spb/wp15_uqo

1\section{Results}2\label{sec:results}34\subsection{The transformation of the intraday market, 1992--2026}56Figures~\ref{fig:seasonality_decade} through \ref{fig:epps} document the7environment in which propagation must be measured, on liquidity-screened8universes with strictly lagged membership.910Three secular changes stand out. First, ordinary minute-level variability11collapsed. Mean absolute one-minute returns on the top-1000 universe fell12decade by decade at every minute of the trading day13(Figure~\ref{fig:seasonality_decade}a), and the frequency of one-minute14returns exceeding 1\% fell from about \ExtremeGtOneNineties{} per 10,000 in15the 1990s to \ExtremeGtOneTens{} per 10,000 in the 2010s---a factor of roughly16\ExtremeDropFactor{} (Figure~\ref{fig:extreme_minutes}). Part of the 1990s17level reflects bid--ask bounce under eighth and sixteenth ticks rather than18true volatility; the decade-by-decade decline survives range-based measures19and coarser sampling, and we flag the tick-regime caveat wherever it binds.2021Second, the collapse was not monotone in the tails. The frequency of22$|r|>5\%$ minutes rose from \ExtremeGtFivePreCovid{} per 10,000 in 2017--201923to \ExtremeGtFiveCovid{} in 2020---a factor of \ExtremeCovidFactor---and 200824shows the same signature (Figure~\ref{fig:extreme_minutes}). Extremes became25rarer but, when the market is stressed, arrive in synchronized bursts; we26return to this in Section~\ref{sec:mechanisms}.2728Third, cross-sectional information transmission accelerated dramatically. In291996 the mean pairwise correlation of one-minute returns among the hundred30largest stocks was \EppsNinetySixOne{}, against \EppsNinetySixThirty{} at31thirty minutes: comovement existed but took tens of minutes to materialize,32the classical Epps effect \citep{epps1979comovements}. By 2015 the one-minute33correlation was \EppsFifteenOne{} against \EppsFifteenThirty{} at thirty34minutes, and 2024 shows the same near-flat profile35(Figure~\ref{fig:epps}). The Epps effect has essentially disappeared from36large-cap U.S. equities: common information is now impounded across the37cross-section within a minute.3839\begin{figure}[t]40\centering41\includegraphics[width=\textwidth]{figE3_seasonality.pdf}42\caption{\textbf{Intraday seasonality by decade.} Minute-of-day means during43regular hours, lagged top-1000 dollar-volume universe, split-window and44flagged bars excluded: (a) absolute one-minute log return; (b) share of the45stock-day's volume; (c) high--low log range.}46\label{fig:seasonality_decade}47\end{figure}4849\begin{figure}[t]50\centering51\includegraphics[width=.72\textwidth]{figE5_extreme_minutes.pdf}52\caption{\textbf{Extreme one-minute returns.} Annual frequency (log scale) of53one-minute absolute log returns exceeding 1\%, 2\%, and 5\%, lagged top-100054universe, regular hours. Pre-2001 levels partly reflect eighth/sixteenth tick55bid--ask bounce.}56\label{fig:extreme_minutes}57\end{figure}5859\begin{figure}[t]60\centering61\includegraphics[width=.62\textwidth]{figE8_epps.pdf}62\caption{\textbf{The disappearance of the Epps effect.} Mean pairwise return63correlation among the top-100 lagged dollar-volume stocks at 1-, 5-, 15-, and6430-minute sampling, previous-tick synchronization within day, for 1996, 2005,652015, and 2024.}66\label{fig:epps}67\end{figure}6869\subsection{Baseline: idiosyncratic shocks do not propagate}7071Table~\ref{tab:baseline_propagation} reports the paper's baseline estimates of72equation~\eqref{eq:dd} for \NEventsReal{} isolated $|z|\ge6$ source events and73\NEventsPlacebo{} matched placebos. The abnormal breadth response is74economically zero at every horizon: at $h=5$ minutes the point estimate is75\DDBreadthFive$\times10^{-4}$ (bootstrap SE \DDBreadthFiveSE$\times10^{-4}$),76and at $h=30$ minutes \DDBreadthThirty$\times10^{-4}$77(SE \DDBreadthThirtySE$\times10^{-4}$). Against a placebo base rate of roughly78$7\times10^{-2}$, the largest estimate in absolute value implies that an79isolated six-sigma shock changes the probability that any given other security80jumps by less than half of one percent \emph{of the base rate}---with the81wrong sign. Abnormal intensity estimates are equally null.8283\input{tables/table4_baseline_propagation}8485Three features of Table~\ref{tab:baseline_propagation} deserve emphasis.86First, this is a powered null: standard errors are small enough to detect a87breadth response of $3\times10^{-4}$---one additional responding security per88seventeen events---at conventional levels. Second, the pre-event falsification89passes: real-event outcomes at $t-5$ equal placebo levels, so the null is not90produced by anticipation contaminating the baseline. Third, the null is91uniform: Figure~\ref{fig:irf_decade} shows the same flat response profile in92each of the four decades, so absorption is not a recent acquisition of93electronic markets---though the composition of what is being absorbed changed94radically, as the descriptive results show.9596\begin{figure}[t]97\centering98\includegraphics[width=.6\textwidth]{figF1_irf_decade.pdf}99\caption{\textbf{Abnormal propagation breadth by decade.} Point estimates of100$\Delta\Delta$ breadth (equation~\eqref{eq:dd}) with 95\% day-block bootstrap101bands, by horizon and decade.}102\label{fig:irf_decade}103\end{figure}104105Conditioning does not resurrect average propagation106(Figure~\ref{fig:gradient_state}): estimates by shock sign and by calm versus107stressed market states are all within two standard errors of zero. The only108suggestive pattern is monotonicity in magnitude---the largest shocks109($12\sigma$--$20\sigma$) carry a positive but insignificant point estimate of110\DDGradLargest$\times10^{-4}$ (SE \DDGradLargestSE$\times10^{-4}$)---which111motivates the concentrated-propagation probes of the next section.112113\begin{figure}[t]114\centering115\includegraphics[width=.66\textwidth]{figF3_gradient_state.pdf}116\caption{\textbf{Shock size, sign, and market state.} $\Delta\Delta$ breadth117at $h=15$ by source-shock magnitude bins, shock sign, and prior-30-minute118market volatility state, with 95\% bootstrap intervals.}119\label{fig:gradient_state}120\end{figure}121