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Sunday, January 14, 2018

Bitcoin Valuation Part II(b): What Might Work

This article concludes my series on Bitcoin valuation techniques. There appear to be three broad techniques that are not entirely psychological. The first would rely on the use of the crypto currency as an intermediary; it needs to have a large enough market capitalisation for transfers through the currency to work. The second relies on the portfolio allocation decisions of the large holders: at what point does it become irresistible to allocate towards other assets? Finally, there is the slim possibility that it is possible to hire labour or buy commodities at a fixed bitcoin price, allowing purchasing power parity (arbitrage) to work.

This article concludes a three-part series:

Purchasing Power Parity

I have discussed this earlier, so I will just briefly recapitulate. If it becomes possible to purchase trade-able goods, or hire labour, at relatively fixed Bitcoin prices, we then would have a true "Bitcoin economy" (albeit split across legal jurisdictions), and so some form of purchasing power parity argument would work. As seen in the currency world, it would not be enough pin down the exchange rate exactly, but it might give an estimate that is within an order of magnitude of observed prices.

Transaction Intermediation

As various anecdotes in the news have pointed out, Bitcoin is not the most efficient payments system right now. I have seen suggestions to the effect that other crypto currencies would be used for small transactions, and Bitcoin allegedly has value as the result of being a settlement currency. If you believes such stories, you would have to value the entire crypto complex first, then assign relative valuations to the various coins. (I leave such an exercise to the reader.) However, such arguments seem curious, as they are akin to arguing that credit card company A needs credit card company B to function, and therefore we need to attribute some of the value association with A to B. (In case the reader is unfamiliar with business practices, credit card company A wants to drive company B out of business, so that A can take over B's market share.)

For this type of analysis, we are looking at transactions in another currency (I will use the U.S. dollar -- USD -- for convenience) that just pass through Bitcoin. For example, Al wants to sent $1000 to Betty. He buys Bitcoin from Martina the Market Maker, transfers the Bitcoin to Betty, and then Betty coincidentally sells back the Bitcoin to Martina. Both parties may pay a transaction fee, and Martina would presumably have a bid-offer spread, but we ignore those for simplicity.

The key point is that Al and Betty end the transaction will exactly the same amount of Bitcoin they started with (which could be zero), as does Martina (once again, assuming no transaction fees or bid-offer spread). Therefore, neither Al or Betty need to care about the value of Bitcoin relative to the U.S. dollar, and all Martina needs to do is keep her quotes on market (so that she can close out her position).

Let us assume that it is possible for Martina to trade Bitcoin back-and-forth rapidly all day in this fashion. If she could intermediate a $10,000 flow every 10 seconds, that would translate into $86,400,000 in daily transactions. That is an impressive multiplier off of $10,000 in holdings.

However, there are limits to this. Firstly, there is a size constraint. The current construction of Bitcoin implies a maximum of 21 million coins. If the network was called on to intermediate a $25,000,000 transaction, we see that the value one Bitcoin has to be greater than $1 USD. This is obviously an extremely conservative valuation technique, but one may note that it is non-zero.

A less conservative technique would be to try to pin down the total fiat currency flow through Bitcoin, and then compare that "market maker" capacity. We do not need dedicated market makers, rather, we just need actors that are willing to post fixed bid/offers on exchanges. We could then try to compare this market-making capacity to transactions, and then guess what functional relationship there is between them. Importantly, the higher the value of Bitcoin in USD, the more USD transactional capacity the same amount of market-making Bitcoin provides. Basically, if Bitcoin is a pipe for transactions, increasing the price in USD terms increases the cross-section of the pipe.

