Bitcoin: something seems to be'fundamentally' wrong

Por: Jose E. Gomez-Gonzalez,
Julian A. Parra-Polania

Núm. 819
2014tá - Colombia - Bogotá - Colombia - Bogotá - Colombia - Bogotá - Colombia - Bogotá - Colombia - Bogotá - Colombia - Bogotá - Colombia - Bogotá - Colo

Bitcoin: something seems to be‘fundamentally’wrong
Jose E. Gomez-Gonzalez and Julian A. Parra-Polania*
Abstract
In the present paper we remark that the absence of an intrinsic or fundamental
value represents a problem for the stability of the bitcoin’s price as an asset.
In addition, we consider some …nancial stability concerns that derive from thehypothesis that the bitcoin will survive as an asset subject to high speculation.
Keywords: bitcoin; fundamental value; …nancial stability.
JEL Classi…cation: E42, G12, G23*Researchers at the Banco de la Republica. Cra 7 #14-78, Bogota, Colombia. Contact e-mails: jgomezgo@banrep.gov.co, jparrapo@banrep.gov.co.

The authors thankFranz Hamann, Jair Ojeda, Oscar Valencia, Carlos Varela, Carmiña Vargas and Hernando Vargas for valuable discussions. The views expressed in the paper are those of theauthors and do not represent those of the Banco de la Republica or its Board of Directors.

1Introduction

Bitcoin is a virtual currency scheme1 designed by a person or a group of people whose
pseudonym is Satoshi Nakamoto. It is a decentralized system (there is no central authority issuing the bitcoin or supervising bitcoin payments) which allows for anonymoustransactions by internet. Its protocol, implemented in 2009, is explained in Nakamoto(2008).
Although it has gained some popularity since 2013, several economists have cast
doubts on the ability of the bitcoin to ful…ll the functions of money and, instead, consider that it resembles more a highly speculative investment (see, for instance, Yermack,2014).
1

A detailed analysis of virtual currency schemes can be found in ECB (2012).

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The bitcoin can be considered, inter alia, as a medium of exchange or as an asset.
As a medium of exchange, the bitcoin has not been supported by any government ormonetary authority which weakens its ability to compete with the legal tenders of eachcountry. When the government declares a currency legal tender, although people may
want to use other currencies to make transactions, it is easy that the one supported by
the government becomes valuable and consolidates as a medium of exchange because
the fact that public wages, taxes and public goods and services have to be paid in suchcurrency creates a huge network around it that makes it worthwhile to use.
The lack of support from any goverment reinforces a vicious circle in which thebitcoin is mainly demanded as an asset for speculative purposes rather than as a mediumof exchange, thereby generating high volatility in its value, which in turn dissuades
people from using the bitcoin as a medium of exchange.2 Similar to hyperin‡ation
episodes, it is di¢ cult to persuade people to make transactions with a currency thathas a signi…cant probability of losing 1 or 2% of its value overnight (of course it canalso gain such value and that is why it can be very attractive for speculative reasons).3
Furthermore, as it has been previously shown (Ron and Shamir, 2013) most bitcoins
have been hoarded rather than used for transactions con…rming the dominant use of
the bitcoin for speculation.
The value of the bitcoin is market-determined. As a medium of exchange, the supplyof bitcoins is stable and will be constant approximately from 2030 on. This feature,
which has been promoted as a good characteristic of the bitcoin, plays against its role
as a medium of exchange since it rules out the possibility of responding to demand
shocks with supply movements that help to stabilize the bitcoin’s value.
As an asset, the bitcoin supply depends on the willingness of its holders to sell
bitcoins at the market price and its demand depends on the willingness of people tobuy it at such price.
The present paper sets up a model which points out some particular features of thebitcoin that are relevant for understanding the problem of its value as an asset. In short,
we remark that a small or nil intrinsic or fundamental value represents a problem forthe stability of the bitcoin’s price (as an asset). Although this would not threaten thefuture of the bitcoin if it were able to gain enough acceptance as a medium of exchange,
2

Similar views have been previously stated. See for instance The Economist, March 15th 2014 andIto, 2014
3For instance, in 42 of the last 100 days (from 01-Mar to 08-Jun-2014), the bitcoin’s price has showna variation greater than 2% with respect to the previous day.

