spb/wp8_uqo

1% ============================================================================2% Section 8: Discussion and Conclusion3% ============================================================================4\section{Discussion and Conclusion}\label{sec:conclusion}56\subsection{What the state prices show}78Negative-risk events on Polymarket provide complete sets of state claims on well-defined macroeconomic and political outcomes, and this paper has used two of them to ask how the Arrow--Debreu pricing restrictions fare in a blockchain market. The answer is in three parts. The complete set of claims is priced at one dollar within the bounds that the platform's own mechanics make executable: the recorded sums of 1.017 (five Fed claims) and 1.015 (seventeen election claims) are statistically above one but economically within the half-spreads of the low-priced legs, they decline steadily towards resolution, they revert within days, and at the one order-book snapshot available the bid-side and ask-side sums bracket one. The normalised prices define a risk-neutral distribution over the June 2026 FOMC decision whose mean moved from $-15.5$ basis points to zero over six months, and that mean moves two to five times more, in variance terms, on FOMC and employment-report days than on other days, while weekend days carry about a third of weekday variance. And daily changes in that mean neither lead nor lag the Treasury, equity, volatility or cryptocurrency markets, although they are contemporaneously correlated with Treasury yields.910Two interpretive points follow. First, the Arrow--Debreu metaphor is accurate but less demanding than it sounds. Completeness is a property of the contract design, not a finding; what the data confirm is the law of one price for the riskless complete set and the absence of exploitable deviations at the quotes. The one genuine departure from the frictionless benchmark---the complete set trades at one rather than at its discounted value---reflects the asymmetry of the executable arbitrage (the sell-side round trip settles immediately through the adapter, the buy-side requires holding to resolution) and the fact that collateral earns nothing on the platform. A trader who buys a complete set is lending at zero; the market prices this correctly by refusing to pay less than one for it. Second, the normalised prices are risk-neutral probabilities and nothing in the data identifies the physical ones. The literature on futures-implied policy expectations has shown that the risk premium in such measures is large and time-varying \citep{piazzesi2008futures}; there is no reason to believe the Polymarket measure is exempt, and our hypothesis tests are designed not to depend on the distinction.1112\subsection{Manipulation, oracles and other threats}1314Three institutional risks deserve explicit mention because they bear on the external validity of any inference drawn from these prices. The first is concentrated position-taking. During the 2024 election a single trader operating several accounts was reported to have taken positions of some \$30 million on the Trump claim, and the platform's own prices moved with those purchases; theory and experiments suggest that such trades are absorbed when other participants anticipate them \citep{hanson2006manipulation}, but the daily data used here cannot separate information from flow, and our pricing results are in any case silent on whether the \emph{level} of any claim was right. The second is resolution risk. Polymarket outcomes are determined by UMA's optimistic oracle, in which disputed resolutions are settled by token-holder vote; in March 2025 a market on a U.S.--Ukraine minerals agreement was resolved against the apparent facts after a concentrated vote, and the platform declined to compensate holders. For the two markets studied here the resolution criteria---an FOMC statement and an election result---are as unambiguous as such criteria can be, but the possibility of an oracle dispute is a basis risk that is priced, if at all, in the small residual mass on improbable states. The third is volume. Reported volumes on unregulated blockchain venues can be inflated by wash trading \citep{cong2023wash}; we have used volume only descriptively, and the depth and spread evidence of Section~\ref{sec:results} is a better guide to the economic size of these markets than the headline figures.1516\subsection{Limitations}1718The study rests on two negative-risk groups observed at daily frequency. The Fed sample has 146 daily closes, thirteen scheduled releases and 110 trading days in common with U.S.\ markets; the announcement-day and lead--lag tests are correspondingly limited in power, and the absence of a detectable CPI effect or of a lead--lag relation is a statement about what daily data from one market can show, not a demonstration of informational equivalence. The pricing tests use recorded daily prices rather than executable quotes, and the single order-book snapshot cannot establish that the bounds held on every day. The alignment of the Polymarket close with the U.S.\ close leaves a residual window of three to four hours; a release in that window---there are none among the scheduled releases studied, but there could be unscheduled news---would appear in the Polymarket close of day $t$ and the U.S.\ close of day $t+1$. The discount factor is computed from the effective federal funds rate rather than from the opportunity cost actually faced by platform participants, which may be higher. And the volatility models of Appendix~\ref{app:volatility}, which an earlier version of this paper presented as a main result, turn out to be fragile: the ARCH-LM test does not reject homoskedasticity, the GARCH estimates sit on the boundary of the parameter space, and the asymmetry parameter is identified by two announcement days.1920\subsection{Conclusion}2122Blockchain prediction markets make complete state spaces tradable and observable. For the two state spaces studied here, the prices behave as Arrow--Debreu theory says state prices should---they sum to the price of a riskless claim within executable bounds, they define a well-behaved risk-neutral distribution, and that distribution responds to scheduled information. They do not behave as some of the enthusiasm around prediction markets would suggest: they do not lead the Treasury or equity markets at the daily horizon, they are not physical probabilities, and their recorded sums should not be read as arbitrage opportunities without the order book in hand. The most promising next steps are intraday, with the futures market as the benchmark, and cross-sectional, across the many negative-risk groups the platform now lists; the framework and the calendar conventions set out here are directly applicable to both.23