Not so fast: Stock-Flow Ratio

A quick look at Bitcoin’s Stock to Flow narrative.

Furion (Viewly One)

Recently we’ve seen the rise of the Stock to Flow narrative on Medium and CT. The original post currently has 14,500 claps, and has been shared extensively in social media.

Furthermore, people have further expanded on the original model by analyzing things such as autocorrelation in residuals, residual distributions, cointegrations, etc, etc. Two examples of such posts are here and here.

In this post we will avoid the fancy statistical tooling, and instead focus on higher level concepts. First we will look at how the SF ratio is confounded with MarketCap, and then we will explore the the idea of base rates.

In the original model, the author proposed a log-log relationship between Stock to Flow ratio and Market Cap.

One potential issue arises from the fact that market cap is a function of price * total supply. Total supply monotonically increases with mining, causing Stock-Flow ratio to increase as well - in other words the SF Ratio and supply are two sides of the same coin. Stock-Flow ratio will appear to have more predictive power over MarketCap, simply because the two are inherenly related.

What we are really interested in is the increase in value of the underlying asset given the SF ratio, without the confounding. To do that, we should use the price of an asset rather than the market cap.

When doing so, we get something that doesn’t look nearly as good as the original plot.

By looking at basic diagnostics, we can see that the residuals are not normal, but exhibit a fat-tailed, multi-modal distribution. There is a high degree of autocorrelation, and the residual trace exhibits heteroskedasticity. In other words, the Stock-Flow Ratio does not explain the price very well.

Spurious correlation?

The SF model hypothesis does have a plausible explanation within the SoV (store of value) - also known as digital gold - narrative.

An important question to ask at this point is whether SF and Value of Bitcoin happen to have spurious association. The SF ratio is designed to always increase trough the mining process. The only way for SF ratio to decrease is if a large portion of Bitcoin were burned or lost.

We only have a few years of Bitcoin history to go by, and most of the years exhibit price appreciation. We simply don’t have enough data to determine with certainty whether SF model actually works, or whether it just happens to be spurious. A prolonged Bitcoin bear market would invalidate the model.

Base rates

The main issue with the SF model narrative is that we are looking at sample size of 1: Bitcoin. To properly validate the SF model, we would need to apply it to more than one asset, and detemine the base rate of success.

We can look at altcoins for a clue, however this is not a proper apples to apples comparsion, because altcoins do not enjoy the same SoV status. The SoV status is our core assumption for a SF model.

Another issue is that altcoins have exhibited high correlation with Bitcoin in the past 1, so ideally we would be using something uncorrelated such as Gold itself.

Unfortunately, Gold is not a great example for a SF model due to confounding in SF variable itself - namely, in the real world of Gold mining, unlike with Bitcoin’s fixed inflation curves - there is a reflexivity element between gold price and its supply. The gold miners expand production when the price rises and new mines become profitable. Similarly, gold miners shut down the mines if the price of gold drops and/or the hedges in the futures market expire.


In my opinion, its premature to assert that Stock-Flow model dictates the price of Bitcoin. We probably need to wait a couple more years to see if the association holds. Furthermore, a validation of the association on another SoV asset would improve the confidence in the model.

Appendix 1: The elephant in the room

A major problem with the original SF model is that it is merely a linear extrapolation. If Bitcoin’s inflation curve does not change, SF will explode in growth as mining rewards dwindle. This would make the model predict ridiculously large prices that could not be realized in the real world. Perhaps a saturated growth model might be more appropriate, where a plausible ceiling is hand picked as per discretion (ie. some proportion of gold’s market share).

  1. The chart shows monthly correlations between BTC and ETH in 2018.