Monday, November 11, 2013

The Price and Future of Bitcoin

Guest post by Evan Jenkins.

It’s time for some Real Talk about Bitcoin.

This past month’s Bitcoin boom has brought out the usual derp from both the True Believers and the Cryptoskeptics. The True Believers point to rising prices as evidence of the impending Fiatpocalypse, while the Cryptoskeptics point to the same rising prices as evidence that Bitcoin is a mere faddish bubble, destined to pop as soon as its so-called investors get kicked out of their parents’ basements and need to pay for food and shelter.

What we haven’t seen enough of is analysis of Bitcoin as an asset. Whatever you may think of Bitcoin, it's an actual commodity with an actual price, and we can use that price to make inferences about its future. You’re welcome to unskew my analysis using whatever set of Bayesian priors you hold, but I hope this will at least give a basis for some actual dialog about the future of Bitcoin. 

Bitcoin is a purely speculative asset (that is, you will never be paid anything just for holding it), which makes its pricing model particularly simple. To further simplify things, we’ll make the not entirely realistic assumptions of a zero risk-free rate and risk-neutral investors, or equivalently, a discount factor of 1. What this means is that the price of Bitcoin now is equal to the expected price of Bitcoin at any time in the future.

As I write this, the price of a Bitcoin is hovering around $300. Does this mean that twenty years from now, the price of a Bitcoin should still be around $300? Of course not! Twenty years from now, either the True Believers or the Cryptoskeptics will be proved right. If the Cryptoskeptics are right, Bitcoins will be worthless in twenty years.

If the True Believers are right, they’ll be worth a lot more than they are now. Determining exactly how much more is a tricky issue. The chart in Guan’s post shows several potential implied values for Bitcoin, based on the total value of all Bitcoins in existence growing to various levels. These values are possibly reasonable short-term goals for the True Believers, but I can’t imagine the Bitcoin hype stopping at any of those levels. In order for Bitcoin to really reach a stable value level that can reliably be used worldwide for online transactions, it’s going to need to become a sizable portion of the world’s currency. One estimate puts the current total value of currency in the world at $58.9 trillion. Let’s say that in the long run, Bitcoin will need to become 1% of that, or $589 billion. This corresponds to a price of about $28,000. (This is a larger value but lower price than the last entry in the table: I’m having this take place in the future, when there will be more total Bitcoins.)

All right, we have our setup. Right now, the price of a Bitcoin is $320. There are two possible futures: in the Cryptoskeptic future, a Bitcoin will be worth $0. In the True Believer future, a Bitcoin will be worth $28,000. What is the probability of each future? If we let \(q\) be the probability of the True Believer future, then \[300 = P_{\operatorname{now}} = E(P_{\operatorname{future}}) = 28000 q,\] so \[q = \frac{300}{28000} \approx 0.01.\] Thus, our model tells us that there’s only a 1% chance that the True Believers are right! The higher you think the future value of Bitcoin is, the less likely that that future will actually happen. (This is what makes the chart in Guan’s post so amusing!)

To finish up, I want to bring up two confounding factors, one of which is bad news for the future of Bitcoin, and one of which is good news for the future of Bitcoin but possibly bad news for the True Believers.

The first confounding factor is that the Bitcoin market, as it exists now, probably does a pretty bad job of pricing correctly. The problem is that it is very difficult for somebody who does not already hold Bitcoins to make a bet against the future of Bitcoin. The only people with the power to move the Bitcoin market down are those who have already bought into the Bitcoin market, and they likely have rosier visions of the future of Bitcoin than the rest of us. This, in my opinion, is the biggest piece of evidence in favor of calling Bitcoin a bubble. In order for the Bitcoin market to price Bitcoin correctly, there needs to be a good way to short Bitcoins. But until there is a reliable way to lend and borrow in Bitcoins, that won’t happen.

The second confounding factor is that if Bitcoin really does establish itself as a legitimate currency, we will need to throw our assumptions of how many Bitcoins there are out the window. In principle, there should be no more than 21 million Bitcoins ever produced. In fact, since Bitcoins can be irreversibly lost, we should actually expect the number of extant Bitcoins to start decreasing at some point. But, as much as the True Believers like to rail against fractional reserve banking, the truth is that once Bitcoins become a real currency, it will start being banked and invested like a real currency, which will effectively increase the number of Bitcoins in existence. Depending on how we measure total “amount of money” in US dollars is anywhere from 10 to 20 times the amount of physical currency in circulation. But there is reason to think that for Bitcoin, the mulitplier could be even higher, as Bitbanks would lack, at least initially, any sort of reserve requirement. This lowers the future price, and thus raises the probability, of the True Believer future. But is this the future that the True Believers want? Not really.

