Bitcoin Valuation Part I: The Wrong Answers

The rise of Bitcoin (and other crypto-currencies) appears that it will have a negative net effect for most law-abiding citizens, but it has provided us with a rather wonderful teaching opportunity. It underlines the weaknesses of existing analytical techniques. (I discussed Bitcoin in a previous article, but I used it to take a sideswipe at DSGE models, and I didn't bother giving the correct answer.)

Due to article length, this article will discuss incorrect valuation techniques. Part II will give the correct methodology.... 

My Key Theoretical Assumption: There is No Bitcoin Economy

I do not hold myself out as an expert on Bitcoin, and so I want to make clear that the following assumption is a guess on my part, based on my scanning various discussions of the crypto-currency. The assumption is that there are almost no long-term commercial contracts that are denominated in Bitcoin. Any quoted prices for goods and services seen for Bitcoin are essentially prices set in another currency, and translated into Bitcoin at some exchange rate. Since Bitcoin is a purely online currency, such a translation is a relatively trivial affair.

Equivalently, this means that we cannot buy goods and services at relatively sticky prices in Bitcoin terms. I can go to the store and have a pretty good idea what groceries will cost, even in during inflationary periods (I grew up in the 1970s).

It should be noted I am ignoring prices for other crypto-currencies. Based on descriptions that I have seen, Bitcoin is the "senior currency" among crypto-currencies, and so other cryptos may be quoted in Bitcoin terms. However, any stability in cross-rates between crypto-currencies does not matter for the cross-rate versus the fiat currencies, which is what I am interested in analysing.

One example that comes up for a pure Bitcoin transaction is ransomware. Hackers seize control of some computer, and demand a ransom in Bitcoin in order to unlock it. It might appear that the amount of Bitcoin demanded is arbitrary, and might appear sticky. However, there is still a range of plausibility for ransomware demands, expressed in fiat currency. If someone seized control of a household's computer and demanded a ransom that is equivalent to $10,000,000, it is most likely that the demand would be ignored, and the household will just buy a new computer. Going the other way, it appears unlikely that people will commit (what I assume is) a felony to gain $1.

However, if there developed a network of firms and workers who set contracts in Bitcoin terms, it would create a true Bitcoin economy, and it could be valued using purchasing power parity. Purchasing power parity only gives a rough idea of valuation, but even so, even sticking within an order of magnitude of fair value would greatly reduce volatility.

Failed Technique: Transaction Demand

One possible technique is to assume that transaction demand can pin down the price. Find the number of transactions, multiply it by some magic parameter, and you get fair value for Bitcoin.

Considering that most transactions in Bitcoin appear to be speculative transactions to purchase the currency, that implies that fair value rises the more speculative activity occurs! If one were to assume model-consistent expectations, it seems very difficult to see that any finite number is the fair value.

Based on the past behaviour of the Monetarist-inclined, one could imagine attempts to "correct" the "money stock" numbers so that the money demand model gives the correct answer. For example, stripping out speculative transactions. However, since transactions are anonymous, there is no obvious way that could be done.

In any event, the technique is tautological. We have no way of inferring the demand function for Bitcoin, and so we would just end up setting the parameter to match observed Bitcoin prices. The fair value of Bitcoin ends up equalling the observed market price, which is not giving us a lot of information.

Failed Technique: Supply and Demand Curves

The first basic problem for using classic supply-and-demand curves is that it is unclear what real world data the "quantity" in them corresponds to. If we follow the analogy to monetary economics, it is the stock of Bitcoin.

However, in monetary models (include stock-flow consistent models), the central back can buy or sell Treasury bills to adjust the supply of money. In Bitcoin, there stock of coins is essentially fixed. (It is fixed in between the "mining of coins," while mining just slowly adds coins towards the theoretical maximum. At best, all miners can do is adjust the pace of mining.)