One immediate objection is that it is unclear that increased transactions must increase the size of the pipe; inadequate transactional capacity will just drive transactions to other means of intermediation. Since slower settlement times imply less efficient market-making, that gives the somewhat counter-intuitive result that being worse as a payments system makes Bitcoin more valuable. (To be fair, I believe that longer settlement times did coincide with increasing Bitcoin prices.) That said, there appears to be a micro argument in its favour: increasing transaction demands will make market-making style trading strategies (anyone following a price-reversion strategy will be a de facto market maker)  more profitable, while their inventory of Bitcoin will be pushed down more, so they will need to nudge up offer prices. (To be fair to John Cochrane, this effect is possibly what he might have meant when he wrote about volatility.) This could probably be demonstrated in a agent-based model, or someone with too much spare time on their hands could try to do it with stochastic calculus.

This argument seems somewhat unusual if we attempt to draw parallels to real world currencies. The U.S. dollar does not need to increase in value in order to allow greater U.S. dollar transaction volume. However, we are not interested in the price of Bitcoin versus a hypothetical sticky-price Bitcoin economy, rather we are interested in its cross rate versus fiat currencies. In the real world, it is clear that the smaller currencies (such as CAD) could not cope with the transaction flow seen in USD and EUR. If there was a reason that transactions had to be routed through a smaller currency, it seems entirely plausible that it would become expensive relative to purchasing power parity fundamentals.

Although I think this does give us an idea for a floor value for Bitcoin (under a going concern assumption, see below), I would not run off to data mine blockchain transaction data and exchange bid/offer data. Realistically, we need to add in the "shadow market makers": investors who would be willing to buy dips, or take quick trading profits on rises. This shadow market maker capacity is pretty much by definition non-measurable; we could only guesstimate it.

In case any readers are worried that I have gone all "new paradigm"-y, I would point out that if the transaction flow falls to zero, fair value under these methodologies drop to zero. It only gives us a positive value if Bitcoin remains a going concern. I think such a going concern is somewhat plausible (as discussed below), but much is dependent upon the actions of authorities, or the rise of a competitor.

In any event, if we grant the going concern assumption, it is incorrect to say that Bitcoin's valuation is entirely dependent upon the "greater fool theory": there is a rock-bottom value it must have if it is to work as a payments system.

Investor Valuations

I believe that using a transactional flow estimate to give a value of Bitcoin is going to give values well below observed market prices (using historical transaction flow; obviously, expected flows can be lower than historical flows). Instead, prices are being set by actors that are increasing or decreasing their Bitcoin holdings in transactions. That is, they are trading Bitcoin for something else. In which case, what they think about valuation matters. (In case the reader missed the previous article, I pointed out that observed financial market prices are where people are willing to transact at, never mind mathematical valuation models.)

The rest of this article discusses how actors will value Bitcoin. Once again, if the reader wants a price target, they will need to go elsewhere. Instead, I explain why I am generally amused by any attempt to give a price target in the first place.

One thing that needs to be kept in mind is that in aggregate, Bitcoin only works with the injection of energy into the system (I ran through the arguments in the previous article). Since miners (who also process transactions) charge in Bitcoin, some actor needs to be injecting fiat currency into the system in order for it to be a going concern. That is, by some means or another, there must be a net investment inflow to cover the energy drain. (Note that we cannot extrapolate current energy consumption forward; if mining volumes fall, the required computational difficulty falls, so that the system can process the same number of transactions with less computations. In other words, energy use is roughly proportional to what miners are willing to spend, although there is a floor amount of activity to keep the system secure.) To be clear, there does not be explicit transactions to cover energy. For example, miners can pay their fiat currency energy bills out of their fiat currency financial assets. Utilities that charge in Bitcoin will have to lay off their risk onto hedgers (unless they can cover expenses in fixed Bitcoin terms, in which case we are back to the Purchasing Power Parity model).

Model-Inconsistent Expectations

It is exceedingly likely that it will be possible to fit observed data to any number of pricing models. The problem is that these models should be expected to blow up out-of-sample. That is, even though observed prices are consistent with some model, they are inconsistent with a hypothetical better model.

I am a post-Keynesian. Even though flexprice markets (anything resembling a financial market) are the closest approximation we have to the flexible markets of general equilibrium theory, prices are still set by human beings, who follow heuristics and convention. They do not set prices based on perfectly lining up supply and demand in all markets for all time. (Doing so is called "rational"; I am avoiding that term since people associate "non-rational" with "crazy.")

