoasset-as-money realm, by definition, MV=PQ. Many others have written about this, most notably Burniske, Evans, and Buterin. It’s helpful to be familiar with those pieces first before reading our thoughts below.

There has been much debate whether, at steady-state equilibrium, growth in cryptoasset Velocity (V) could outpace growth in cryptoasset GDP (PQ), which could reduce the Monetary Base (M), and cause a decline in token Price (P). However, we argue that it is incorrect to discuss “the velocity problem” in terms of magnitudes, and not in terms of rates of change. Additionally, we believe that correlation is ineffective at capturing the relative magnitude of changes in PQ and V.

Before we explore the issues associated with this way of thinking, it’s worth explicitly stating the underlying assumptions of using MV=PQ as a tool for contemplating future cryptoasset price.

  1. Assumptions of MV=PQ in cryptoasset valuation
  2. Beta of velocity: why is it useful?
  3. Historical beta of velocity for bitcoin
  4. Appendix

Cryptoasset valuation methods (unlike traditional monetarism) first focused on M as the dependent variable and PQ as the independent variable. Burniske’s initial work set V as a parameter (fixed value).

Because Evans uses average M (“Average VOLT Balance Held in U.S. Dollars”), not M at any given moment, the reasoning in his model is a bit different. The “VOLT Model” sets PQ as the independent variable, derives average M based on this PQ, and then derives V endogenously.

, where


, so


Evans acknowledges that it is the general relationship between PQ and V (relative to each other) that is informative when thinking about forecasting token price movement over time.

As it seems that most investors implicitly think in terms of the simple valuation methodology, MV=PQ (as per Burniske), and not in terms of Baumol-Tobin, the methodology we consider is:

  • First set M aside completely, V = dependent variable, PQ = independent variable. Determine V based on PQ.
  • Then bring in M: M = dependent variable, (PQ/V) = independent variable. This solves for the implied monetary base at a given moment in time.

At a high level, the real question is, “Does this approach make sense?” If only thinking of cryptoassets as money, in a Medium of Exchange (MoE) capacity, this model has some merit.

  • At any given moment in time, MV=PQ is true by definition. Thus, we are not as concerned with the specific magnitude of the variables. Instead, we are only interested in the interactions between changes in the variables themselves
  • Do changes in PQ drive changes in V, or do changes in V drive changes in PQ? Which way does causality go?

It is our view that changes in PQ drive changes in V. Crypto core teams (and ultimately an ecosystem of stakeholders) determine what attributes and incentives support the specific use cases they want a token to provision. It would be nonsensical to arbitrarily “choose” a certain velocity, and then use that to determine PQ. In our view, crypto core teams “choose” PQ by determining which existing target market to disrupt (or in some cases, create innovative attributes and use cases that create entirely new markets). As an example, when the Filecoin team chose to attack the cloud storage market, they essentially chose a certain market size to go after, and consequently, the aggregate demand for the goods being provisioned, PQ.

As a result, the magnitude of velocity is highly sensitive to the specific PQ chosen. For example, for a Store of Value (SoV) use case, the magnitude of V is likely low, which is what many believe to be driving bitcoin price appreciation.

As a corollary, changes in PQ (e.g., growing the network by adding more active users to the cryptoasset network, or existing users increasing their usage) are the driving factor behind how velocity changes over time. If many people held bitcoin as a SoV in the early days, but 100% of new users exclusively use it for payments, it’s obvious that this specific increase in PQ causes a corresponding increase in V (the degree of this increase would be determined by the “beta of velocity”, which we define below). At the same time, complex interplay can exist between growth in PQ and prior existing PQ. (i.e., It is possible that the way new users are using a cryptoasset may influence the specific ways that existing users derive utility from the cryptoasset.)

Lastly, M is determined by the interplay between the relative growth rates of PQ and V.

In this conception, M isn’t chosen by a core team. Core teams choose the specific attributes and use cases that their token provisions. This effectively determines the PQ of the network (i.e., capturing a certain percent of the market, following a particular adoption curve). In turn, that “chosen” PQ determines the velocity because specific user holding or usage behavior is inseparably embedded in the chosen PQ. Thus, any change in velocity is determined either by existing users changing their usage behavior, or by new users with different behavior patterns, and more than likely, some combination of both of these effects. Through this process, M, being the required size of the monetary base, constantly fluctuates at every moment depending on the relative changes in the growth rates of PQ and V, or the quantity (PQ/V).

This seems to be the most robust justification for using the basic formulation of MV=PQ in cryptoasset valuation.

We believe that reducing cryptoasset ecosystems to simple monetary economies obscures many other new possibilities that are enabled by cryptoassets. We are currently exploring frameworks beyond the simple “cryptoassets-as-money” formulation.

In his exploration of the velocity thesis, Evans writes:

“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). 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.” (emphasis our own)

Evans acknowledges that what matters is the rate of growth in PQ relative to the rate of growth in V. This is intuitive in the “instantaneous” MV=PQ formulation:

  • If PQ grows faster than V grows, then M increases (and token value in USD increases, all else equal)
  • If V grows faster than PQ grows, then M decreases (and token value in USD decreases, all else equal)

However, correlation alone is insufficient to describe the relationship between V and PQ.

To observe the mechanics clearly, consider two hypothetical economies, both with the same GDP growth over time.

What do you think?

10 Points
Upvote Downvote

Leave a Reply

Your email address will not be published. Required fields are marked *

GIPHY App Key not set. Please check settings

🤖 BotHunter 🏹 Launch Soon 🎯

Hiring – Solidity Developer (W2, 100% Remote w/ Stock and Token Options)