Price modeling
Why Your Bitcoin Price Model is Probably Wrong (and How to Fix It)
Explore how a synthetic, constraint-based model tests support for competing Bitcoin price trajectories and how evidence helps distinguish them
The Mirage of Price Agreement
In Bitcoin price forecasting, agreement on a price chart is a dangerous mirage. Two models can converge on the exact same price at any arbitrary point in time, yet mask massive structural disagreements regarding the economic reality required to get there. One may assume a flood of external capital arriving in the ecosystem, while another assumes a silent explosion in subjective investor value. Because historical agreement provides only one "restriction" on a model, it fails to identify the specific resources, expectations, and continuation assumptions that dictate the path ahead.
This post explores gives a quick summary of the new FIR "Inverse Framework" developed by Murray Rudd. Rather than attempting a standard curve-fitting exercise, this methodology works backward from a target price trajectory to expose the underlying assumptions necessary to support it. By peeling back the labels of three popular valuation approaches, we find counter-intuitive truths that challenge the very foundation of how sophisticated investors view Bitcoin price projections.
The full paper is available here (be forewarned, it is a math-heavy read).
Given how technical the paper is, I also generated a couple of NotebookLM files for non-math visitors. They don't get all the technicalities exactly right, but are a good way to get the drift of the paper without having to consider all the equations.
8-minute video explainer
19-minute simulated audio podcast
The "Price Mirror" Trap: Different Realities, Same Chart
The most persistent trap in Bitcoin modeling is the assumption that a model matching historical prices is fundamentally sound. This research identifies a "Price Mirror" effect, where a "lower endpoint" price path and an "upper endpoint" path appear virtually identical historically but rely on substantially different funding and valuation-growth assumptions.
Consider two distinct scenarios from the research that satisfy the same historical price agreement:
- Scenario A (Lower Path): Driven by high external funding (1.2 resource units) combined with a stagnant valuation reference (g = 0).
- Scenario B (Upper Path): Driven by low external funding (0.4 resource units) paired with high internal valuation growth (g = 1.25).
For the investor, this is a crisis of hidden variables. Historical price agreement supplies only one restriction, but a robust assessment must identify the "resources, expectations, and continuation assumptions" that carry an explanation forward.
Without this, you cannot know if the price is fueled by new liquidity or simply a shift in subjective belief. Therefore, you cannot predict how the model will react when those specific conditions change.
Why "Who Holds the Coins" Matters More Than the Price
If price history alone is an insufficient filter, we must look to the ledger. The research demonstrates that observing portfolio holdings - the actual distribution of coins across groups - is a far more powerful diagnostic for truth than the price ticker.
Holdings observations can eliminate support for a price path even when the price itself seems "compatible" with history.
In the experimental framework, analyzing historical accounts was the only way to resolve the massive funding discrepancies between models. While the price of the lower path in Scenario A looked plausible, the actual accounts required to support that path were non-existent on the ledger.
"Information about historical accounts has resolved the large funding difference between the two endpoint explanations while leaving smaller differences in the behavior."
The Hidden Engine: The Subjective Valuation Reference
The "silent engine" of Bitcoin appreciation is the Valuation Reference (represented as A_t). This variable tracks the evolution of subjective value growth among investors. While external funding provides the fuel, A_t is the mechanical process that translates that fuel into a clearing price.
The power of this hidden variable was proven in a "Frozen-Reference" experiment. By freezing the growth of A_t at Month 36 while keeping all funding and behavioral coefficients identical, the projected Month-60 price index dropped from 112.36 to 108.42 .
This quantitative delta proves that "historical compatibility does not independently establish" that price growth will continue. A projected trajectory requires a hard commitment to a future valuation process. If that subjective engine stalls, the price path collapses, regardless of how perfectly the model fit the past.
Descriptive vs. Explanatory: The Limit of "Scaling Laws"
Sophisticated analysts must distinguish between "Model S" (Temporal Scaling/Power Laws) and mechanistic models like "Model O" (Optimizing Investors) or "Model T" (Signal-based allocation).
Scaling laws are often celebrated for their mathematical elegance but they are structurally "blind" to the mechanics of liquidity. Because Model S lacks a mapping for investor accounts or cash balances, it cannot react to a "funding pulse" or a "policy intervention." It is a descriptive tool that summarizes where we have been but it fails to explain the mechanism of the future. In the research, this specific scaling specification was rejected by the monthly price panel because it could not reconcile the high-resolution movements of the market.
Scaling Laws are often descriptive of the past but fail to explain the mechanism of the future.
The Value of Information: Portfolios > Predictions
When trying to reduce terminal price uncertainty, there is a clear hierarchy of information. According to the "Worst Remaining Width" data (Table 3 in the download), not all data points are created equal:
- Group Holdings (Highest Value): Offers the most "guaranteed reduction" in uncertainty by narrowing the range of possible future paths.
- Cash Balances (High Value): More effective than price observations, though less definitive than holdings.
- Future Price Observations (Lowest Value): In a shocking finding for ticker-watchers, an additional Price Observation at Month 37 offered "0.0000" guaranteed reduction in uncertainty at the 0.005 precision level.
This suggests that investors should spend significantly more time analyzing on-chain distribution and liquidity flows than monitoring daily price volatility.
Conclusion: The "Model Label" Fallacy
A trajectory is only as reliable as the assumptions you cannot see. We often fall victim to the "Model Label" fallacy, adhering to a name like "Power Law" or "S2F" without realizing that a presumably long-run trajectory can lose its supporting explanation while being "carried" by another - such as a shift in investor subjective value.
The label is a distraction; the underlying assumptions about behavior, funding, and subjective value growth are the only things that matter.
If your favorite Bitcoin price model was stripped of its labels, what specific assumptions about your behavior - and the behavior of every other holder - is it actually making?