spb/phd_thesis Public

1\begin{landscape}2\begin{table}[htbp]3\centering4\small5\caption{Descriptive Statistics: Rolling Realized Measures (5-Minute Window)}6\label{tab:desc_rolling}7\begin{threeparttable}8\begin{tabular}{lrrrrrrrrrrr}9\toprule10 & $N$ & \multicolumn{5}{c}{Realized Volatility (bps)} & \multicolumn{2}{c}{$\log(\text{RV})$} & \multicolumn{3}{c}{Realized Beta vs.\ ES} \\11\cmidrule(lr){3-7} \cmidrule(lr){8-9} \cmidrule(lr){10-12}12Contract & & Mean & SD & P5 & P50 & P95 & Mean & SD & Mean & SD & P50 \\13\midrule14E-mini S\&P 500 & 35,668 & 3.43 & 5.68 & 0.00 & 2.41 & 10.38 & -11.78 & 6.55 & 1.000 & 0.000 & 1.000 \\1510Y T-Note & 35,668 & 1.41 & 1.63 & 0.00 & 1.31 & 3.81 & -14.11 & 7.09 & -0.018 & 0.395 & 0.000 \\165Y T-Note & 35,668 & 0.79 & 1.15 & 0.00 & 0.66 & 2.36 & -14.77 & 6.86 & -0.007 & 0.225 & 0.000 \\17Dollar Index & 35,668 & 0.78 & 3.45 & 0.00 & 0.00 & 3.53 & -19.32 & 6.34 & -0.010 & 0.482 & 0.000 \\18Crude Oil WTI & 35,668 & 5.86 & 9.47 & 0.00 & 3.97 & 17.90 & -11.24 & 6.67 & 0.184 & 1.472 & 0.006 \\19Gold & 35,427 & 3.64 & 4.64 & 0.00 & 2.73 & 10.51 & -11.29 & 6.30 & 0.044 & 0.958 & 0.000 \\20VIX Futures & 31,330 & 11.16 & 23.33 & 0.00 & 0.00 & 52.40 & -18.31 & 7.74 & -0.714 & 4.451 & 0.000 \\21\bottomrule22\end{tabular}23\begin{tablenotes}[flushleft]24\small25\item \textit{Notes:} Statistics computed across all minute-level observations within $\pm 30$ minutes of FOMC announcements ($K = 5$ min rolling window, NA-tolerant with up to 20\% missing data). RV is the NA-tolerant rolling realized variance defined in Section~\ref{sec:methodology}, displayed in square-root (volatility) units in basis points; $\log(\text{RV})$ is computed on the realized variance in raw decimal-return units, so its level is not directly comparable to the bps columns. $\beta_t^{\text{real}} = \text{RCov}(r_i, r_{\text{ES}}) / \text{RVar}(r_{\text{ES}})$. ES beta is 1.000 by construction. $\log(\text{RV})$ is near-Gaussian, validating its use as a regression dependent variable.26\end{tablenotes}27\end{threeparttable}28\end{table}29\end{landscape}30