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1\begin{table}[htbp]2\centering\small3\begin{threeparttable}4\caption{Granger causality between the Fed state-price panel and U.S. asset returns}5\label{tab:granger}6\setlength{\tabcolsep}{4pt}7\begin{tabular}{l rrr rrr}8\toprule9 & \multicolumn{3}{c}{VAR($p^*$), $p^*=1$ (AIC)} & \multicolumn{3}{c}{$p$-value at fixed lag} \\10\cmidrule(lr){2-4}\cmidrule(lr){5-7}11Direction & $F$ & $p$ & $p$ (HAC) & $p=1$ & $p=2$ & $p=5$ \\12\midrule13 $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ $\to$ 10-year yield & 0.19 & 0.666 & 0.534 & 0.666 & 0.252 & 0.370 \\14 $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ $\to$ SPY & 0.90 & 0.345 & 0.198 & 0.345 & 0.364 & 0.253 \\15 $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ $\to$ VIX & 0.39 & 0.533 & 0.505 & 0.533 & 0.373 & 0.059 \\16 $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ $\to$ BTC & 1.75 & 0.188 & 0.264 & 0.188 & 0.629 & 0.006 \\17 10-year yield $\to$ $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ & 0.13 & 0.718 & 0.635 & 0.718 & 0.277 & 0.706 \\18 SPY $\to$ $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ & 0.35 & 0.557 & 0.228 & 0.557 & 0.816 & 0.908 \\19 VIX $\to$ $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ & 0.29 & 0.589 & 0.463 & 0.589 & 0.369 & 0.835 \\20 BTC $\to$ $\Delta\mathbb{E}^{\mathbb{Q}}[\Delta r]$ & 0.02 & 0.897 & 0.884 & 0.897 & 0.983 & 0.747 \\21\bottomrule22\end{tabular}23\begin{tablenotes}24\small25\item \textit{Notes:} Bivariate VAR Granger tests on $T=110$ U.S. trading days (12 Dec 2025 -- 21 May 2026). The Fed variable is the daily change in the risk-neutral expected June 2026 policy change (basis points), measured at the Polymarket close of the same calendar day (00:00 UTC, about four hours after the U.S. cash close); changes over weekends are assigned to Monday, as for the financial series. TNX is the daily change in the CBOE 10-year Treasury yield index (bps); SPY, VIX and BTC are daily log changes in percent. The lag order is selected by the AIC on the five-variable system (BIC selects 0, HQIC 0). $F$ and $p$ are the conventional Granger $F$-test; $p$ (HAC) is the Wald test with Newey--West (5 lags) covariance. $^{***}$, $^{**}$, $^{*}$: 1\%, 5\%, 10\%.26\end{tablenotes}27\end{threeparttable}28\end{table}