Why the Inventory-to-Circulation Bitcoin Valuation Mannequin Is Flawed

By | June 30, 2020

Nico Cordeiro is the chief funding officer and fund supervisor at Strix Leviathan. He oversees quantitative analysis, technique improvement, threat administration and portfolio allocation. An extended model of this submit will be discovered here.

The stock-to-flow mannequin (SF), popularized by a pseudonymous Dutch institutional investor who operates underneath the Twitter account “PlanB,” has been broadly praised and is the main valuation mannequin for bitcoin proponents. SF has achieved viral reputation and impressed rags-to-riches desires for these playing all of it on the way forward for bitcoin. Nonetheless, we consider the mannequin’s accuracy will seemingly be about as profitable at forecasting bitcoin’s future worth because the astrological fashions of the previous had been at predicting monetary outcomes.

Stanford Professor Paul Pleifderer coined the time period “chameleons” to explain fashions which can be constructed upon doubtful assumptions and are given extra credence than they deserve. An preliminary analysis of any mannequin ought to start with a vital take a look at the mannequin’s theoretical assumptions, he says. For instance, Pleifderer provides the next state of affairs:

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Think about an asset pricing mannequin primarily based on the belief that there isn’t any uncertainty about any asset’s returns. … No severe particular person would recommend that the predictions of the mannequin ought to be subjected to rigorous empirical testing earlier than rejecting it. The mannequin will be rejected merely on the premise {that a} vital assumption is contradicted by what we already know to be true.

Chameleons are significantly troublesome to identify and dispute as a result of they look like significant. It’s solely underneath additional scrutiny that you just notice they’re constructed upon assumptions that don’t map to what we find out about the true world. 

Introducing stock-to-flow

PlanB’s paper “Modeling Bitcoin Value with Scarcity” states that sure valuable metals have maintained a financial function all through historical past due to their unforgeable costliness and low fee of provide. For instance, gold is effective each as a result of new provide (mined gold) is insignificant to the present provide and since it’s not possible to duplicate the huge shops of gold across the globe. PlanB then argues this similar logic applies to bitcoin, which turns into extra worthwhile as new provide is lowered each 4 years, finally culminating in a provide of 21 million bitcoin. 

Low fee of provide, which PlanB defines as “shortage,” will be quantified utilizing a metric known as Inventory-to-Circulation (SF), which is the ratio between present provide and new provide.

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This premise is then translated into the speculation, “…that shortage, as measured by SF, instantly drives worth.” PlanB then plots bitcoin’s SF towards USD market capitalization in addition to two arbitrarily chosen SF knowledge factors for gold and silver.

PlanB then runs a linear regression utilizing the pure logarithm of bitcoin’s SF metric because the impartial variable and the USD market capitalization because the dependent variable. The paper ends with the conclusion that there’s a statistically important relationship between USD market capitalization and SF values, as evidenced by the linear regression leading to an R2 (a statistical measure of how shut the info suits to a regression line) of ~0.95. The 2 randomly chosen knowledge factors for gold and silver are according to bitcoin’s trajectory and offered as additional proof of the speculation. 

PlanB means that buyers can forecast the long run USD market capitalization of bitcoin utilizing the above method. This has helped give credence to these $100,000 bitcoin projections.

Issues abound

There are a number of deficiencies inside the paper, each in its theoretical proposition and its empirical basis.

From a theoretical viewpoint, the mannequin relies on the relatively sturdy assertion that the USD market capitalization of a financial good (e.g. gold and silver) is derived instantly from their fee of latest provide. No proof or analysis is supplied to help this concept, apart from the singular knowledge factors chosen to chart gold and silver’s market capitalization towards bitcoin’s trajectory. 

This turns into fairly apparent when one extends the mannequin into the close to future. By 2045, the mannequin estimates every Bitcoin shall be value $235,000,000,000.

The second is the naïve utility of a linear regression that ends in a excessive likelihood of a researcher discovering spurious outcomes. “Good” statistical outcomes, similar to a excessive R-square, don’t represent a significant discovering. It is not uncommon for researchers to underestimate how typically such methods result in false outcomes. And significantly on this scenario, the place there’s a giant diploma of freedom for random knowledge to suit a selected consequence.