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this situation seems to be highly improbable due to the reasons explained above.
In addition, we consider some …nancial stability concerns that derive from the hypothesis that the bitcoin will survive as an asset subject to high speculation.

2A simple model to analyze the bitcoin as an asset

Let us think of a demand-supply model for any asset in the following way. We divide
the demand of an asset X (consider that, for instance, X represents famous paintings)
into three components. First, an ‘autonomous’ component, which is independent of
the price. This component intends to capture the fact that, no matter the price (atleast within a wide range), some people simply want/need to have/use X. Second, acomponent related to the fact that X provides utility to its holder. Third, a component
related to speculative purposes, i.e. the attempt to pro…t from the ‡uctuations ofthe market value of X (for simplicity we assume that the opportunity cost of suchinvestment is zero). The demand equation is as follows:
Xtd = a0;ta1;t pt + a2;t Etd pt+1

pt

(1)

where pt is the price in period t and Etd pt+1 corresponds to the expected value in t ofpt+1 by those who are willing to demand/buy X.
The supply of X has three analogous components: an autonomous component (people who simply need to sell X, no matter the price), a non-speculative component relatedto the fact that producers of X are encouraged by a higher price and the speculativecomponent.
Xts = c0;t + c1;t pt c2;t (Ets pt+1 pt )(2)
For the speculative component, there is a continuum (of measure one) of agents
who extract noisy signals from the market and form their expectations. Each period ta proportion c2;t receives signals from the market such that each of them is willing tosell a unit of X, and the rest of agents (a2;t = 1 c2;t ) receive signals that make eachof them willing to buy a unit of X.
The market equilibrium (Xtd = Xts ) yields:
pt =a0;tc0;t + c2;t Ets pt+1 + (11 + a1;t + c1;t3c2;t ) Etd pt+1(3)which can be written as
pt =st + c2;t Et pt+1 + (1twhere t(1 + a1;t + c1;t ) 1 ,follows a random walk:

tc2;t ) Etd pt+1a0;tc0;t . We assume the autonomous factor

t =t 1 + "t(4)t(5)

Each agent i receives a signal yi;t+1 on the shock "t+1 (the noise in each signal isassumed to be independent from the others) and constructs a forecast of the shock,that is, b"i;t+1 E ["t+1 j yi;t+1 ]. A relatively high (low) value of b"i;t+1 implies that thesignal from the market is indicating that the future price may be high (low) with respect
to the current one, and therefore such signal makes its receiver willing to buy (sell) X.
The signal yi;t+1 is independently distributed with mean "t+1 . Consequently, although
in a large sample such signal should be unbiased, for a particular period and for theR1
average of agents it can be biased: 0 b"i;t+1 di = "t+1 .
Without loss of generality we can order the forecasts from the lowest to the highest.
The lowest will be b
"0;t+1 and the highest b"1;t+1 . The average forecast that is constructed
R1
1by those who demand X is denoted by b
"dt+1b"di, and, analogously, for
1 c2;t c2;t i;t+1
Rc2;t1b"i;t+1 di. For simplicity, we also assume thatthe supply side we use b"st+1c2;t 0
parameters a1;t and c1;t do not vary over time, and hence t = .
To obtain a solution for the price of X we postulate the following form:
pt = A"t+1t + A"e(6)where A and A" are constants to be determined. This implies that the agent i’s priceexpectations are
Ei;t pt+1 = A ( t + b"i;t+1 )(7)

and the average expectations for the demand and the supply sides are
Etd pt+1 =1
1 c2;tandEts pt+1 =

1c2;tZ 1

Z c2;t04

Ei;t pt+1 di(8)Ei;t pt+1 di(9)c2;trespectively. Then substituting (7), (8) and (9) into (4), we obtainpt =[(1 + A )"t+1 ]t+A e