Every financial market I am aware of has such behaviour.
  • In fixed income, it used to be a majority belief that the fair value for a nominal bond yield is the potential real GDP growth rate plus inflation expectations. (I am unsure how many people who believe this are left.)
  • Any strategist that shows a chart with two time series superimposed, with different left/right axes. The classic recent example being the S&P 500 price/Fed balance sheet chart. However, that's only the latest in a long line of "short-term correlation is causation" charts.
  • Valuing internet companies based on "eyeballs."
I cannot view such beliefs as "crazy." After all, who's crazier: the person who made money trading the relationship between the Fed's balance sheet and the S&P 500, or someone who went the other way based on some theoretical principle? (Admittedly, it was unlikely that anyone was crazy enough to try that.)

The key problem with such models is that they work -- until they don't. Unless there is a way to lock in an arbitrage, discounted cash flows to the investor, or someone that is obligated to buy the instrument at a fixed price, there is no reason that any such model must work. Since I am not going to invest in Bitcoin (in either direction) for prudential reasons, I do not follow the blockchain enthusiast literature enough to say that their research falls into this category. All I can suggest is that the reader keep these fundamental questions in mind.

Illicit Activity

For obvious reasons, most blockchain enthusiasts are not happy with the perceived link to organised crime. However, it is clear that illicit activities matter for valuation.

Firstly, the design of Bitcoin is designed to support activity beyond the reach of authorities. It is not a stretch to accept that it (or a similar product) is going to be a major player in underground transaction flow, particularly for electronic transactions.

Additionally, it solves the money laundering problem. It is extremely obvious that redeploying the proceeds of illicit activity is difficult. There are not a lot of alternatives for portfolio diversification for crime lords. As a result, they are a natural accumulator of crypto currency assets.

The existing Bitcoin hoards of merchants also acts as a limited line of defence for the crypto-currency versus new technologies. They are unlikely to adopt a new coin that completely wipes out the value of their existing holdings.

Furthermore, the risk calculus is completely different. A person who has received a $1 million bribe presumably looks at risks very differently than an individual with $1 million in a retirement account.

The analytical problem is that practically everyone who comes up with estimates of illegal activity has an incentive to shade the figures in one direction or another.

Small Holders: Squeezing the Shorts

My working assumption is that Bitcoin holdings are extremely unequal (as based on various news reports). One could calculate a Gini coefficient of wallet sizes, but that only provides a lower bound: one individual can hold multiple wallets. Under this assumption, "small" holders of Bitcoin are only holding a "small" amount of the total stock.

Even among the small holders, anecdotes suggest that most were relatively early adopters. This means that unless Bitcoin prices crash a lot, the bulk of Bitcoin is held by people sitting on paper gains. Psychologically, they are playing with house money.

It appears that most of these early adopters are in the technology industry, or libertarians who are not completely fixated on gold and silver. On the technology side, I would argue that they sound exactly like the tech industry participants of the 1990s. (As an electrical engineer that ended up in finance, I had a lot of contact with that culture.)

Anyone that is tired of tech true believers will probably conclude that this is just a repeat of the tech bubble. The key difference is that the bulk of the individuals involved are far less exposed to the "crypto industry" than tech workers were in the 1990s. In the 1990s, a technology worker was considered highly diversified if five different tech companies represented 100% of their retirement portfolio. When the tech industry crashed and burned, they lost their jobs, their options were worthless, and their portfolios were trashed.

In this case, they are much less at risk. They have the capacity to keep diverting some their income to buy the dips. Their salarial mass is considerable; it would be interesting to compare it to the energy cost. Therefore, there is the capacity to keep the show on the road.

Furthermore, if one strips their arguments of all the blockchain jibber-jabber, one realises that they are aware that they are in the driver's seat. They have the strong hand, and they are squeezing the shorts.

