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 of16roughly \ExtremeDropFactor{} (Figure~\ref{fig:extreme_minutes}). A large17part of the 1990s level is bid--ask bounce and price discreteness under18eighth and sixteenth ticks rather than volatility19\citep{roll1984simple,harris1991stock}: a single tick on a \$20 stock is a200.6\% return, and about half of all one-minute returns in the mid-1990s are21exactly zero (Online Appendix). The decline is nonetheless not only a tick22artifact. Measured from 2002, the first full year after decimalization, the23frequency of $|r|>1\%$ minutes falls from \ExtremeGtOneTwoThousandTwo{} per2410,000 to \ExtremeGtOneTens{} in the 2010s, roughly tenfold, and the25cross-section of daily realized variance shifts down over the same years26(Online Appendix).2728Second, the collapse was not monotone in the tails. The frequency of29$|r|>5\%$ minutes rose from \ExtremeGtFivePreCovid{} per 10,000 in 2017--201930to \ExtremeGtFiveCovid{} in 2020, a factor of \ExtremeCovidFactor{}, and 200831shows the same signature at a smaller scale (Figure~\ref{fig:extreme_minutes}).32Part of the 2020--2021 level reflects the composition of the top-100033universe in those years, which dollar-volume ranking populates with34leveraged exchange-traded products and distressed issuers that we cannot35label; the qualitative pattern---extremes became rarer but, when the market36is stressed, arrive in synchronized bursts---survives the exclusion of37heuristically identified non-common tickers and is the subject of38Section~\ref{sec:mechanisms}.3940Third, cross-sectional comovement at the one-minute horizon rose from nothing41to most of its half-hour level. In 1996 the mean pairwise correlation of42one-minute returns among the hundred largest stocks was \EppsNinetySixOne{},43against \EppsNinetySixThirty{} at thirty minutes: comovement existed but was44invisible at the minute, the classical Epps effect45\citep{epps1979comovements}. By 2015 the one-minute correlation was46\EppsFifteenOne{} against \EppsFifteenThirty{} at thirty minutes, and 202447shows the same near-flat profile at a lower level (\EppsTwentyFourOne{}48against \EppsTwentyFourThirty{}; Figure~\ref{fig:epps}). Two mechanisms49produce this flattening and our previous-tick synchronized grids do not50separate them. One is mechanical: nonsynchronous trading and stale prices51attenuate measured high-frequency correlation52\citep{reno2003closer,hayashi2005covariance,zhang2011estimating}, and the53share of stale one-minute prices fell from \ZeroRetNinetySix\% to54\ZeroRetTwentyFour\% between 1996 and 2024. The other is economic: common55information is now impounded across the cross-section within the minute.56\citet{toth2009epps} reach the same conclusion for 1993--2003 and find that57denser trading explains only part of the change. Whatever the mix, the58operational consequence for this paper is the same: one-minute residual59correlations identify economic neighbors far more sharply after 2005 than60before, a point we carry into the interpretation of the network results.6162\begin{figure}[t]63\centering64\includegraphics[width=\textwidth]{figE3_seasonality.pdf}65\caption{\textbf{Intraday seasonality by decade.} Minute-of-day means during66regular hours, lagged top-1000 dollar-volume universe, split-window and67flagged bars excluded: (a) absolute one-minute log return; (b) share of the68stock-day's volume; (c) high--low log range.}69\label{fig:seasonality_decade}70\end{figure}7172\begin{figure}[t]73\centering74\includegraphics[width=.72\textwidth]{figE5_extreme_minutes.pdf}75\caption{\textbf{Extreme one-minute returns.} Annual frequency (log scale) of76one-minute absolute log returns exceeding 1\%, 2\%, and 5\%, lagged top-100077universe, regular hours. Pre-2001 levels largely reflect eighth/sixteenth78tick bid--ask bounce.}79\label{fig:extreme_minutes}80\end{figure}8182\begin{figure}[t]83\centering84\includegraphics[width=.62\textwidth]{figE8_epps.pdf}85\caption{\textbf{The flattening of the Epps curve.} Mean pairwise return86correlation among the top-100 lagged dollar-volume stocks at 1-, 5-, 15-, and8730-minute sampling, previous-tick synchronization within day, for 1996, 2005,882015, and 2024. Correlations are computed on calendar-clock grids and are89therefore attenuated by nonsynchronous trading at short intervals, most90strongly in 1996.}91\label{fig:epps}92\end{figure}9394\subsection{Baseline: isolated shocks and market-wide tail activity}9596Table~\ref{tab:baseline_propagation} reports the baseline estimates of97equation~\eqref{eq:dd} for \NEventsReal{} isolated $|z|\ge6$ source events and98\NEventsPlacebo{} matched placebos. The difference-in-differences breadth99response is economically negligible at every horizon: at $h=5$ minutes the100point estimate is \DDBreadthFive$\times10^{-4}$ (bootstrap standard error101\DDBreadthFiveSE$\times10^{-4}$), and at $h=30$ minutes102\DDBreadthThirty$\times10^{-4}$ (\DDBreadthThirtySE$\times10^{-4}$). Against103a placebo base rate of about \BaseBreadthShare{} (Table~\ref{tab:design_checks},104Panel~A), the largest estimate in absolute value implies that an isolated105six-sigma move changes the probability that any given other security shows a106tail exceedance by about a third