Bitcoin Has Not Yet Fundamentally Recovered At This Time – A Mathematical Case

I wrote about a week ago that Bitcoin does not seem to have recovered yet (here and here), following the Bitcoin correction to about $6K and after it seemed to be recovering and had risen again to about $11K. At the time, many Bitcoin watchers were already predicting recovery and new highs. The problem is that trading analysis, as useful as they are in certain scenarios, simply lack the information to see fundamentals that underlie the value of some assets. Meanwhile, that fundamental value is what gives rise to sentiment, which is what chart analysis can then attempt to measure; sometimes with some success.

That said, fundamentally, based on an analysis spanning the 9 years of information available to us, the current metrices are pointing to issues persisting with Bitcoin adoption rate as well as several other metrices. Some of these are described below. But first, a brief, not too technical description on the math behind this review.

Mathematical Modeling of Bitcoin Sentiment Value

(This section may be skipped by any not disposed to math without affecting the enjoyment of the rest of the article.) Since Bitcoins are not exactly pegged to any value (just like pretty much every modern currency right now anyway), the value essentially is a market value driven by demand and its deflationary supply scheme. This sounds simple, and the supply side is, given that it is a constant rate of 12.5 BTC roughly every 6 minutes. The demand side on the other hand is where the action is, as it is dependent on several valuables, and that is where the action is. Mathematically, this can be represented as:

Which simply states that D is a function of n variables, represented by X₁, to X_n. The challenge then is to determine what those variables are firstly. Next is to determine the how D reacts in response to changes in those variables. This part is much easier and there are tools in multivariable calculus that allows this to be done. This step also gets much easier if an analysis of the effect of those variables can prune them down to one or two that are more dominant in influencing D, or if it can be determined that a few of the variables seldom change much allowing the model to consider them to be fairly constant without much loss in accuracy.

(Sometimes, it could also be that the effect of some of the other variables are transient on a smaller scale, for instance in days, such that if we are only interested in modeling D on a longer time scale, such as in months, then the effect of those variables can be dropped since they would average out over a monthly time scale.)

In leading up to the paper: “Digital blockchain networks appear to be following Metcalfe’s Law”, the author reviewed several of the metrices available on the blockchain, and showed that the value historically could be fairly well modeled by the daily unique adoption rate. The rationale behind why this variable is probably a strongly characteristic one is explained below.

Daily Adoption Rate

The daily new unique addresses (DUA) on the blockchain points to the adoption rate of Bitcoins more than any other metric on the blockchain. (And the blockchain is a mathematical modeler’s dream because it provides more information on a real time basis than almost any other financial system hitherto available; most of which are quite opaque.)
The popular elasticity curve and equations used by economist to model demand and supply is developed for a system in equilibrium, and is not suited to rapidly growing systems that have not yet reached an equilibrium state, such as the bitcoin network. So other approaches were explored in the referenced paper.

In a growing network with constant supply rate, the demand can be shown to be driven mostly by the rate at which new users are being added to the network. If a user acquires bitcoins, for instance at say $1, and a new user attempts to join the network, with the limited supply they would need to get an existing user to part with some of their holdings. The existing user is then able to demand a premium over how much they obtained it to sell to the new user. If the value demanded by the existing user is too high, then the new user either looks for another user willing to part with theirs for less, or waits, or just does not join the network.

The faster new users wish to join the network, the faster the value will slowly rise. And the more people join the network, the more they share and introduce the network to their social circles, which then leads to new adoption. And the more people join the network, the more other people they have to use and exchange the network’s resources with, making the network more useful and valuable. This is referred to as the network effect. It turns out in that paper that using approaches based on network effect theory on the daily unique addresses was found to model the price of bitcoins fairly well over the prior 8 years of data available at the time.

Modeling the Value as a Function of the DUA

The DUA was modeled using several network models in the referenced paper. The Metcalfe law was found to be a fairly good approximation. A new model was also proposed by the author, which showed potential to model cryptographically-enforced digital currencies about as well. The two most successful models in that study have the form as follows:

It should be noted that the accuracy of the models as presented in the paper was about 9% over the 8 years of data. This indicates that significant deviation from the model should not be expected over spans of longer than about 6-9 months. And indeed we saw significant departure around 2014 essentially forming a bubble, with a snap back to the model within months. We also see a departure during the run up of values to over 19,000 by the end of 2017 with a snap back closer to the model’s value of about 5,000 by early February 2018.

So it seems fundamentals will never go away for long – they can only take temporary vacations.

Where Are We Now?

The current values of the DUA shows that the metric has not yet recovered. The DUA is shown below over the past 6 months. The rate is currently back to levels last seen in August 2017. The Metcalfe model at such low DUA places the value closer to $4,800 than where it has currently “recovered” back up to. (Note that the DUA is uncharacteristically and could well recover before dragging the price down to this level.)

Source: Blockchain.info on Feb 21 2018.

What this essentially means is that new users are not be joining the network at the exponential growing rate that was observed the prior 8 years. This might be temporary but just lasting unusually long right now. It might also point to an enduring shift in the cryptographic-enforced digital currency space. If it is temporary then growth is expected to return, and only then will the current correction be over. If the price continues to rise now without that adoption rate picking up, it will almost surely snap back eventually. Where would the value growth be coming from? The adoption rate might pick back up on its own although this is the longest stretch we have seen where it has departed from the netoid function that was used to model it in the paper. The growing adoption rate could also return with the introduction of the Lightning network that will address the scalability issue and increasing fees that might have contributed to the retreating adoption growth rate.

However, if this new lower adoption rate is enduring then the current correction should persist because the major driver for increases in value was previously indicated in the growing adoption rate. That manifested the overall sentiment to the asset. Could different new sources of value boost bridge the gap in that lost adoption growth rate? It is possible. For instance, institutional resources pouring in through newly established futures market may add new demand for some time, but it is unlikely to sustain the previous price growth rate long term if not accompanied by close to the same old growth rate from actual users. The adoption rate drop off from the bitcoin network could then simply transfer to other alternatives. If this is the case, the shift will likely take several months to unfold.

References
https://www.sciencedirect.com/science/article/pii/S1567422317300480”.

Legal Disclaimer: I am not a financial advisor and this is not financial advice. The information provided in this post and any other posts that I make and any accompanying material is for informational and educational purposes only.

It should not be considered financial or investment advice at all. You should consult with a financial or investment professional to determine what may be best for your individual needs.

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