So, what conclusions do I choose to draw from this analysis? First, Bitcoin is in a massive bubble that will in all likelihood eventually pop. Second, even if I’m wrong and Bitcoin does manage to establish itself, it will end up looking a lot more like a traditional currency than the True Believers envision. Indeed, it’s possible that Bitcoin will succeed but still settle at a significantly lower price than it’s at now, due to the power of fractional reserve banking. But it’s hard to imagine a path from here to there. The True Believers are likely to resist any attempts to turn Bitcoin into a stable store of value precisely because the means to do so are antithetical to their cause. A Bitcoin future will require a concordance between the True Believers and the Cryptoskeptics, and right now, the cultural gap just seems too large to bridge. Some sort of cryptocurrency may indeed establish itself, but the signs right now do not point to Bitcoin.

Evan Jenkins is a Visiting Fellow at the Pinion Institute for Econotrolling. He occasionally rants about provincial urban development issues at his blog, Let the Midway Bloom. Follow him on Twitter at ejenk.


  1. "The higher you think the future value of Bitcoin is, the less likely that that future will actually happen."
    That is an absurd statement. In your model, yes. But your model is ... quite simple.

    "The first confounding factor is that the Bitcoin market, as it exists now, probably does a pretty bad job of pricing correctly." And that is 100% true. But we have to take into account Bitcoin consists of two layers (tradingwise). The first is the Blockchain and Bitcoin, this is just a common database. And this is what Bitcoin as core feature really is. The second one is Bitcoin as (maybe) currency. This is an derivative on the database. And the current pricing is completly broken, with Bitcoin we are in the pre Black–Scholes area, where no one got a clue what Bitcoin as money is worth.

  2. Anonymous12:56 PM

    Your analysis of P_t=E_t[m_t+k*P_t+k] completely misses the point that the equation must also hold true at time t+k. With zero risk-free rate the Euler equation works fine. As soon as Rf>1, there must be some reason to hold an asset which is dominated in terms of return. Actual money seems to be dominated by bonds and there are two theories for this. (1) The monetarist view that money is required for transaction and is thus special. You implicitly take this approach; "if Bitcoin really does establish itself as a legitimate currency". The second view is the "fiscal theory of the price level" based on the present value of government primary surpluses and the assumption that people pay their taxes. Under this approach, Bitcoin is always worth zero since there is no tax mechanism to draw the currency back to the "government". Adam Smith notes this as "The paper of each colony being received in the payment of the provincial taxes, for the full value for which it had been issued, it necessarily derived from this use some additional value, over and above what it would have had, from the real or supposed distance of the term of its final discharge and redemption." This is the basis for seigniorage that we see in modern fiat currencies.

  3. Bitcoin is a commodity. Similar to other commodities like gold, silver, etc. but it exists only in the digital, information space. The only physical manifestation of Bitcoin is the crypto-chain that represents the Bitcoin you have. The security of the encryption is what gives holders confidence that the Bitcoin won't be stolen by others, and that counterfeit Bitcoins won't be created. So, the confidence in Bitscoins is predicate on the confidence in crypto computer security.

    One other difference of Bitcoin from physical commodities is that a per-determined maximum number of Bitcoins, which is 21million, will ever exist.[1] Thus unlike gold, we know how many Bitcoins will exist so the chance for a "gold rush" find that would significantly change the supply, and hence worth, of Bitcoins doesn't exist.

    What does this mean for the value of a Bitcoin? Depends on why people want them. If it is for small transactions then the concern with the value and security is not so great. In this case the Bitcoin is more of a curiosity and the willingness to take some loss if the Bitcoin is compromised is an easy one to make. To use Bitcoins for large payments, may require some history of use first. Two principle characteristics are required: 1) confidence in the security of the Bitcoin, which we said is tantamount to the confidence in the computer crypto system. 2) price stability over the time span of the transaction or holding time. I think that crypto computer security has been adequately demonstrated by those who take care to setup systems that are designed to be secure, but not everyone is at that point yet. This second criterion is the one that is yet to be settled. With the widely varying price in traditional currencies like the USD and EUR, confidence in the value of the Bitcoin is yet to be established.

    There are some related issues like divisibility; currently Bitcoins are not divisible. Speed of settlement; currently it takes about 10min for a peer-to-peer consensus to be reached as to the legitimacy of a transaction. This may be too long for some uses.

    For now, the Bitcoin is a fun toy to speculate with. It's kinda like gambling. Will the value go up? Or is it currently in a bubble and it will go down?

    When sufficient history for the Bitcoin has been accumulated, and some expectations established, then it might server as some kind of reliable medium of exchange. But for now, it's the wild west. Enjoy the ride!