Therefore our postulated form is consistent as long as A
2= (1) and the solution for the price of X is4
pt =1== (1( t + "t+1 )) and A" =(10)Equation (10) allows us to point out two features of the bitcoin that are relevant forunderstanding the problem of its value as an asset.
1. The existence of a fundamental value (a1 ; c1 > 0) serves as an anchor to make
Equation (10) to converge to a real solution (i.e. < 1). In the absence of thesefactors, a1 ; c1 = 0 and = 1, there is no convergence of the equation and one
would expect frequent emergence of bubbles as remarked by several economists,including the Nobel Prize winner Robert Shiller.5 Even if the fundamental value
is not zero, if it is positive but small enough a similar result holds. If a1;t + c1;t isclose to zero is close to one and any change in the autonomous factor or in theaverage market signal will have a huge impact on the asset’s price.
While paintings may give some utility to their holders (or shares give dividends
to stockholders), it is not clear what is the utility or the non-speculative pro…tderived from holding bitcoins. The situation is di¤erent if we consider the bitcoin
as a medium of exchange but, as explained above, it still seems to be di¢ cult thatthe bitcoin gets support to be regarded as a convenient medium of exchange.
2. In situations in which the average market signal is negative, i.e.
"t+1 < 0
the size of the autonomous demand factor relative to the autonomous supply
factor becomes crucial to avoid that the price may go down to zero. a0;t > c0;t! t > 0. In the case of the bitcoin, the autonomous demand seems to be mainly
related to a very undesirable situation: some people use it for illegal purposes
4

Based on the model’s results it can also be veri…ed that, for any agent i in the demand sideb"i;t+1 "t+1 and, for any agent k in the supply side b"k;t+1 < "t+1 .
5See, for instance, http://www.businessinsider.com/robert-shiller-bitcoin-2014-1

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because transactions are completely anonymous and they are not subjected to
the regulation of any authority, and therefore using the bitcoin (no matter theprice) becomes a good way to avoid the law.
As an additional point, notice that Equation (10) shows that a signi…cant part ofan asset price volatility can be related to the volatility of noise in the signals. Investors
extract signals from information related to the fundamental value of an asset, i.e. thecompany’s balance sheet, the outlook for the sector’s production... in the case of thebitcoin it is expected that the noise volatility may be much higher since it is not clear
what is the reference information related to the fundamental value.

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Some Financial Stability Considerations Regarding the Bitcoin