Since quantity supply is largely fixed, all the supply-demand curve formalism tells us that the observed market price is where the fixed quantity hits the demand curve. The volatility of Bitcoin prices implies that the demand curve is jumping all over the place.

We could try to adjusting the stock of Bitcoin in some fashion to create an "effective supply" measure, but that would probably just turn into an exercise in data mining.

John Cochrane's Rational Expectations Valuation

Professor Brad DeLong has a not very flattering description of a John Cochrane article on whether Bitcoin is in a bubble. Technically, I think John Cochrane's logic is valid -- within the unusual world of mainstream economic logic.

I would wildly paraphrase Professor Cochrane's logic as follows. (I must emphasise that I have completely made up the wording here, in order to use more familiar terminology.)

• We assume that the world is modelled by a general equilibrium model, and prices are set by rational expectations.
• Bitcoin prices are in fact, prices.
• Therefore, the price of Bitcoin is set by agents using rational expectations, and thus the agents (and the price) are rational.

Sure that sounds ridiculous. The problem (based on my terminology) is the use of the word rational. It has a technical meaning in finance and economics, but it also has a common language meaning. We tend to associate "irrational" with "crazy," so that we think that if prices are set by rational expectations, the investors are not crazy.

If we replaced "rational expectations" with a more neutral "model-consistent expectations," we can immediately see the problem with Cochrane's argument. He has a lot of hand-waving, but not an actual model. (As I discuss later, invoking volatility does not cut the mustard.)

The Nice Fat Zero Option

At some point, it will be very easy to value Bitcoin. Once all the servers go dark, all the records will effectively cease to exist. It will be literally impossible to buy or sell Bitcoin, and hence it would have no value. The question is timing.

• An optimist would say that the servers will only be stopped by some cosmological catastrophe. Perhaps Bitcoin will have taken off to become the galactic crypto-currency before then!
• A pessimist might argue that government intervention/an angry mob with pitchforks/hacking could end the era of Bitcoin any minute now.

The zero valuation is mesmerising (even John Cochrane discusses it), but I think we cannot get too distracted by it (unless you have some reason to put a firm timeline on the termination date). We can make similar arguments about fiat currency and non-dividend paying equities, and yet they have value. Also, we use infinite horizon discounting in dividend discount models, and for valuing consols and preferred shares. Unless we can pin down the termination date, the convention is to assume that the future is shrouded in uncertainty, and make an assumption that the security will be a going concern for any finite horizon.

Obviously, any discounted cash flow analysis should incorporate the probability of termination, but the effect is highly sensitive to the assumed timeline.

Can We Do a Non-Trivial Cash Flow Valuation?

One may immediately note that it is possible to give a definitive Bitcoin valuation using discounted cash flows: one Bitcoin (instrument) has the Net Present Value (NPV) of one Bitcoin (unit of account). This relationship holds by definition. (It is painful to see how it could be anything else. This is less true of other currencies, where we can have multiple "monetary" instruments that can conceivably trade away from par.)

However, nobody cares about the NPV measured in Bitcoin, they want it measured in some (fiat) currency. I will assume that the fiat currency is U.S. dollars.

Furthermore, for this article, I am assuming that we are attempting to do the valuation solely using marginal arguments. That is, we are using the same sort of valuation techniques that are used in financial theory: we are attempting to value Bitcoin based solely on the behaviour of one unit of the instrument, and we are not taking into account the stock of the instrument. (As an astute reader may guess, this assumption needs to be relaxed when we are doing the correct valuation technique, which is the subject of the next article.)

As an instrument, Bitcoin is designed to never produce U.S. dollar cash flows. So we cannot apply any off-the-shelf valuation tricks. Instead, we need to find away of pinning down a future price, and then discount it to a present value.

If we had a credible party that stated a willingness to buy large amounts of Bitcoin at a certain price, that might create lower bound for the price. For example, if the Fed announced that it will buy any Bitcoin offered to it on January 1, 2019 at $100,000 per Bitcoin, that would presumably be enough for people to assume that the future value is $100,000. However, this is only a lower bound. If the Fed announced that it would buy all Bitcoin offered to it next week at $1 per Bitcoin, it is likely that nobody would take them up on the offer (and the market price would remain above $1).