of one percent of the base rate, with a107negative sign that is statistically distinguishable from zero at $h=30$.108Difference-in-differences intensity estimates are of the same order and109alternate in sign.110111\input{tables/table4_baseline_propagation}112113The design diagnostics of Table~\ref{tab:design_checks} qualify this null in114three ways. Panel~A shows that real events do not arrive in ordinary minutes:115five minutes before the event, breadth is \PreBreadthReal$\times10^{-4}$ for116real events against \PreBreadthPlacebo$\times10^{-4}$ for placebos, a117difference of \PreBreadthDiff$\times10^{-4}$ (standard error118\PreBreadthDiffSE), and intensity is higher by \PreIntensityDiff{}119(\PreIntensityDiffSE). A six-sigma idiosyncratic move is thus more likely on120days and in minutes when the whole cross-section is already active, even121though the market factor is calm by construction. This is exactly the122ambient level that the inner difference of~\eqref{eq:dd} removes, and it is123the reason the difference-in-differences, not a post-event comparison, is the124baseline; but it also means that the ``no pre-event response'' statement125sometimes made for designs of this kind does not hold here as a statement126about levels, and we do not make it.127128Panel~C reports the three estimators side by side. Without pre-differencing,129real events show \PostDiffFive$\times10^{-4}$ more breadth than placebos at130$h=5$, almost exactly the pre-event gap, so that the difference-in-differences131is close to zero. Within deciles of the pre-event level, the gap is132\StratFive$\times10^{-4}$ (\StratFiveSE) at $h=5$ and133\StratThirty$\times10^{-4}$ (\StratThirtySE) at $h=30$. As argued in134Section~\ref{sec:design}, the two estimators bracket the market-wide135response: between zero and roughly \StratShareOfBase\% of the base rate.136Either bound is small relative to the network response of137Section~\ref{sec:mechanisms}, and the conclusion we draw is correspondingly138bounded: isolated idiosyncratic extremes raise market-wide tail activity by at139most a few percent of its base rate within two hours.140141Panel~B separates events by the number of source events detected in the same142minute. For the \ShareSingleton\% of events that are alone in their minute,143the difference-in-differences is \DDSingletonFive$\times10^{-4}$144(\DDSingletonFiveSE) at $h=5$ and \DDSingletonThirty$\times10^{-4}$145(\DDSingletonThirtySE) at $h=30$: slightly positive and within two standard146errors of zero. The negative full-sample estimates at longer horizons come147from minutes with three to five co-arriving events148(\DDMultiThirty$\times10^{-4}$, \DDMultiThirtySE, at $h=30$), which are the149minutes with the most elevated ambient activity and the strongest reversion.150The negative sign of the pooled estimate is therefore a mean-reversion151artifact of co-arrival minutes, not evidence that shocks calm the market.152153Three further features of Table~\ref{tab:baseline_propagation} deserve154emphasis. First, this is a powered null: the minimum detectable155difference-in-differences at $h=5$ is about \MDEFive$\times10^{-4}$, one156additional responding security per \MDEEventsPer{} events. Second, the null157is uniform in time: Figure~\ref{fig:irf_decade} shows the same flat response158profile in each of the four decades, and the Online Appendix shows it year by159year, so absorption is not a recent acquisition of electronic markets---though160the composition of what is being absorbed changed radically, as the161descriptive results show. Third, Panel~D of Table~\ref{tab:design_checks}162shows that the standard errors are insensitive to the clustering unit for163the market-wide statistics.164165\begin{figure}[t]166\centering167\includegraphics[width=.6\textwidth]{figF1_irf_decade.pdf}168\caption{\textbf{Difference-in-differences breadth by decade.} Point estimates of169$\Delta\Delta$ breadth (equation~\eqref{eq:dd}) with 95\% day-block bootstrap170bands, by horizon and decade.}171\label{fig:irf_decade}172\end{figure}173174\input{tables/table9_design_checks}175176Conditioning does not change the picture (Figure~\ref{fig:gradient_state}):177estimates by shock sign and by calm versus stressed market state are within178two standard errors of zero. Across magnitude bins the point estimates rise179from significantly negative for $6\sigma$--$8\sigma$ events, which are the180most numerous and the most affected by the co-arrival reversion just181described, to a positive but insignificant \DDGradLargest$\times10^{-4}$182(\DDGradLargestSE) for $12\sigma$--$20\sigma$ events. The signed response of183Panel~E is noisy and never significant: the cross-section does not drift in184the direction of the source shock. None of this resurrects market-wide185propagation; it motivates asking where a concentrated response would hide,186which is the subject of the next section.187188\begin{figure}[t]189\centering190\includegraphics[width=.66\textwidth]{figF3_gradient_state.pdf}191\caption{\textbf{Shock size, sign, and market state.} $\Delta\Delta$ breadth192at $h=15$ by source-shock magnitude bins, shock sign, and prior-30-minute193market volatility state, with 95\% bootstrap intervals.}194\label{fig:gradient_state}195\end{figure}196