Bitcoin Generalized Stock-to-Flow (S2F-G) Model
By Bitcoin.Modeling ( https://twitter.com/Bitcoin_Model ), 5th September 2022
The Original Bitcoin Stock-to-Flow Model (hereafter “Original Model”) was proposed by Plan B in his famous paper, “Modeling Bitcoin Value with Scarcity” [1], where the following formula was utilized to model the price of Bitcoin:
In Equation (1), ‘Stock’ or S refers to the existing reserves of Bitcoin, and ‘Flow’ or F is the annual rate of production of Bitcoin. C and k are determined by fitting the data to the model equation. Using only these four numbers — two parameters (S & F), a scaling exponent (k) and a constant (C) — the Stock-to-Flow Model has been predicting with reasonable accuracy the Bitcoin Price up to the present day. For the Original Model, the paper [1] determined that C = 0.4 and k = 3 for a good data-to-model fit.
However, there is some scope for improvement in the above Stock-to-Flow model equation, which the present write-up accomplishes by introducing a new parameter that offers a superior data-to-model fit:
The above is called the “Generalized Stock-to-Flow Model” (hereafter “Generalized Model”). The scaling exponent k in the Original Model is effectively split into two different scaling exponents m and n, permitting Stock and Flow to affect the Bitcoin Price to different extents. Setting m = n = k in Equation (2), reduces it to Equation (1). The latest equation generalizes the Original model, rendering the Stock and Flow exponents independent of each other.
Using the method of multiple log-linear regression, the constant and exponents for the Generalized Model were determined to be: C = 2.8294×10^(–21), m = 5.0046 & n = 2.0669. Had the magnitudes of the Stock and Flow exponents matched closely, then the Original model equation would’ve made sense, where the two exponents collapse into one. However, the absolute value of the Stock exponent is more than double that of the Flow exponent, indicating that Stock and Flow ought to be modeled as separate parameters with their own individual exponents, rather than as (Stock/Flow). The results are plotted in Fig. 1 below, comparing the Original Model with the Generalized one.
As can be readily seen from above graph, both the Original and Generalized models are practically identical in their predictions until the May 2020 halving, after which they begin to diverge substantially. For the present cycle (2020–24), the Original Model predicts $55K for the Bitcoin Price, whereas the Generalized Model projects only $30K. The gap between the two models widens with time, and for the 2024–28 cycle, the Original and Generalized models output $500K and $170K respectively, which is a significant difference. Only time will tell as to which model eventually prevails as correct. A limit of $400K is suggested to break the tie for the 2024–28 cycle — if the cycle peak exceeds $400K, then the Original Model is right; if not, the Generalized Model wins!
References:-
[1] “Modeling Bitcoin Value with Scarcity”, by Plan B, on the Medium publishing platform, dated 22nd March 2019: https://medium.com/@100trillionUSD/modeling-bitcoins-value-with-scarcity-91fa0fc03e25
(Disclaimer: Not Financial Advice. Invest at your own risk.)