As we mentioned above, there are reasons for not being very optimistic about theconsolidation of a decentralized virtual currency such as the bitcoin. However, it resultsinteresting to analyze some of the consequences that an eventual positioning of thebitcoin may bring for …nancial stability.
For that purpose, let’s suppose that the bitcoin (or any other virtual coin) obtains
enough public acceptance either as a medium of exchange or as a less liquid asset used
for speculative purposes in an economy. In other words, let’s assume that a signi…cantnumber of transactions are done with virtual money or that a signi…cant number ofindividuals buy bitcoins hoping they can exchange them for more dollars in the future
in order to have capital gains.
Let’s think about two di¤erent situations: one in which there is no bitcoin-denominateddebt, and another one in which some debts are denominated in bitcoins.
Under the …rst scenario, …nancial stability concerns are less meaningful than under
the second one. In both cases, households, …rms and banks handle virtual wallets
and use bitcoins either for transactions or for speculative purposes. Assuming fullconvertibility between the dollar and the bitcoin, then they use the dollar (legal tender)
to obtain bitcoins (either to make transactions or to speculate), but since there’s no
bitcoin-denominated debt, banks don’t have deposits denominated in such currency.
Banks only handle bitcoins for buying goods and services that are paid with this virtualcoin, or hold them in their balances as an investment.
6In this scenario, macroeconomic stability concerns appear when there are considerable oscillations in the dollar/bitcoin exchange rate. Devaluations of the dollar withrespect to the bitcoin, or expectations of devaluation, may induce agents to prefer toaccept bitcoins instead of dollars generating additional exchange rate pressures and,eventually, speculative attacks. This concern worsens when we think that expected
appreciations of the bitcoin are probably followed by a larger demand for it. Substantial exchange rate movements may a¤ect the willingness of individuals to accept dollar
payments, reproducing a situation similar to a hyperin‡ation.
The main challenge related with …nancial stability under this …rst scenario deals
with the willingness that agents may have of leveraging their bitcoin holdings. Agents
can issue dollar-denominated debt for buying bitcoins if, for instance, they expect anappreciation of this asset. Whenever their expectations result invalid in the future, boththeir incentives and capacity for repaying such debts decrease, reproducing a situationin which agents appear to be over-indebted. A high enough degree of over-indebtedness
may result in a debt-de‡ationary process which may lead to serious problems relatedwith …nancial instability. However, as in this …rst scenario all debts are denominated indollars, the Fed, the FDIC and other regulatory institutions can respond to situations
in where there is an accelerated increase in agents leverage using several policy tools(ex-ante measures such as imposing maximum debt to income ratios, capital surcharges,etc.; and ex post measures such as lender of last resort actions).
Probably the most challenging scenario for …nancial stability is the second one,relating to an economy in which bitcoin denominated debt is allowed. Let’s suppose that
one agent borrows a bitcoin from another with the promise of repaying the principal andan interest rate in bitcoins. Let us …rst assume that credit is not intermediated by formalbanks, but through bilateral relationships established between individuals. It would be
extremely di¢ cult to impose any regulation over those debts. They would operate as
informal credit somehow similar to supplier credit, but denominated in foreign currency.
Large exchange rate movements can cause di¢ culties for repaying bitcoin denominateddebts. If the debtor needs to buy bitcoins for repaying his debt, abrupt changes in theprice of bitcoins will signi…cantly a¤ect his paying capacity.
Now, let us assume there are formal banks for issuing bitcoin-denominated debt.
These banks could be those that are actually established or may also be individuals
or coalitions of individuals engaged in borrowing and buying bitcoins as their maineconomic activity. They accept deposits of small denominations in order to lend toborrowers requiring loans in higher denominations. Regulating and supervising these7

banks may be extremely hard for governmental agencies, because these banks may
easily be established as shadow banking.
In the absence of a lender of last resort in bitcoins, a generalized fear from depositors
could easily lead to bank runs. Su¢ ciently large bank runs could lead to bankruptciesof several virtual banks. Even in the case in which no traditional banks are involved
in bitcoin lending, these banks may result a¤ected from virtual banks’ bankruptcies
whenever virtual banks use dollar-funding provided by the traditional ones.

4Conclusion

This paper points out that a small or nil intrinsic or fundamental value represents a
problem for the stability of the bitcoin’s price as an asset. In the absence of fundamental
factors a rational expectations equilibrium for price is not guaranteed. If such factors
are small enough any small change in the market’s conditions will have a huge impact
on the bitcoin’s price and one would expect frequent emergence of bubbles as remarked
by several economists, including the Nobel Prize winner Robert Shiller.
Some …nancial stability concerns derived from the hypothesis that the bitcoin willsurvive as an asset subject to high speculation are also highlighted. In particular in a
scenario in which a bitcoin-denominated debt market develops, a generalized fear from
depositors could easily lead to bank runs due to the absence of a lender of last resortin bitcoins.
REFERENCES
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http://www.bloomberg.com/news/2014-04-01/bitcoin-s-swings-hurt-viability-as-currency-fed-economist-says.html, Bloomberg, March 31.
3. NAKAMOTO, Satoshi (2008), "Bitcoin: A Peer-to-Peer Electronic Cash System," unpublished paper, retrieved at http://bitcoin.org/bitcoin.pdf.

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4. Ron, D. and A. Shamir (2013), "Quantitative Analysis of the Full Bitcoin Transaction Graph," in Financial Cryptography and Data Security, Springer, eds.
Sadeghi, A. 17th International Conference, FC 2013, Okinawa, Japan, April 1-5,
2013, Revised Selected Papers.
5. The Economist (2014), "Money from Nothing," March 15.
6. Yermack, D. (2013), "Is Bitcoin a Real Currency? An economic appraisal," Working Paper No. 19747, NBER, December.

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