Gold and the greenback

From a theoretical perspective, what PlanB defines as “shortage” shouldn’t be shortage by definition. PlanB makes use of “shortage” to explain an asset’s provide progress fee or new manufacturing as measured by the SF metric. This assumes that growing new provide depresses worth by way of elevated promoting stress from producers and vice versa. 

This appears cheap at first look till one considers {that a} excessive SF represents a dynamic the place new provide is insignificant to the present provide. PlanB quotes “Bitcoin Standard” writer Saifedean Ammous saying as a lot: “For gold, a worth spike that causes a doubling of annual manufacturing shall be insignificant, growing stockpiles by 3% relatively than 1.5%.”

Maybe unsurprisingly then, SF has no direct relationship with gold’s worth during the last 115 years, as will be seen within the scatter plot beneath. Gold’s market capitalization held valuations between ~$60 billion to ~$9 trillion, all on the similar SF worth of 60. A variety of $eight trillion shouldn’t be very indicative of explanatory energy and lends itself to the apparent conclusion that different components drive gold’s USD valuation.

Recall that the worth of gold/USD is the ratio of buying energy between gold and the USD. When the buying energy of the greenback decreases, the worth of gold/USD will increase and vice versa. With relative stability within the buying energy of gold, we discover that roughly 88% of the variability in gold’s worth during the last 115 years will be defined by the substantial lower within the buying energy of the USD, with $1 in 1915 now value simply $0.04. Most market members perceive this dynamic intuitively, shopping for and promoting gold primarily based on USD inflationary expectations. 

Whereas a better SF worth could also be a vital characteristic for a commodity to function “onerous cash,” the metric itself says nothing about how market members worth stated commodity. Many cryptocurrencies which make the most of Bitcoin’s code have the very same provide schedule as Bitcoin and everybody understands their SF values don’t have anything to do with their future (or present) valuation.

We’re left with a speculation that applies to no financial belongings besides bitcoin and whose solely proof is a linear regression with questionable utility and clear choice bias. 

$235 billion bitcoin to infinity

A whole overview of linear regression and its mathematical foundation is past the scope of this evaluation. Nonetheless, there are a number of implementation errors well-established within the research community that reveal why the SF mannequin is prone to be spurious. Obscure math has allowed SF proponents to dismiss all criticism so it could be extra intuitive to grasp conceptually why the SF mannequin is irrelevant for future worth predictions.

The mannequin provided within the SF paper is similar slope-intercept equation everybody learns in 7th grade: y = mx + b. A standard-least-squares (OLS) regression shouldn’t be a predictive mannequin however relatively an estimation of the m and b values that reduce the distinction between the precise y values and the estimated y values given by the equation mx+b. In different phrases, each change in x equates to a corresponding change in y.

Recall that OLS is estimating how a lot y (Market Cap) modifications for a given change in x (SF). On a month-to-month foundation by which the mannequin is derived, the change in x is successfully 0. Consequently, the OLS mannequin is doing nothing greater than estimating Bitcoin’s historic progress fee. This turns into fairly apparent when one extends the mannequin into the close to future. By 2045, the mannequin estimates every Bitcoin shall be value $235,000,000,000 earlier than finally converging to infinity as bitcoin’s movement approaches 0.

Utilizing the estimated slope-intercept method is making essentially the most naive prediction doable, as a result of bitcoin grew by X up to now, it can develop by X sooner or later. One ought to do not forget that previous outcomes usually are not consultant of future returns.

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Darrell Huff wrote in “How to Lie with Statistics“: “Many a statistic is fake on its face. It will get by solely as a result of the magic of numbers brings a few suspension of frequent sense.” Upon reflection, few would take significantly the concept gold’s USD worth is a perform of its personal provide fee and due to this fact so is bitcoin’s. But, the supposed mathematical precision offered within the paper has resulted within the SF mannequin persevering with to be closely promoted in each retail {and professional} funding channels. 

Buyers ought to be extremely skeptical of this mannequin even when they consider bitcoin is digital gold. The SF paper shouldn’t be correct empirical evaluation, however extra akin to a advertising and marketing piece by which the writer is attempting to persuade readers that bitcoin goes to be value much more tomorrow. This will or could not end up true, but it surely has little to do with bitcoin’s provide schedule.

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