    Lastly, Bitcoin is not unique. Unlike gold, digital commodities can be created by whomever wants to create a new one. Let's say I create a new digital commodity called Digicoin with all the same properties of Bitcoin. Why wouldn't someone take my Digicoin instead? or in addition to Bitcoin? We could have thousands or millions of digital commodities each with the same guarantees of uniqueness and rareness as Bitcoin. It would be like people creating their own new elements to add to the periodic table, only this is the digital table of commodities.

    See more at:


    1. I'm glad to see somebody else pointing out that bitcoin can be endlessly duplicated.

      For an index of faults with bitcoin, see my bitcoin entry at Critiques Of Libertarianism.

    2. It cannot easily be duplicated because the network effect means the first one into the new territory owns the territory. That is to say, if your option is to use Bitcoin#1 and trade with 10000 people or use Bitcoin#2 which is exactly the same but only allows you to trade with 10 people, anyone would choose the larger network. The new guy needs some compelling argument to drag people in the door.

      However, the difficulty of achieving a duplication is not an outright block on duplication ever happening. It can be done, and no doubt will be done. Just not all that often.

    3. @Mike_Huben: Bitcoin has already been endlessly duplicated. (Having open source code tends to allow that.) Still hasn't killed it, thanks to network effects.

      Didn't know bitcoin was part of libertarianism, but whatever.

  4. I wrote up my thoughts on "The Rise and (Inevitable) Fall of Bitcoin" ( ) which is in some ways an expansion on your point that "The higher you think the future value of Bitcoin is, the less likely that that future will actually happen." It's based on the Paradox of Thrift and drawing out what would happen when Bitcoin supply growth ceases.

  5. "Bitcoin is a purely speculative asset ... which makes its pricing model particularly simple. "

    It does? Sometimes the "simplest" things are the hardest to explain.

    "To further simplify things, we’ll make the not entirely realistic assumptions of a zero risk-free rate and risk-neutral investors, or equivalently, a discount factor of 1."


    1. Anonymous11:03 PM

      Its the assumptions necessary to make mathematical equations. Economics is full of them and they are all hogwash. Of the thousands of economic equations out there not one of them even remotely resembles the real world because of the simplifications on human behavior, institutional qualities and frictionless behavior of humans in groups.

  6. Is it not ironic that Bitcoin is priced in dollar? Traded in dollars?

    It occurs to me that Bitcoin is really like sex for money, you can pay whatever you think he/she/it is worth to you, and, price for a Bitcoin is whatever two make out to be.

  7. Anonymous4:12 PM

    The author ought to be harsher on the bitcoin believers. The recent crop of bitcoin articles has puzzled me a bit since they've been painting the situation as an all-or-nothing scenario (bitcoin becomes the primary currency after fiat money collapses or else it vanishes into obscurity and everyone invested in it goes broke), but that seems wrong to me. Bitcoin will probably be useful for some time (e.g. for illegal trade, scamming suckers, &c.) but it will only become a widely used currency when legal businesses start accepting them as payment, which will only happen when businesses can use bitcoins to pay off their debts, which will only happen when a government enforces the validity of bitcoins. Since that's never going to happen, the only alternative which makes bitcoin realistic is anarchy/apocalypse. That bitcoin enthusiasts seem to be betting on the total collapse of all world governments strikes me as insane, and I am of the opinion that every honest anit-bitcoin post ought to point out that insanity.

    1. Schadenboner9:12 AM

      Moreover, in the (vanishingly improbable) case of an apocalypse, since Bitcoins are dependant on a more-or-less functional Internet they are an even worse store of value than gold (which, unless you're setting up a Mad Max Electronics and Dental Implants business, is also a pretty useless thing to be stuck holding "after the bomb").

      The credulity of those professing such cynicism never fails to astound (he said, without a hint of irony, not a goddamn hint).

  8. Anonymous9:26 PM

    Bitcoin is NOT an asset. Bitcoin is NOT a currency. It has no intrinsic value, whatsoever.

    Because Bitcoin has no intrinsic value I had a hard time finding an appropriate historical comparison. Dot coms? No. Tulip bulbs? No. Various commodity bubbles? No.

    Bitcoin is none of those. Bitcoin is a flat-out pyramid scheme.

  9. Do you realize that, implicit in your pricing formula for bitcoin, is the assumption that bitcoin is not a bubble? If there truly is a 1% likelihood that each bitcoin will be worth $28,000 for a perfectly reasonable reason (bitcoin becomes an established currency like any other), then where is the irrationality? A bubble means that, inevitably, the price will fall below its current value. A bubble means that, for the price not to collapse, it must grow at a rate such that the asset's value will eventually exceed GDP. According to the analysis in this piece, why is investing in bitcoin any different from buying the currency of some newly established, unstable government that may dissolve soon?

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