**Intro**

I have seen quite a few posts on the issue of trying to value Bitcoin. I particularly liked this by Robert Sands. However, I wanted to review in more detail some of the assumptions and how they impact the analysis. I hope the framework I am laying out helps all. ** Bitcoin might be worth a few thousand dollars in the short term or up to several million out there in the future**.

**Does it matter?**

Not to transactional users today. No matter how the value changes in dollars, their use for quick purchases/sales should be unaffected. However, it has many other impacts, to be discussed somewhere else.

**The model**

When the phenomenon is large enough that tenured professors can work on it full-time, there will be many refined theories and empirical research. However, one can right now set orders of magnitudes by using, as many have done, the *Quantity Theory of Money* (QTM) in one or other of its variations.

**M x V = Q x P**

In order to make this useful for this discussion, let’s say Q x P is the total value of goods and services being transacted in an ecosystem. If we value it in USD fiat, Q, P and M are known quantities, so V can be derived. That is done for the US dollar by the St. Louis Fed.

The same equation can be rewritten in the different units of measure, where the subscripts b and d represent BTC and USD. Calling Bd the BTC/usd rate and playing around (see at the bottom for the intermediate steps.)

**Bd = (Q x Pd) / (Mb x Vb)**

One immediate satisfaction can be derived by assuming that the ecosystem is the entire world economy and Vb equals Vd(M2). In that case (sources below),

**Bd = 180 trillion usd / (21 million BTC x 1.5) = 5.7 million usd**

*What is the appropriate V for Bitcoin at worldwide level? *

Probably not 1.5 (M2). However, not the US M1 money velocity (7) either. There is no B1 and B2 (so far), so BTC would probably be used a lot more as a savings mechanism than greenbacks and checking accounts. On the other hand, the velocity of money is driven today a lot more by commercial practice than technological restraints. When galleons and horse carriages moved money around, the technological constraint made sense, but today’s electronic fiat system are not a big damper on money velocity. Rather, the fact that we get paid once a month, companies might have an average of 45 day-sales-outstanding (DSO) and that we want to save a part of our wealth in currency, determine that money circulates only a few time a year.

I doubt Bitcoin would drastically change that in our lifetimes. In that sense I could not imagine the Bitcoin money velocity being something like 70. Just to reinforce the behavioral aspect, let’s think of Weimar in the twenties or Zimbabwe lately. People can get paid daily and not extend any credit, in which case V approaches 365, infinity for all practical purposes. But in our current economic environment, I doubt it could be anything more than single digits.

So, why not derive V from the classical equation? (World transactions: see bottom)

**World V = World transactions / World M2**

**Vw = 180tn / 84tn = 2.14**

If Vb were assumed equal to Vw, Bd would be around 2.7million usd.

**Bd = 180tn / (21m * 2.14) = $4 million**

**Some more immediate implications**

Note that this is done, for pure exercising reasons, with today’s economic size and 2040 BTC stock. Having developed this at length, let’s now play around a bit. Today’s BTC economy is minuscule, and, from the fact that after five year more than half the coins have never been spent, BTC’s current V is well below 1.

It probably could absorb a multiple of the current transactions just by circulating a just little faster, although the large holders probably do not have any incentive in spending while it is perceived as cheap.

Today, we might assume

**Mb = 12million**

**Vb = 0.5**

**Bd = 450usd**

Then

**Qb x Pb = $2.7bn commerce**

If we added 10% of Amazon’s sales (10bn)

**Bd = 13bnusd / (12m x 0.5) = $2,167**

Assuming A Bitcoin ecosystem of 1% of US transactions, plus 5% of a “select” group of countries with weak currencies and some more coins in circulation moving a little faster:

**Bd = 1.6tn / (15m x 0.75) = $140,000**

**Disclaimers: **

– I do not claim having invented any new economic theory and the Quantity Theory of Money has plenty of detractors and reformulations,

– Sources and calculations are quick and dirty, only intended to provide directional guidance. I take responsibility for poor approximations, of course and will edit this post to correct where possible,

– Quite a few assumptions are very strong and may prove to be invalid in the future, among them the irrelevance of altcoins, the regulatory reaction, the behavior of hoarders, quantum computing, the discovery of alien life forms, but

*Isn’t it interesting?*

**Issues to develop further:**

- Measure current BTC Money Velocity based on Blockchain
- Look for trends in M, V and Bd in time series
- Review issue of speculative demand vs. transactional demand and its effect on aggregates.
- Regulatory action.
- Altcoin interaction
- Review issue of GDP vs Gross Production

**Sources:**

- Money velocity in the US:

The St. Louis Fed provides different Vs, depending on the monetary aggregate used. To simplify things, one could use M1 velocity at approx. 7 today or M2 velocity, now at around 1.5.

- I World Transactions / Production:

One needs to use Gross Production and not GDP, because intermediate transactions require payments as well.

I assume that Gross production is around three times GDP. That means that your burger is purchased three times on average, first as a cow, then as ground beef and lastly by you at the drive-in. The multiplier is surprisingly low, but off-hand I cannot find good references to provide. I would be grateful if someone would help me with this.

- World GDP:

http://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal)

- World M2:

M2 in local currency: http://data.worldbank.org/indicator/FM.LBL.MQMY.CN

Exchange rates: http://treasury.un.org/operationalrates/OperationalRates.aspx

- Derivation of Bitcoin pricing calculation

Let’s call Pd the price level in usd and Pb the price level in Bitcoin. By definition,

**Pb = Pd / Bd or **

**Pd = Pb x Bd or**

**Bd = Pd / Pb **

where Bd is the BTC/usd rate. Then the QTM equation could be written as:

**Md x Vd = Q x Pd in fiat and **

**Mb x Vb = Q x Pb in BTC which can be expressed as **

**Mb x Vb = Q x Pd / Bd then, **

**Bd = (Q x Pd) / (Mb x Vb) **(as used at the top of the document)

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Marni,

Thanks for your words. I was delighted to read your article, a wonderfully broad brush covering many of the issues in the bitcoinsphere.

Hello Claudio,

Both you and Robert Sands have produced an excellent armchair analysis and computation that illustrates what I have long tried to explain (without the math, for which I applaud you). That is, if Bitcoin is adopted for even a tiny fraction of online commerce—and nothing else—the very nature of a supply cap will force the exchange value to be very high.

After all, even 1% of the world’s transactions will require that each unit is shaved into small fractions of the eventual supply (only 21 million units can ever be “coined”). Today, we require trillions of US dollars (a medium without a finite cap), just to satisfy each day’s dollar-based exchange needs. I am not referring to the national debt…just the national float. It includes commerce, settlement of debts, gifts, and any that is held in abeyance, pending another short-term transaction.

When I try to describe the fallout of growing BTC adoption, my argument is somewhat abstract, because I hadn’t backed it with math (even back-of-the-envelope numbers will do just fine). Your simple analysis does this with aplomb. Thank you, Claudio!

My thoughts on Bitcoin are at AWildDuck.com (set category filter to bitcoin).

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