Nobody should run a long book in crypto's bottom capitalisation decile. Ballis and Ioannidis report 27.49% a week there in the 2013-2017 frontier era, market-adjusted, before costs and among coins that survived. Their own tests show how little of that return a trader could hold.

What the rank tests measure

Ballis and Ioannidis take every CoinMarketCap asset reporting a market cap and sample it each Sunday from April 2013 to July 2026. That gives them 690 cross-sections and 8,970 assets. They use CMC's numeric IDs, avoiding false histories stitched together from reused tickers. Following the whole reporting population also lets a delisting appear as an event. Each week, coins enter capitalisation deciles; a Markov chain tracks moves among them, with an entry state and an absorbing exit state. Breaks identified in earlier work divide the sample into frontier (to November 2017), expansion (to July 2021) and consolidation.

Their weak-form efficiency tests impose two conditions on those moves. Conditional symmetry requires equal odds of moving up or down from any decile. Reversibility requires stationary probability flows to balance between each pair of deciles. Their index A averages the absolute up-down probability gap across deciles 2 to 9. The proposed economic reason for a size gradient is equilibrium compensation: small coins attract less attention and face a greater risk of dying, so investors should demand a higher return.

Every era rejects both conditions. In consolidation, the Wald statistic reaches 2,548.3 and the Bowker statistic 1,652.0; permutation p-values hit the 0.001 floor. A declines from 0.0399 to 0.0282 to 0.0218. Its rolling 52-week measure falls from an October 2014 peak of 0.062 to 0.018.

Why did the ranks converge?

The paper's best move is to hold decile boundaries fixed at the week's start and measure where each coin ends up. Entry and exit elsewhere in the universe can no longer shift that coin's destination. On this measure, own-valuation asymmetry edges upward, from 0.0251 to 0.0257 to 0.0264. The entire decline in the reported index therefore comes from compositional churn as weekly entry falls from 3.93% of the universe to 0.75%. Levels tell a separate story: consolidation-era own-valuation asymmetry of 0.0264 exceeds the measured 0.0218. And the time-series evidence complicates the decomposition. In first differences, entry has the wrong sign (t=-2.63), as the authors report.

The abstract acknowledges the composition result. Two paragraphs after its headline claim, the conclusion says convergence "is primarily driven by changes in market composition rather than by changes in individual assets". The market "has moved steadily closer to Markov mobility efficiency" under the paper's definition, which concerns the transition matrix. My objection is to the headline language: calling slower listings "efficiency" can sound like a claim about prices.

The connection between rank symmetry and returns is weaker again. The authors demonstrate this themselves with log-symmetric returns, zero predictability and weekly vol of 0.30. Their simulation still generates an up-plus-down payoff gap of +4.7% for one-decile moves and +30.3% for three. They say their efficiency conclusion does not depend on the symmetry tests. I agree. Those tests capture rank predictability, and the decline from 0.0399 to 0.0218 comes from churn.

The frontier bottom decile's 27.49% week

Among survivors, the equal-weighted bottom decile earns a market-adjusted 27.49% a week in the frontier era (t=3.69). The figure drops to 8.05% in expansion and 2.78% in consolidation. Charging exits at -100% reduces the frontier return to 20.41% (t=2.84). One dollar in the survivor portfolio grows to roughly 10^33 dollars.

The typical coin fares differently outside the frontier era. Its median weekly return in that era is +7.17%, against -2.60% in expansion and -0.06% in consolidation. In consolidation, 47.3% of bottom-decile coin-weeks show zero volume, and the median price is $0.00043. Requiring a one-cent price cuts the frontier premium by about two thirds to 9.39%. In the later two eras, stale quotes and tick jumps supply the mean's right tail. Even in the frontier era, the one-cent floor leaves 9.39%.

Which decile can you trade?

Apply a $10,000 daily-volume screen after sorting the full universe, and the consolidation-era bottom decile retains 44.8 names. It earns 1.97% a week (t=5.45). Yet those are the smallest listed coins that happen to trade, rather than the smallest tenth of a tradable universe. Re-form deciles within the $10,000 universe and top minus bottom is 0.01% a week (t=0.04). Returns are U-shaped: +0.45% for the bottom decile (t=2.60) and +0.46% for the top (t=3.34).

Expansion still offers a tradable size gradient. Top minus bottom is -2.32% a week (t=-2.14), though a trader holding the tradable bottom decile would have watched that advantage decay.

By consolidation, it was gone.

$3,757 a week from the screened bottom decile

Take the favourable portfolio anyway. Weekly turnover is 17%; with 2% one-way costs, its net return is 1.28%. Limit participation to 10% of the thinnest coin's daily volume and median capacity comes to $292,700, producing $3,757 a week. Value-weighting that participation limit permits $2.8 million and roughly $36,000 a week. At a $1 million volume screen, the bottom decile loses 3.69% a week net and contains about 1.5 coins.

Skipping a week leaves 1.12% a week (t=3.23) in consolidation when the $10,000 screen follows the full-universe sort. The edge therefore extends beyond bid-ask bounce. It belongs, however, to the portfolio whose return disappears when deciles are formed inside the tradable universe. Capacity remains the open question. Costs are an assumed flat 2%, while capacity uses CMC-reported 24-hour volume; neither input can be verified. The authors say their non-investability conclusion does not rely on the cost assumption. Their case rests on the absent tradable size gradient and on capacity. At 1% costs, only the $100,000 consolidation cell changes sign, from -0.08% to +0.38%. Wash trading would overstate the reported volume, making $292,700 an upper bound in my view. Add the screen, exits at -100%, costs and cash during untradable weeks: the fully investable version turns $1 into about $0.08. The value-weighted market turns it into about $207.

The attention framework

On the full population, the ordering tests for persistence, exit hazards and conditional returns are not jointly rejected (consolidation p=0.247). Weekly exit hazards decline from 2.01% in decile 1 to 0.19% in decile 10. The authors caution that some recorded exits could be reporting failures rather than delistings. They set the persistence threshold k*=4 using frontier-era staying probabilities, leaving the frontier and full-sample persistence columns in-sample. They fairly use the later eras as validation. Return ordering fails for tradable consolidation-era universes: p=0.0104 at $10,000 and 0.0009 at $1 million. At $100,000, p=0.0533 is not a rejection. The authors identify this as their key qualification and argue that their return prediction's stated scope condition anticipated it.

Why we did not rebuild the 8,970-coin panel

Our crypto data covers roughly 50 liquid assets. We lack point-in-time circulating supplies and listing and delisting histories, so we cannot rank 8,970 coins or price their exits. A test restricted to liquid coins would remove the segment producing the return.

The paper makes the strongest case against crypto size as executable alpha that I have read. A positive bottom-minus-top spread among re-formed tradable deciles after 2026, in a portfolio able to hold more than $2.8 million, would change my mind.