Quantitative analyst Benjamin Cowen has developed a new Bitcoin price model that quantifies the diminishing returns of cryptocurrency speculation. According to the paper titled Asymmetric Tail Curvature in Bitcoin Price Quantiles, the model uses 16 years of daily data through May 2026 to analyze Bitcoin's price distribution. The analysis reveals that Bitcoin's price distribution is flattening faster at its ceiling than at its floor, with the upper bands bending inward and compressing over time while lower bands remain relatively straight.
Cowen's research benchmarks three established Bitcoin price models against actual price data from 2019 to 2026. As reported in the paper, the original power-law fit overshot prices on 77.2% of trading days with an average error of 32.1% above actual. PlanB's stock-to-flow model overshot on 94.9% of days with an average error of 294.5%, while the S2FX model projected a 1,699% overshoot, implying Bitcoin prices above $5 million. Bitcoin currently trades just below $70,000 with a market cap above $1.4 trillion.
The new model formalizes what traders have called the diminishing returns thesis through the concept of diminishing reflexivity. According to the paper, early Bitcoin required only a few hundred million dollars of capital to produce 10,000% price moves in a year, but as market cap climbed into the trillions, the same percentage moves now require vastly more capital. Cowen's analysis shows that upper-tail curvature measures approximately minus 0.33, which is statistically distinguishable from zero, while lower-tail curvature sits near minus 0.02 and cannot be distinguished from a flat line. The model demonstrates that each cycle's blow-off top lands closer to the long-run trend than the previous cycle.
The research suggests that Bitcoin's four-year cycle still holds, but with narrower plausible peak heights compared to previous cycles. As reported in the paper, Bitcoin reached an all-time high near $126,080 in October 2025 and has since fallen approximately 44%. The asset is down 33% over the past year. Cowen argues that percentage gains at future cycle peaks will continue compressing if the upper-tail curvature is real and stable, consistent with lengthening Bitcoin cycles and shrinking upside potential.
