Digital Finance has been transforming from a niche space for tech enthusiasts to a mainstream area of investment strategy. There is so much more to this space than just alternatives to fiat currencies, as needed as those are. However, in this article I’ll to take a step back from the larger evolution and explore some theories regarding the drivers of Bitcoin valuation, since its price action is, after all, why many are giving it their attention. There are two commonly-cited drivers, Scarcity and Network Effects, to which Bitcoin’s price is attributed, although frequently each is considered in isolation rather than in tandem. Scarcity can be represented by Stock-to-Flow, a framework that comes from the valuation of other precious commodities. Network Effects can be evaluated by a measure of its size, or simply put the number of people participating in it. Let’s dive in.

Scarcity and Stock-to-Flow

There are a variety of reasons why an object might be valued. It could be essential to human life, such as water. It might also be something non-essential but that people like because it’s shiny and they can make jewelry with it, such as gold. To attribute value to this type of material, it should probably be somewhat rare. One way to measure scarcity is with the Stock-to-Flow Ratio, where Stock refers to the amount of the material already in existence, and Flow is the rate at which new amounts of it are discovered or mined. For precious metals, there is a direct relationship between this ratio and the value of the material. For example, the Stock-to-Flow ratios of Gold > Silver > Copper, in alignment with their relative prices. The insightful leap of applying this to Bitcoin valuation was made by PlanB. Many swear by a chart overlapping Bitcoin price with Stock-to-Flow for technical indicators as to when to trade the crypto currency profitably. Something important to point out about Bitcoin mining that leads to the stepped nature of the charts is the Bitcoin halving events. At prespecified milestones on its way to the cap of 21 million coins, the reward to Bitcoin miners for a new block is reduced by a factor of 2. Below is the schedule so far, with the next halving expected in 2024:

Bitcoins per block Date
50 9 Jan 2009 (initial)
25 28 Nov 2012
12.5 9 July 2016
6.25 11 May 2020
3.125 projected 2024

There has been debate as to whether these events are directly related to pricing. Many cite predictable increases in Bitcoin price surrounding these events, while others (famously Ethereum founder Vitalik Buterin) claim this is not the case. Regardless, Stock-to-Flow is arguably the biggest single factor that is often followed by those who wish to predict Bitcoin price movements.

Network Effects and Active Bitcoin Addresses

Another important determinant for Bitcoin valuation may be the extent to which it is held or is in use by the human population. This principle can be referred to as following Metcalfe’s Law. Originally postulated to propose valuation for a telecommunications network based on the number of its users (n), the law states that the value of the network is proportional to \(n^{2}\). In words, the value increases in a greater-than-linear way as new users are added. This can be understood in terms of valuing an important type of network that we have today, a social one. If you and your friend are the only ones sending each other videos of your latest dance moves, don’t expect an IPO any time soon. But consider a network with users in the millions or even billions, together with machine/deep learning algorithms suggesting content you might like, and you’ve got something immensely valuable. A measure that approximates the size of Bitcoin’s network is the daily number of active addresses.

Bitcoin Stock to Flow, Active Addresses and Price

Here is a plot of each day’s Bitcoin Price, Stock-to-Flow, and Active Addresses from mid-2010 to the end of May 2021.

Data and Models

Stock-to-Flow and Bitcoin Addresses were explored using daily data obtained from Coin Metrics. Both Bitcoin Scarcity (Stock-to-Flow) and Network Size (Active Addresses) were considered simultaneously by estimating their effect on price for the period from mid-2010 to present (May 29, 2021). Log10 of both of these values, along with centered calendar time and a cyclical term representing month, were included in a Generalized Additive Model (GAM) with log10 Bitcoin price as the response. One way to think of this type of modeling is that is allows more of a conversation between the modeler and the data than in models where the functional form of the relationship between the predictors and response is set beforehand. In a linear model, for example, the effect of the feature on the response is fixed across it’s range, i.e. there’s just one estimated parameter, no matter what the value the features has. Small values, big values, same per-unit effect on the response. Not so with the GAM, where the effect can change depending on the feature value. Further, the functional form of this relationship isn’t specified beforehand, but is estimated from the data using smooth terms. More details on the data and modeling process can be found here.

GAM Model Fit

In the final GAM model, all of the terms appear to be highly significant in relation to Bitcoin price, and appear to explain virtually all of its variation (over 99%). Below are the smooth model coefficients and what they indicate for each parameter.

Active Addresses

The smoothed effect of the number of Active Addresses on price is less complex and requires fewer smoothing terms than for time and Stock-to-Flow, so it is easier to interpret. The coefficient is always positive and appears to be increasing as the number of active addresses increases. This is consistent with Metcalfe’s Law, which indicates a larger increase in value as the network size increases. What’s more, using the smoothed parameter estimate, we could estimate the critical mass at which the network growth really begins to accelerate its effect on price at about \(10^{3.5}\) which is just over 3000 addresses. This might be useful for evaluating the price movements of other digital currencies. Another observation is that, although theory would suggest that a network would eventually exhaust itself, there are no indications of having reached saturation at this point in the smooth term.