What is Stock-to-Flow Model? definition, context and sources

01What is Stock-to-Flow Model?

Stock-to-Flow Model is a family of valuation hypotheses popularized for Bitcoin by PlanB. The underlying ratio divides existing stock by the rate of annual new issuance; a subsequent statistical model estimates market value or price from it. The ratio describes supply, while the valuation relationship requires separate empirical validation.

02The ratio of stock to annual additions

PlanB defines stock as the existing inventory and flow as yearly production. In our explanation, BTC stock is divided by the rate of new issuance in BTC per year; the result has the dimension of time. It expresses how many years it would take at that unchanged rate to produce an amount equivalent to the stock. It is neither the remaining mining time nor a price. [1]

03First establish exactly what is counted

Coin Metrics distinguishes measures of new issuance; the original PlanB article also makes its own stock adjustment for presumed lost coins. Our example makes no such adjustment. For a real series, the stock definition, observation time and method of annualizing flow must be documented. Transaction fees and transfers of existing coins are not new issuance. [2] [1]

04Halving changes the rate, not mechanically the market price

Bitcoin Core reduces the subsidy according to elapsed halving intervals. With the same stock and block count, halving the subsidy therefore means half the issuance flow and twice the ratio. This is a conditional arithmetic relationship. In reality stock continues to grow and the number of blocks in a calendar window varies; a retrospectively measured annual flow need not change in the same way as the annualized current rate. [3]

05The valuation model adds an estimated relationship

PlanB’s original article estimates a regression between the logarithm of Stock-to-Flow and the logarithm of market value. It thus adds a testable hypothesis to the descriptive ratio. Market capitalization and price per BTC are different quantities: conversion between them requires the corresponding stock. Regression parameters are not consensus rules, and a change in the ratio alone does not determine a price change. [1]

06The same issuance ratio does not rule out different demand

Bitcoin.org explains price through supply and demand. In our interpretation, this means Stock-to-Flow alone contains neither holders’ willingness to sell, buying interest, market liquidity nor risk valuation. The same stock and issuance rate therefore do not themselves force a single market price. Our example illustrates this logical boundary without making a claim about a particular historical market. [4]

07A good fit between two trends need not be causal

Hyndman and Athanasopoulos show how non-stationary time series can produce a spurious regression relationship; they also highlight residual autocorrelation. For our explanation, this implies a need to diagnose data and errors, not an automatic verdict on every variant of this model. A high in-sample fit alone proves neither a causal mechanism nor a reliable forecast. [5]

08Test forecasts outside the calibration data

Forecasting: Principles and Practice distinguishes fit quality from accuracy on new data. For a reproducible test of this model, we therefore record the version, calibration period, horizon and error measure in advance. A later coefficient adjustment is not a success of the original forecast. Evaluation must include comparison with a simple benchmark and disclosure of deviations. [6]

09Other variants and the zero-issuance boundary

PlanB presents S2FX as a different construction with clusters and other assets instead of the original time series. Its parameters and results must therefore not be conflated with the original model. In our underlying ratio, division by zero flow is undefined; for positive flow approaching zero, the ratio grows without bound. This mathematical limit does not imply an infinite bitcoin price. [7]

ExampleEXAMPLE · S2F

The same issuance ratio, different assigned prices

Our own fictional example compares three alternative situations A, B and C at the same instant, not three consecutive years. Each has an existing stock of 1000 BTC. Annual new additions used as a constant rate are [100, 50, 50] BTC. Dividing stock by the respective annual rate gives Stock-to-Flow ratios of [10, 20, 20] years. This is the time needed to produce the equivalent of current stock at that rate, not the network’s remaining lifespan. Independently assigned model prices are [20, 20, 5] USD/BTC; we do not calculate them from the issuance ratio. Market capitalizations, stock times price, are therefore [20000, 20000, 5000] USD. Relative to A, B has half the flow and twice the ratio, but its assigned price is unchanged. B and C have the same stock and flow, yet we assigned them different prices. This arithmetic example shows that the issuance-ratio inputs alone do not uniquely determine price; it is neither an empirical refutation nor a calibration of a particular regression. The chart shows only the three ratios in years, without a dollar axis or a line connecting a time evolution. With zero annual flow the ratio would be undefined, so we draw no bar for it. The example includes no actual network values, lost coins, transaction fees, trades or return forecast.

Separate the issuance ratio from the regression estimate of market value.
State the stock definition, time window and annualization of new issuance.
The same Stock-to-Flow alone does not force the same price.
Test a predetermined version on new data and acknowledge its errors.

Read in context

For the clearest picture, read this entry together with Halving, Stock-to-Flow, On-chain Analysis, Backtesting, Overfitting.

?Practical questions

01Does twice the Stock-to-Flow automatically mean twice the price?

No. The ratio may rise when issuance slows, but it contains no rule for converting it to a price. A price or market-capitalization model adds a separate estimated relationship, and its forecasts must be tested outside the calibration data.

02Does the end of new issuance mean an infinite price?

No. With zero flow the stock-to-flow quotient is undefined. Growth in the ratio as positive flow approaches zero does not prove an infinite market price. Market valuation requires demand and cannot be determined merely by dividing issuance quantities.