Bitcoin valuation – hold the equations

In my prior post, I tried to create a framework to understand what can drive the value of Bitcoin, not the small events that can move it day-to-day, but rather how its increased adoption can influence its exchange rate vs. fiat currency and, ultimately, its value as a unit against everyday commodities.  Let me try to say the same things with more words and less equations.  It won’t be dumber or shorter, just more conceptual.

The idea is very simple.  Money has to be enough to support commerce.  If the number of pieces is smaller, each piece will be worth more and vice versa.  Ultimately, that is what drives inflation in fiat moneys and, over and over, it has been proven (at least directionally) right.

All calculations are purely exercises based on very restrictive assumptions but I hope they help frame understanding.  The idea from the exercise is that Bitcoin is either worthless or worth substantially more than its current value.


The approach follows a few assumptions that are widely used and posted in the bitcoinsphere (while a few years back you could only hear them in the corridors of econ departments).

  1. Currency or money derives value from its nice features as: a) medium of exchange (MOE), b) store of value (SOV) and c) unit of account.  Some mention a fourth d) liquidity, but I think this one is more a quality of the other three than a separate function.
  2. The demand for money determines its price, and therefore its exchange rate.
  3. Critically, for the price to be stable at some point, the total amount of a currency in circulation must be enough to satisfy its users, but unlike apples, or gasoline, whose usefulness depends on an absolute quantity consumed, money can just be sliced in smaller units and still perform the same functions.  In other words, users don’t care if something is worth 1 BTC quoted @$500/BTC or 0.1BTC @$5000/BTC.

So, what does this mean for Bitcoin?

The Quantity Theory of Money (QTM) says basically that all money has to be enough to buy all stuff that gets bought in the market (sorry fellow economists).  So, unless someone manufactures more units, the more a currency is used, the more each unit is worth.  That is abstract math and holds true regardless of whether you think BTC will be successful in the future, whether you think it will be regulated or used only as a collector’s item.  But QTM also considers that each bill or coin or gold slab or seashell can be used multiple times within each time period.  If a coin is used once in the year and then lies in a drawer, it will support half the transactions than if it is used by the seller again within the year.

So if in an ecosystem there are one hundred apples and two hundred coins and farmers collect the coins and store them underground for a year, after some bargaining (economists would say price discovery), an apple will be worth two coins.

If someone minted another two hundred coins, the price of apples would double.  If bugs ate half the apples, the price would also double.

Now imagine that farmers turn around and buy apples themselves (kind of silly, but to keep the example simple).  The same coin could be used twice in the year.  Therefore, it would have the same effect as minting more coins.  The price would be double again.  QTM folk call that money velocity.  There is a nice site by the St. Louis Fed, that estimates money velocity for the US dollar which, by the way, is around 7 if you consider just basic money (or M1) and 1.5 if you add in other quasi-money, such as CDs and money market funds (M2).

So the value of a bitcoin can be linked to how much it is used.  For instance, if there were only Bitcoins to use as money in the whole world (and they were exchanged with the same velocity as today’s fiat money), in order to have enough currency to complete all transactions, the existing BTC would have to have the same value as all the money that is currently in use.  Today there are 84 trillion in M2 (my estimate based on World Bank and UN data).

Value of 1BTC = 84trillion / 21 million = 4 million

That may be totally unrealizable, but it is a useful reference.

Today, however, there are, for simplicity, 12 million BTC and, since there is so much hoarding, I will assume that they get used rather slowly, say once every two years, i.e. money velocity is 0.5.

With these assumptions, the commerce supported today by Bitcoin would be

12million BTC x 0.5 x $450 (current value) = $2.5 billion in commerce

It is probably in the ballpark.  Here the velocity assumption is crucial and playing with it would yield different numbers.

What would the value on BTC in dollars (Bd) is you add 10% of Amazon’s business (10bn)?

Bd =$13bn/(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 (totaling 1.6 billion in transactions) and some more coins in circulation moving a little faster:

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

But if hoarders started spending their BTCs, say in consumer goods or in starting companies, the velocity might climb to the current worldwide M2 velocity of 2.14,

Bd = $1.6tn / (15m x 2.14) = $50,000

Is this scenario too farfetched?  I do not think so.  Is it imminent?  Probably not.

So What?

In the end, the value of Bitcoin as a unit will be driven by how much it is used.  If it were the only currency around and it ends up used a lot as a MOE, it value would be in the low millions of today’s US dollars.

Just a small increase from today’s use could bring a large hike in its exchange rate, though an increase in the use as MOE would increase it velocity and that would moderate the price.

I welcome comments and encourage reading the fuller post here, where you can also find sources for the data.


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