Facebook Stock not so different from Bitcoin?

I just read the NYT article from Rob Cox Facebook Stock not so different from Bitcoin.

It has many useful thought starters, although I do not know exactly what to do with it. Of course a vet sees a diseased organ where a chef sees a juicy dish and PETA sees an abused goose. So Rob Cox sees Bitcoin as a startup company.  He is probably not wrong, from his point of view and the final proof of his correctness will be in the payout of his financial bets.

I want to mull around more on some of his insights and will write on them on a later post.  I would like to point out however to the infectious nature of some disinformation and on how it becomes more insidious as it is digested  and diluted around.  Mr. Cox mentions (without specifics) an article from Technology review by David Yermak (commented by me here), which in turn refers to an NBER paper by the same author.

The extremely questionable statistics have made it now into mainstream journalism and become fact for the general public.

Friedman and Hanke on Bitcoin

Check out this Cato article.

I sympathize with Mr Hanke, Mr. Friedman and Cato Institute’s mission, but what a self important and valueless article!

By reading you get the following:

1. Three lines on the birth of BTC.

2. Seventeen lines on how cleverly Friedman foresaw BTC in 1999.  Quite silly.  In 1990 I was part of the Cypherpunks mailing list (as a reader, not a contributor) and you could see digital money in utero right there.

3. Second half of the article is “I am so smart I know about the Tulip Bubble and I think this is the same thing because I say so“.  Mr. Hanke affirms that Bitcoin is volatile without using any objective measurement and does not consider that this volatility could be price discovery in a very uncertain new market.  Not to mention that measures of volatility need to extricate trend, as trendy series tend to be more volatile.

Unfortunately, the Cato Institute blog does not permit comments to the articles.  However, if you are interested, they provide contacts in case you would like him for a speaking engagement.

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.

The Value of Bitcoin


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


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


–       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:

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


  1. 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.

  1. 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.

  1. World GDP:


  1. World M2:

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

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

  1. 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)

Yermak Again

David Yermak came out with an article in my Alma Mater’s publication Technology Review.  I had already commented on his NBER “paper” on the topic of Bitcoin.  This new article is somewhat more “diet”, but contains more of the same inaccuracies and intellectual difficulties.  Below is the link to the article and a verbatim of my comment on TR’s site (some minor typos corrected.)


My Comment

Many of the weaknesses have already been addressed by others. I would only like to point out to Mr. Yermack’s statement on deflation.

 It is far from clear that a wider adoption of Bitcoin would imply deflation.  If Bitcoin became the only medium of exchange in a given community (or the world) though, then there would be deflationary pressures, although issues like money velocity would need to be accounted for.

 It seems the deflation issue is raised as a scarecrow (your salary will be cut!)  I would point out that the best parts of our economy have been in permanent deflation for the last half century and that doesn’t seem to have had any detrimental effect or prevented countless of our best minds to try and get in on these industries.  Try explaining consumers they need to pay Intel, Microsoft or Apple as much for unit of their product as in 1984.  Try telling these companies they need to pay their employees the same salary per kilobyte, petaflop or coolness index produced as they did in 1994.

 Maybe Bitcoin will help usher an era when adjustments to relative price are accepted by members of society without the need to recur to the stratagem of inflation.

 I looked up the author, Mr. David Yermack, who is a professor of Finance at NYU, but also the author of a powerpoint presentation called “The Michelle Markup, the First Lady’s impact on stock prices of fashion companies”.   I have no doubt Mr. Yermak must have worked hard for his professorship at NYU and knows a lot more economics and statistics than I do (just like P.Krugman, another Bitcoin basher), but I think he does not look his best here.

 It is notable that this is a summary of an NBER paper from late last year. Unfortunately, you need to shell 5 bucks to buy the article and read it.  And it ain’t worth it.  Despite the formal academic structure of the paper: abstract, notes, references, black ink on white paper, I think it contains nothing if not the writer’s feelings as described in the free abstract. It is full of inaccuracies, crass errors in basic concepts of statistics and lack of common sense.If it weren’t coming from an established academic, I would figure it was written by a student.

 To save TR readers the five bucks (or to entice them to read it for themselves), a few points on the NBER paper:

 – Like any good academic paper, there are references: two of them! They are Satoshi Nakamoto’s original paper and an article on Wired.

 – The impressive looking tables show volatility measures and correlation with other currencies. Those tables are a sham. We all know the usd/BTC rate is highly volatile, but any statistician worth two cents will tell you that the measure of volatility is highly impacted by trend, and btc shows a clear trend: Up. 

 – Also, the correlation tables are badly designed. There is a conceptual error and also a Stat 101 error (carelessness or intention?)

 — The operational Stat 101 error is that the eur/eur rate could not correlate 100% with the usd as the author shows in the table. The correlation must be 0, since eur/eur equals 1 and a constant series is 0-correlated with any variable series. The author is making the point that btc correlates poorly, so he could not show a 0 there.

 — The conceptual error is claiming that btc is poorly correlated. It is indeed (depending on what r-squared you consider poor), but so is the yen and gold. On the other side, eur, gbp and chf are correlated among themselves, since they are all rather connected to the same EU economic environment. This does not prove anything, but the author hopes no one will really look at the tables.

– Lastly, the big nonsense is claiming that btc is a poor risk management tool because it is not correlated. The first thing you learn in finance courses is that good risk management seeks diversification, and diversification is best achieved by owning assets whose performance is uncorrelated!  This statement is modified in the current article, because someone must have pointed out the problem.  It now says that the Bitcoin risk cannot be hedged. This is partly true, but not very relevant to a forward looking article, since the author does not claims that a hedge is impossible (too silly a claim), only that no market to hedge is there yet.



I have found myself commenting more and more on different sites and having trouble keeping all my opinions together.  From now on I will try to post everything here so it doesn’t get lost.  Most posts will be in English, but some may be otherwise.

Everything published here is my responsibility and a reflection of my opinions only.  However, I will try to provide references to anyone I am quoting from.  If I fail to do so, please contact me and I will be happy to rectify.