You take the dividend drop without the dividend

Crypto venues increasingly list perpetual futures on equities and other real-world assets. They trade continuously while referencing stocks that pay dividends, and the paper states the consequence in a line: a long equity perpetual marked to the ex-dividend cash price bears the ex-dividend drop without receiving the dividend.

The question is whether the funding architecture those venues run can repair it. Premium-index funding is set from the contemporaneous basis — the difference between the perpetual price and the spot price — rather than from a carry target. The authors ask whether such funding can replicate shareholder cash flows for traders entering and exiting at arbitrary times, and conclude that it cannot.

The reason is structural rather than a matter of calibration. Funding performs two jobs that coincide for non-dividend crypto assets and come apart for equities: controlling the basis, and settlement. The obstruction the authors identify is measure-theoretic. A predictable dividend is an atom, and no absolutely continuous funding path can replicate an atom over a holding interval, even in the weak limit, so fairness has to match an atom with an atom — an explicit event credit rather than a smooth adjustment.

Exchange-native data supports the argument. At each covered ex-date one venue posts a discrete funding atom equal to minus D over Mark minus D, while a standard premium-index venue posts none, which transfers the dividend across venues from native funding alone, with no external spot involved. The paper also gives a fair-funding identity, casts timing fairness as an optimal-stopping condition, and characterises when the basis is a sufficient statistic for the fair target.