Thoughts on Plan B’s Stock-2-Flow Model – Andy Wong

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One of the base principles of economics is that prices will change up to a point where supply and demand balance each other and equilibrium is achieved. This equilibrium is short lived most of the time as supply and demand change rapidly as news are available or preferences change. This post will delve deeper into these demand and supply mechanics by discussing the “Stock to Flow Model” in accounting, the Stock to Flow (S2F) model proposed by Plan B and his recently published Stock to Flow Cross Assets (S2FX) model.

In the Wikipedia entry of precious metals, this chart can be found. It shows the scarcity index against price.

While the mass abundance index (parts per billion units of mass) is a good indicator of scarcity the price does not always follow, as can be seen with Ruthenium and Palladium. With Ruthenium being more scarce than gold, platinum, and Palladium but lower in price. The deviation in price can be attributed to the demand, the ability to unearth more of the resource, or recycling efforts.

The vast majority of palladium is currently being used in devices that turn toxic gases into less harmful gases. Mainly carbon monoxide and nitrogen dioxide to nitrogen, carbon dioxide, and water vapor. Due to tightening regulations and more stringent checks on greenhouse emissions, the demand for palladium from carmakers has increased sharply. And in turn the price rises. Ruthenium, on the other hand, is used for hardening platinum and palladium alloys. Very little is needed for the desired effect. And the demand for it is not as high as for palladium itself.

A good addition to the scarcity index is the Stock to Flow (S2F) ratio of the metals. With stock referring to the total amount of metals unearth and flow the yearly production. To reach the equilibrium between supply and demand the S2F ratio plays an important role.

The S2F ratio for gold is estimated to be around 56~. There is debate over the S2F ratio of silver but the ratio ranges from 3~ to 20~ and up. For Platinum the S2F ratio is around 0.4 and for palladium the S2F ratio is even negative 22. The demand is higher than supply can handle. These S2F ratios will be discussed at the conclusion of the article.

Bitcoin can be modeled similarly. However there is one important difference. The total number of Bitcoin mined is predictable, the amount of Bitcoin being mined each year is also predictable because the inflation rate is known. Based on those variables, a stock to flow ratio can be calculated. Different from precious metals, the S2F ratio of Bitcoin can only go up and whereas the S2F ratios from the metals can fluctuate depending on the price.

In Plan B’s article he calculated the stock to flow ratio (S2F) based on the annual production rate of a few precious metals.

This is the table he used. Gold has an SF of 62. Bitcoin’s S2F ratios can be seen in the chart below. The yellow points in the chart denote a halving event.

By modeling Bitcoin’s S2F against the market value in a log-log scale Plan B made this scatter plot. In a different article by Nick “Btconomics”, the reasoning behind the log-log scale is examined. He came to the conclusion that the log-log scale was an appropriate approach in plotten the data points.

Each dot in the scatter plot representing a point in time (monthly) of S2F against the entire market value of Bitcoin. By performing a linear regression it becomes clear what already could be confirmed by the naked eye. Scarcity seems like a good predictor of the total market value.

This concludes Plan B’s stock to flow model. He predicted that as scarcity rises, the market value rises.

On April 27 Plan B published a new model the Stock to Flow Cross Assets model. This time he started with different phases of a material. He draws a comparison of how water and the US Dollar have different properties during different phases and claims it to be the same for Bitcoin. He defined four different phases for Bitcoin

  1. “Proof of Concept” → After bitcoin white paper
  2. “Payments” → After USD parity (1BTC = 1$)
  3. “E-gold” → After 1st halving, almost gold parity (1BTC = 1 ounce of gold)
  4. “Financial asset” → After 2nd halving ($1B transaction per day mile stone)

By clustering the monthly point with a clustering algorithm he derived at the plot above. Four clusters which could indicate the different phases in Bitcoin. He then explains that each cluster has a different S2F ratio and market value.

  1. SF 1.3 with a total market value of $1M
  2. SF 3.3 with a total market value of $58M
  3. SF 10.2 with a total market value of $5.6B
  4. SF 25.1 with a market value of $114B

To simplify, the only difference between the two models is that in the S2FX model Plan B decided to get rid of some of the noise by clustering monthly S2F ratios together. In essence, the same data is used and a linear regression is made. By clustering the monthly S2F ratios and the use of logarithmic values on the axis a small deviation in the regression could have immense differences in absolute values.

Gold and Silver

In both of his models, he added gold and silver as a benchmark to his regressions. In the first model, gold and silver did not quite fall into the regression line. However, with the second model, there was a better fit. Both gold and silver fall in line with the proposed model. Which could imply that the regression line could be a promising predictor for market values by S2F ratios. However a few questions should be asked. How did plan B arrive at a S2F of 22 for silver? In our own research we’ve found that the S2F ratio for silver is ranging from 3~ to over 30~ depending on how much you take for the stock.

The Twitterverse is currently still in debate over the previous S2F model. A lot of it boils down to whether the relationship between S2F and market cap is cointegrated. If it is cointegrated, the model still stands. If the relationship is not cointegrated this would mean that the correlation between S2F and price is spurious. This wasn’t a new discussion. The debate has been going on since the debut of the model. Different people in the industry have tried to falsify the model but failed to do so and even became supporters of the model by concluding that is cointegration between the S2F ratio and price. However, the debate is long from over. There still isn’t clear evidence for cointegration, there are certain tests and frameworks that point to that direction but it is not set in stone yet.

Another point that could be discussed is why only gold and silver are added to the model. Or even why gold and silver? At the time of writing the price of 1 ounce of gold is $1701 and 1 ounce of palladium is $1775. So not only does palladium is in more abundance than gold it is more expensive. During our own research of the S2F ratio of silver, the ratio fluctuated between 3~ and 20~, depending on how the stock is measured. In Plan B’s case if the S2F is indeed around 20 it would fit the line. However S2F ratios below 11 won’t fit the line at all.

The final point is that the model proposed by Plan B didn’t take demand and utility into account. Naturally, a model can not contain all the variables. But in this case, maybe it should. In the world of commodities, S2F ratio can fluctuate depending on the demand. This is not the case for Bitcoin. Therefore adding S2F points of commodities that does fluctuate in the current model can be misleading.

This post was originally posted on https://icoinic.org/blog/stock-to-flow-across-assets/

Sources used:

Plan B’s S2F — https://medium.com/@100trillionUSD/modeling-bitcoins-value-with-scarcity-91fa0fc03e25

Plan B’s S2FX — https://medium.com/@100trillionUSD/bitcoin-stock-to-flow-cross-asset-model-50d260feed12

https://www.silverinstitute.org/wp-content/uploads/2020/04/World-Silver-Survey-2020.pdf

http://silverseek.com/commentary/silver-above-ground-stocks-mere-fraction-global-assets-17801

https://www.voimagold.com/insight/how-much-silver-is-above-ground

https://goldsilver.com/blog/what-if-everyone-in-the-world-wanted-a-one-ounce-silver-coin/

https://www.forbes.com/sites/greatspeculations/2019/10/25/silver-prices-10-year-price-analysis-and-production-demand-gdp-dynamics/

https://platinuminvestment.com/supply-and-demand/platinum-quarterly

https://www.bloomberg.com/news/articles/2019-10-28/why-palladium-is-suddenly-a-more-precious-metal-quicktake-k2ap4ryc

https://s3-us-west-2.amazonaws.com/cdn.ceo.ca/1ekok71-MF+Platinum+and+Palladium+Focus+2019-com.pdf

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