A token release makes a clean short in this model only when it permanently cuts the market maintainer's stake below an unmeasured threshold. If retention stays above that line, a smaller stake raises the price toward which a surviving bubble settles.
The locked stake pays for upkeep
Dong, Wang and Wu give their token no dividend, transaction service or redemption right. Its price rests entirely on resale. Someone must maintain the venue that makes resale possible.
Each period in their overlapping-generations setting, the young buy the fixed unit supply from the old. A share s of each cohort joins a sponsor partnership whose tokens are locked after trade. The sponsor pays a convex cost ψ(q) to choose a hidden survival probability q. Because it keeps only the fraction s of the benefit, its choice maximizes sγqB(t+1) minus ψ(q). Households price the token according to B(t)u'(e1 - B(t)) = γq(t)B(t+1). There is no outside cash flow: every positive price transfers wealth from young to old. The locked stake gives the sponsor a reason to pay for upkeep.
A positive stationary price exists if and only if s ≥ s_min. The minimum ranges over survival probabilities above q̄ = u'(e1)/γ, which lies in (0,1). It compares marginal maintenance cost ψ'(q) with γB(q), the value of survival to all holders. With weak convexity of u' and ψ', every s above s_min supports exactly two positive stationary equilibria: q̄ < q- < q+ < 1. The transition map has slopes 0 < T'(B-) < 1 < T'(B+). A live path starting below B+ therefore converges to B-; B+ sets the ceiling. The feasible price set is (0, B+(s)].
Theorem 3 delivers the sharp result. Suppose it becomes common knowledge at date τ that retention will remain at or below some ŝ < s_min for every date from a finite t* onward. Then B(τ) = 0. At t* there can be no positive resale price, so the cohort at t* - 1 pays nothing. The same reasoning works backward to τ.
The announcement is the trigger, regardless of the mechanical release date.
What would a trader have to measure?
The event requires common knowledge at τ, a drop below s_min and permanence for every n ≥ t*. The paper identifies the relevant observations: the maintainer's effective unhedged exposure, recipient identity and residual insider holdings. It supplies values for none of them.
Start with s_min. It depends on u, ψ, γ and e1: preferences, a maintenance cost curve and an endowment. The paper gives these no empirical counterparts, and we did not find a calibration. The observable substitute for s is usually whether tokens are vested or reserved. Howell et al., whom the authors cite, report insider vesting at 22 percent of more than 1,500 ICO issuers; 43 percent set tokens aside for a foundation, bounty or endowment. The authors draw a stricter distinction: "The relevant empirical state variable is the maintenance provider's effective, unhedged exposure, not the aggregate fraction of tokens reported as locked." Transferability alone does not establish that exposure has fallen. Insiders may continue holding.
The starting price remains free as well. Zero is an equilibrium, as is any value in (0, B+(s)]; the dynamics determine where a live path goes, not where it begins. Even after guessing the threshold and finding a proxy for s, an implementer must choose that initial price.
A smaller stake can raise the resting price
For s > s_min under the curvature assumptions, Lemma 4 gives dB+/ds > 0 and dB-/ds < 0. Live paths below B+ converge to B-. A release that leaves s above s_min thus raises the model's resting price and lowers its ceiling B+. The authors state the lower-branch sign, although the abstract and Corollary 1 emphasize the ceiling: greater retention widens the feasible interval. For a trader asking where the price settles, the lower branch gives the opposite direction.
Lower retention also raises the continuation price needed to justify a fixed current price, as the paper notes. That conditional appreciation requirement supplies no direction for today's price. Apart from a jump to zero, a sell signal arises only when the price sits above the new, lower B+.
Pre-release declines against a zero-price prediction
The authors cite several news episodes. During the week of 27 November 2023, scheduled token releases totaled almost $650 million, including DYDX, OP and SUI. DYDX fell 7 percent ahead of about $480 million due on 1 December, a release reported to nearly double circulating supply. OP fell nearly 6 percent before about $40 million came due. SUI fell 8.8 percent with about $48 million due. Over that week, the CoinDesk Market Index fell 1.5 percent. AXS lost more than 12.5 percent over 24 hours on 21 October 2022. The reverse move appeared on 25 January 2023: DYDX rose as much as 21 percent when an extension postponing 150 million tokens from 3 February to 1 December 2023 became public.
None of those moves approaches zero. The authors allow that real tokens with a fundamental component need not reach zero. They also acknowledge that anticipated selling pressure could generate the same moves with fixed total supply. Their conclusion is explicit: "the episodes therefore motivate the mechanism rather than identify it." Their own argument poses another problem for these examples. If a qualifying release schedule is common knowledge when trading starts, the bubble never forms. The dYdX schedule, with monthly releases through June 2026, was public. A test must therefore identify genuinely new information rather than treat the known schedule as news of a permanent drop below s_min.
The closest benchmark offered is equity. Field and Hanka report a three-day abnormal return of -1.5 percent across 1,948 IPO lock-up expirations. Those shares also have cash-flow claims.
We could not backtest this. Doing so would require point-in-time records of each controller's retained and hedged holdings, along with dated evidence of when revised schedules first became public. We have neither. Our crypto news archive does not provide a structured announcement record.
The theory neatly shows why a locked holder might pay to maintain a bubble. As a trading signal, it depends on an unobservable threshold and a ceiling that is just as hard to locate. Holdings data could change my view if announcements pushing a maintainer's unhedged stake below any plausible threshold produced collapses far larger than the declines of nearly 6 to more than 12.5 percent cited here.