The Shorts: Anyone Who Believes Modern Portfolio Theory

All we need to get the price of crypto-currencies to be even higher is to get pension consultants to brand them as an "asset class." At which point, all the pension funds will be "underweight" -- effectively short. All we need is a pension consultant to say that x% of pension assets should be in crypto currency, and we are off to the races.

The Big Holders: Trapped

What tempers the potential price explosion are the portfolio allocation preferences of large holders. If your $1000 investment in a crypto currency turns into $20,000, that's great, but that's not enough enough to greatly change your lifestyle. However, if you are sitting on $20 billion in crypto assets, one imagines that one begins to ponder what else can be done with that wealth. After all, there is a limit to the recreational pharmaceuticals one can buy off the dark web.

In other words, even if one thinks that crypto currencies will be the monetary unit used on Martian colonies, there is a limit to how big those holdings can get relative to real world assets ahead of the migration to Mars. After all, we need to invest to build those colonisation rockets in the first place.

The other unknown is the relative size of the large holders' fiat currency assets. They may need to step in to stabilise prices during the periodic sell-offs, in order to preserve the value of their Bitcoin holdings. Given that it appears that the most likely panic sellers have relatively small holdings, it may be incorrect to say that the large holders are "doubling down," rather "110%-percenting down." That said, they still need to have fiat currency ammunition to intervene (on top of any energy costs from mining that they are probably already absorbing). If those other assets happen to be shares in technology companies, a stock bear market could have the side effect of taking out this line of defence of the crypto-currencies.

The issue is that there does not appear to be an exit door large enough to accommodate the large holders. Trying to sell $1 billion of an asset by $10,000 increments on a public exchange is not the optimal execution strategy. After the first $100 million or so, people catch on.

This creates a game-theoretic dilemma. The first big holder to cash out is going to get much better execution than the second. Even if one believes in buy and hold, one can look at the chart of gold prices during the 1980s and 1990s (particularly versus tech stock price charts of that period) to know how painful it is to hold a dead money asset -- even if it does not go to zero.

The usual outcome in the real world is the formation of a cartel to hold the line on pricing. I am not an expert on the literature, but it may provide some useful insights. Of course, the existence of such a cartel would be denied.

Obviously,  being able to dump your holdings on pension funds is the optimal outcome for all the big holders, and so far, they remain disciplined.

If the financial bid does not appear, observed Bitcoin prices are capped by the unknown ceiling created by large holder selling. One could attempt to infer such levels by using the market capitalisation of Bitcoin, and comparing them to other assets, but that is arguably guesswork. The only people who know for sure what the ceiling price is are the large holders themselves.

Historical Example: The Hunt Brothers

The gold/silver price boom in the late 1970s/early 1980s shows the importance of large actors. In particular, there allegedly was an attempt to corner the market in silver by the Hunt Brothers (Wikipedia link). Since there may be those that dispute what exactly happened during that episode, I will not attempt to provide a story about what happened. Rather, I just want to underline that the antics of large actors is not just hand-waving when we are discussing price action.

Concluding Remarks

People who want to believe that there is a scientific story behind the value of Bitcoin are not going to be happy with the explanation is that the price is being set by a tug-of-war involving blockchain enthusiasts and (virtual) shorts, with a floor set by transaction activity, and a ceiling by the presumably unknowable motivations of large holders. Well, there is no reason that the world has to conform to your analytical beliefs.

Appendix: Pricing Theory and MMT

One of the sillier complaints is that Modern Monetary Theory (MMT) has no theory of price formation. This three-part article outlines the theoretical issues associated with the price formation for just a single asset. Meanwhile. other prices are set in a completely different fashion. Although my arguments here may not be part of "standard MMT," most of them could presumably be traced back to some argument or another in the post-Keynesian tradition.

When we look at the complexity of just the case of Bitcoin, any theory that offers a mono-causal explanation of the formation of all prices looks monumentally naïve.

(c) Brian Romanchuk 2018


  1. If the value of a country's currency is created by taxation, perhaps the value of bitcoin is created by avoiding taxation. ;)

    And a Happy New Year! May you short bitcoin just before the crash. ;)


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