spb/wp15_uqo

1\section{Mechanisms}2\label{sec:mechanisms}34The baseline null says that isolated idiosyncratic shocks do not raise5market-wide jump activity. This section asks where transmission lives if not6there: in the shocked stock's network neighborhood, in transient responses7between measurement points, and in the systemic co-jump minutes that the8idiosyncratic design deliberately sets aside.910\subsection{Network-concentrated propagation --- and its intensification}1112Market-wide breadth spreads any response across five hundred receivers; a13transmission channel operating through economic or statistical linkages14concentrates it among a handful. For every event we therefore compare the15response of the source's twenty closest lagged-correlation neighbors with the16response of all other receivers, real minus placebo17(Table~\ref{tab:network_mechanism}).1819The differential is large, precisely estimated, and horizon-decaying: five20minutes after an isolated $|z|\ge6$ shock, the source's neighbors are21\NetDiffFive$\times10^{-4}$ more likely than non-neighbors to exceed22$|z|>2$---relative to placebo---with a bootstrap standard error of23\NetDiffFiveSE$\times10^{-4}$ ($t\approx34$); the differential declines to24\NetDiffThirty$\times10^{-4}$ at thirty minutes. Against the $\sim700\times2510^{-4}$ base rate, a neighbor's jump probability rises by roughly nine26percent of its unconditional level. Idiosyncratic shocks do propagate---to the27connected few, not to the diffuse many, which is precisely why market-wide28breadth cannot detect them.2930\input{tables/table7_network}3132The evolution across decades is the paper's sharpest dynamic fact33(Figure~\ref{fig:network}): the five-minute neighbor differential was34\NetDiffFiveNineties$\times10^{-4}$ in 1992--1999 and35\NetDiffFiveOughts$\times10^{-4}$ in 2000--2009, then jumps to36\NetDiffFiveTens$\times10^{-4}$ in 2010--2019 and37\NetDiffFiveTwenties$\times10^{-4}$ in 2020--2026---a tripling concentrated38exactly in the era of algorithmic liquidity provision, correlation-aware39execution, and index intermediation. Propagation along the statistical network40became roughly three times stronger while market-wide spillover remained zero:41transmission grew \emph{sharper}, not broader.4243\begin{figure}[t]44\centering45\includegraphics[width=.62\textwidth]{figF4_network.pdf}46\caption{\textbf{Network-concentrated propagation by decade.} Neighbor minus47non-neighbor $\Delta\Delta$ breadth at $h\in\{5,15,30\}$ with 95\% day-block48bootstrap intervals. Neighbors are the source's top-20 absolute-correlation49partners estimated on prior-month residuals.}50\label{fig:network}51\end{figure}5253\subsection{Cumulative responses}5455Point-in-time breadth at $t+h$ misses a receiver that jumps at $t+3$ and is56quiet at $t+15$. Cumulative breadth over $(t,t+h]$, differenced against its57mirrored pre-window and the placebo, remains null at the market level (at58thirty minutes: \CumThirty$\times10^{-4}$, SE \CumThirtySE$\times10^{-4}$).59The market-wide null is therefore not an artifact of sampling the response at60isolated instants; transient market-wide cascades after isolated idiosyncratic61shocks are absent as well.6263\subsection{Systemic co-jump minutes: where fragility lives}6465The isolation filters exclude minutes in which more than 2\% of the universe66jumps simultaneously. These minutes are the natural home of the fragility67hypothesis, and their time series (Figure~\ref{fig:cojumps}) delivers two68messages. First, the ordinary cross-section \emph{de-synchronized} secularly:69with idiosyncratic tail activity a hundred times rarer, minutes breaching the70fixed 2\% threshold fell from near-ubiquity in the sparse, wide-tick 1990s to71about one minute in eight today---a comparability warning we take seriously,72and the reason the fixed-threshold count is not itself a fragility measure.73Second, conditional severity moves the other way in stress: within co-jump74minutes, the mean share of names beyond $4\sigma$ averages75\CoJumpSevCalm\% in calm recent years but reaches \CoJumpSevGFC\% in 2008 and76\CoJumpSevCovid\% in 2020, and severe-synchronization minutes (more than 10\%77of the universe jumping together) spike from \SeverePreCovid{} per 1,000 in782017--2019 to \SevereCovid{} per 1,000 in 2020. Combined with the79figE5 evidence that $|r|>5\%$ minutes rose by a factor of80\ExtremeCovidFactor{} in 2020, the pattern is consistent across measures:81modern stress arrives as market-wide synchronized minutes, not as82single-name events.8384\begin{figure}[t]85\centering86\includegraphics[width=\textwidth]{figF5_cojumps.pdf}87\caption{\textbf{Systemic co-jump minutes, 1992--2026.} (a) Minutes per 1,00088in which more than 10\% of eligible top-500 names exceed $|z|>4$89simultaneously (log scale). (b) Mean affected share within co-jump minutes90($>$2\% threshold).}91\label{fig:cojumps}92\end{figure}9394Taken together, the mechanism evidence resolves the baseline null into a95sharper statement: idiosyncratic shocks propagate narrowly along the lagged96correlation network, that channel strengthened threefold in the algorithmic97era, and market-wide fragility is the province of common-shock minutes whose98severity---not frequency---is the binding object.99