Modeling Bitcoin’s Price with a Decomposition of Stock-to-Flow

Decomposing the stock-to-flow into parts reveals growth that diminishes faster than predicted by time-based models.

By Quantodian, a collaboration of InTheLoop and Harold Christopher Burger

How fast is bitcoin’s price going to increase in the long-term? A popular model using stock-to-flow as input forecasts non-diminishing returns of eight to ten-fold every four years. An alternative, more conservative model is based upon time as the predictor variable (see here and here), showing a continuing price growth for bitcoin as well, but at a rate diminishing with time. In this paper, we see if we can shed some light on this huge contrast in the future price trajectory of these two models.

Until today, both stock-to-flow and time have been shown to closely correlate with the historic price of bitcoin, but the two models differ wildly in their forecasts of bitcoin’s price. This difference is so pronounced that in the coming few years at least one of these models will be falsified, because the fit as dictated by that model will no longer apply. In this paper, we examine what is driving this difference. We decompose the input variable of the stock-to-flow model and see that only one of the resulting components generates non-diminishing price growth. We show that if this component is allowed to be weighted separately in order to best fit bitcoin’s realized price history, it steers price in the opposite direction than the other components. This confirms bitcoin’s observed diminishing returns. It also indicates that the conservative time-based model might be somewhat too bullish, and thus the stock-to-flow model seems much too bullish. This doesn’t say that bitcoin is not a great asset to invest in, because exceptional returns (compared to many other asset classes) are still supported for years to come. But it puts the non-diminishing exponential growth phase of the stock-to-flow model to question.

Time-based model

The motivation of a time-based model is that historic price versus time until now appears linear in a log-log plot. Price is modeled as:

where time refers to the time passed since a given event such as the genesis block. The variables a and b are found via linear regression as to best fit bitcoin’s realized price data.

Stock-to-flow model

The stock-to-flow model has been described in Modeling Bitcoin’s Value with Scarcity. Stock-to-flow is programmatically laid down in the bitcoin protocol and the paper proposes to use it as a measure of scarcity that drives price. Like the time-based model, the motivation of the stock-to-flow model is that the historic price versus stock-to-flow until now appears linear in a log-log plot. The model equation is:

where S2F refers to the stock-to-flow value, and c and d are found via linear regression.

Comparing the models

Superficially, the two models look very similar: both predict the price of bitcoin based on the logarithm of the underlying variable. The difference in the models comes solely from the use of a different input variable, with the stock-to-flow model producing much more bullish forecasts than the time-based model as can be observed in this chart.