A new Bitcoin price model from quantitative analyst Benjamin Cowen places a statistical bound on the asset’s diminishing returns. The work shows that Bitcoin’s price distribution is flattening faster at its ceiling than at its floor.
The paper, titled Asymmetric Tail Curvature in Bitcoin Price Quantiles, builds on the broader Bitcoin price model literature. It challenges famous frameworks that kept projecting ever-higher cycle peaks. The analysis uses 16 years of daily data through May 2026.
Why The Old Bitcoin Price Models Kept Missing
In Section 3 of the paper, Cowen benchmarks three of the best-known Bitcoin price models against the price record from 2019 to 2026. All three were too optimistic. The size of the miss grew as the model’s ambition increased.
The original power-law fit, calibrated through 2018, overshot price on 77.2% of trading days. The average error ran 32.1% above actual.
PlanB’s stock-to-flow model overshot on 94.9% of days, with an average error of 294.5%. Its cross-asset cousin, the S2FX model, projected a 1,699% overshoot, implying Bitcoin prices above $5 million.
Cowen’s diagnosis is direct. These models baked in Bitcoin’s early reflexivity, when tiny capital inflows produced huge price moves. They projected that behavior forward into a market now dominated by institutions and trillion-dollar valuations.
Bitcoin currently trades just below $70,000, with a market cap above $1.4 trillion. The asset has fallen 4% in the past 24 hours and remains the largest cryptocurrency by market value.
What The New Paper Actually Found
Cowen’s setup turns the standard Bitcoin power law into a curve. Instead of one straight line on a log-log chart, he fits a fan of bands at different price percentiles. He then asks whether the top bands bend differently from the bottom bands.
The result is the paper’s headline finding. The upper bands, those tracing speculative peaks, bend inward and flatten over time. The lower bands, those tracing structural support, stay roughly straight. Tops compress relative to the trend with each cycle. The floor keeps climbing along its old path.
The numbers tell the same story. The upper-tail curvature measures roughly minus 0.33 and is statistically distinguishable from zero. The lower-tail curvature sits near minus 0.02 and cannot be distinguished from a flat line. The difference is significant at the 1% level under the paper’s bootstrap test.
Across 27 expanding windows of historical data, the upper-tail curvature stays in a tight band near minus 0.3. Every single window rejects the symmetry test.
Diminishing Reflexivity, Formalized
The mechanism Cowen offers in the back half of the paper is what traders have called the diminishing returns thesis for years. He calls it diminishing reflexivity.
Early Bitcoin was small. A few hundred million dollars of capital could push the price up 10,000% in a year. As Bitcoin’s market cap climbed into the trillions, the same percentage move required vastly more capital. So each cycle’s blow-off top lands closer to the long-run trend than the one before.
The reflexivity amplitude in his model decays as Bitcoin grows. Structural demand for Bitcoin as a monetary asset continues compounding along a steady power-law path. Speculative amplitude shrinks. Together, those two forces produce a fan of bands that pinches at the top.
The framing matters because it gives the diminishing-returns thesis a single number with a confidence interval. That replaces three or four eyeballed cycle ratios with a formal estimate.
How Seriously To Take The Finding
The paper devotes seven sections to its own caveats, and that candor is part of what makes it credible.
The first caveat is sample size. Bitcoin has lived through only four halving cycles. On short sub-windows, Cowen’s curvature parameter swings to absurd values, which he flags as weak identification.
The second is anchor sensitivity. Shift the model’s starting point from January 2009 to January 2010, and the upper-tail curvature shrinks to roughly zero. The finding depends on how much weight the thin liquidity data from 2010 to 2011 carries.
The third is functional form. A negative curvature in log-log space implies that, as it approaches infinity, the fan eventually predicts that Bitcoin prices will decline. Cowen states explicitly that this has no literal interpretation. The model describes a finite horizon, not a price target.
The fourth is the floor itself. The lower band has been pierced in past episodes, including the 2010 to 2015 stress events and the FTX collapse in November 2022.
Cowen writes that non-rejection of lower-tail flatness is not the same as acceptance. The confidence interval is wide enough to hide real curvature.
What It Means For The Bitcoin Next Cycle
For readers tracking the Bitcoin four-year cycle, the practical implication is to set expectations, not to market-time. If the upper-tail curvature is real and stable, percentage gains at future cycle peaks will continue compressing.
That fits the pattern of the current cycle. Bitcoin reached an all-time high near $126,080 in October 2025 and has since fallen about 44%. The asset is down 33% over the past year.
Cowen himself argues the four-year cycle still holds. If true, the range of plausible peak heights is now narrower than during the 2017 or 2021 cycles, consistent with lengthening Bitcoin cycles and shrinking upside.
The paper does not predict where Bitcoin trades next month, next quarter, or in 2028. What it offers is a more honest shape for the long-run distribution. It builds on the same power-law tradition pioneered by Trolololo, Giovanni Santostasi, and the quantile-band approach of Plan C.
One observation worth carrying forward concerns those moonshot models. They did not fail because Bitcoin disappointed. They failed because they extrapolated a regime that no longer exists.
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