The "credibility" of the buyer also matters. I could offer to buy one-billionth of a Bitcoin for $1 -- that is, valuing one Bitcoin at $1 billion. However, nobody sensible thinks that an offer to purchase $1 worth of Bitcoin will move its price by that amount.

In any event, there are no such fixed offers to buy Bitcoin around. And despite John Cochrane's assumptions, the illicit use of Bitcoin is not enough to create a fixed future price. For anyone who is using Bitcoin to transact, and not as a store of value, the U.S. dollar-Bitcoin exchange rate is largely a piece of trivia. As I discussed earlier, Bitcoin prices appear to be just fiat currency (e.g., U.S. dollar) prices translated into Bitcoin. So long as the "market makers" have a sufficient stock of Bitcoin, they can support the same flow in U.S. dollar terms across a huge range of Bitcoin prices.

(My notion of market makers here are holders of Bitcoin who are willing to buy and sell in the exchanges in a way that allows supply and demand to meet, and they presumably act in a way to help stabilise the exchange rate. Of course, they are probably not people with "market maker" on their business cards, but are investors that wish to trade the swings in Bitcoin.)

If we just make up a future price for the exchange rate, we are entirely reliant on the Greater Fool Theory. For example, we could assume that someone will pay $1 million next year for a Bitcoin, and so we are probably buying at a price lower than that (modulo the extremely low nominal discount rate). We could try throwing in premia to account for volatility (or other effects), but that is only a distraction. The effects of volatility and so forth would only result in a percentage discount/premium over a raw valuation, so if we double the assumed future price, we double the calculated fair value.

(One could try to use the Greater Fool Theory to argue that the fair value of Bitcoin is infinite. Since there are no obvious upper limits to the valuation if we limit ourselves to marginal arguments, and everyone knows it, we should always be able to find a Greater Fool willing to pay more than any arbitrary price. This obviously does not work when we look at the correct valuation technique.)

Almost a Solution: Commodity Arbitrage

If some credible entity offered to sell or buy a commodity at a fixed Bitcoin price, we could then use commodity market arbitrage to get a rough idea for fair value. For example, if firms started pricing Western Canada Select (a grade of heavy crude oil from the tar sands) in Bitcoin, energy market traders would then be able to compare its price to other grades of crude, and then decide what their relative attractiveness is.

However, my opening assumption (that there was no Bitcoin-denominated legitimate industry) precludes this option. However, it should be clear that if Bitcoin were acceptable to commodity producers, Bitcoin could then develop a valuation anchor.

Almost Solution: Energy Cost of Mining

Unless the Bitcoin miners managed to wangle contracts denominated in Bitcoin, their energy-intensive activities are denominated in a fiat currency. If the spot price of Bitcoin is much higher than the expected cost of discovering one coin, then they have an incentive to ramp up mining activities.

However, this linkage is extremely weak. In addition to getting new coins, miners earn Bitcoin based on transaction fees. Even if the expected cost of mining a new coin is extremely high relative to the spot price, they can pay for their activities by raising transaction fees. (This is how the system is supposed to survive once the difficulty of discovery becomes extremely high as the number of coins closes in on the maximum.)

Meanwhile, Bitcoin mining is ridiculously energy-intensive, and so it is not possible to bring new capacity online very quickly.

Finally, even if the discovery of new coins is stopped, that does nothing to eliminate any overhang of holders that might want to sell.

Concluding Remarks

The second part of this analysis will drop the assumption that we can price Bitcoin at the margin, and we can then come up with a way to think about valuation.

This series ended up being split into three articles.

• Part II(a)
• Part II(b)

Disclaimer: No, I don't own any crypto-currency, either directly or in some derivative form.

(c) Brian Romanchuk 2018