spb/wp15_uqo

1\section{Mechanisms}2\label{sec:mechanisms}34The baseline bounds the market-wide response to isolated idiosyncratic5extremes at a few percent of the base rate. This section asks where6transmission lives if not there: in the shocked stock's network neighborhood,7in transient responses between measurement points, and in the systemic8co-jump minutes that the idiosyncratic design deliberately sets aside.910\subsection{Network-concentrated propagation}1112Market-wide breadth spreads any response across several 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 network differential is large relative to the market-wide estimates,20precisely estimated, and decays slowly with the horizon: five minutes after21an isolated $|z|\ge6$ move, the source's neighbors are22\NetDiffFive$\times10^{-4}$ more likely than other receivers to show a tail23exceedance, net of the same contrast for placebos, with a day-block bootstrap24standard error of \NetDiffFiveSE$\times10^{-4}$ and a ticker-cluster25standard error of \NetDiffFiveTickerSE$\times10^{-4}$; the differential26declines to \NetDiffFifteen$\times10^{-4}$ at fifteen minutes and27\NetDiffThirty$\times10^{-4}$ at thirty. Against a neighbor base rate of28about \NeighborBaseShare{}, a neighbor's exceedance probability rises by29roughly six percent of its unconditional level. The response is symmetric in30the sign of the shock (\NetDiffNeg$\times10^{-4}$ after negative and31\NetDiffPos$\times10^{-4}$ after positive moves). Idiosyncratic extremes do32propagate---to the connected few, not to the diffuse many, which is why33market-wide breadth cannot detect them.3435\input{tables/table7_network}3637Table~\ref{tab:network_components} decomposes the differential into its38four components. Over the full sample the contrast is driven by the real39arm: neighbors of a shocked stock show about $61\times10^{-4}$ more40exceedances than other receivers, while the placebo contrast is41$-2.7\times10^{-4}$. By decade, however, both arms move. In the 1990s,42neighbors show \NetRealNdNineties$\times10^{-4}$ more exceedances than43other receivers after a real event and \NetPlaceboNdNineties$\times10^{-4}$44more at placebo minutes; in the 2010s the real contrast is45\NetRealNdTens$\times10^{-4}$ and the placebo contrast is46\NetPlaceboNdTens$\times10^{-4}$. The placebo contrast is thus far from zero47within decades even though it averages to nearly zero over the sample: in the 1990s, the twenty most correlated names are simply the most48actively traded names, which show more exceedances in every minute; after492000, the neighbors of a stock that is quiet at the placebo minute are50themselves quieter than the rest of the universe, as correlation implies.51The network differential is therefore legitimately a difference of two52contrasts, and only the real-minus-placebo column of53Table~\ref{tab:network_components} carries a propagation interpretation.54Panel~B of Table~\ref{tab:design_checks} adds that the differential survives55the restriction to minutes in which the source is the only $|z|\ge6$ event56(\NetDiffSingleton$\times10^{-4}$, \NetDiffSingletonSE), so it is not an57artifact of correlated pairs moving in the same minute and remaining active58five minutes later, although co-arrivals do account for about a fifth of the59pooled estimate.6061\input{tables/table10_network_components}6263The evolution across decades (Figure~\ref{fig:network}) is the paper's64sharpest dynamic fact and its most delicate one. The five-minute network65differential was \NetDiffFiveNineties$\times10^{-4}$ in 1992--1999 and66\NetDiffFiveOughts$\times10^{-4}$ in 2000--2009, then rises to67\NetDiffFiveTens$\times10^{-4}$ in 2010--2019 and68\NetDiffFiveTwenties$\times10^{-4}$ in 2020--2026, a threefold increase that69coincides with the era of algorithmic liquidity provision, correlation-aware70execution, and index intermediation, and that occurs while market-wide71spillover stays bounded near zero. Two readings are consistent with this72pattern and the data do not separate them. Under the first, transmission73along economic linkages became stronger and faster---basket arbitrage and74statistical-arbitrage strategies convert a move in one name into trades in75its peers within minutes, as \citet{bendavid2018etfs} and76\citet{foucault2016news} would predict. Under the second, transmission was77always present but the one-minute correlations from which we identify78neighbors were too noisy in the 1990s to find the true peers: with the Epps79effect of Figure~\ref{fig:epps}, the prior-month one-minute residual80correlation of a genuine industry pair in 1996 is barely distinguishable from81sampling noise, and a neighbor set contaminated by false peers dilutes the82contrast mechanically. The decline of the 1990s differential at $h=5$83relative to $h=30$ (Table~\ref{tab:network_mechanism}), the opposite of the84decay seen in later decades, is consistent with the second reading, since85slow comovement is what an Epps-era network would transmit. The honest86summary is that propagation along the measured network at least tripled, and87that transmission became sharper rather than broader; how much of the88increase is a change in the market and how much a change in the measurement89requires neighbor sets built on coarser-sampled or transaction-time90correlation estimators \citep{hayashi2005covariance}, an extension we leave91for future work.9293\begin{figure}[t]94\centering95\includegraphics[width=.62\textwidth]{figF4_network.pdf}96\caption{\textbf{Network-concentrated propagation by decade.} Neighbor minus97other-receiver breadth at $h\in\{5,15,30\}$, real minus placebo, with 95\%98day-block bootstrap intervals. Neighbors are the source's top-2099absolute-correlation partners estimated on prior-month one-minute residuals.}100\label{fig:network}101\end{figure}102103\subsection{Cumulative responses}104105Point-in-time breadth at $t+h$ misses a receiver that moves at $t+3$ and is106quiet at $t+15$. Cumulative breadth over $(t,t+h]$, differenced against its107mirrored pre-window and the placebo, remains null at the market level (at108thirty minutes: \CumThirty$\times10^{-4}$, standard error109\CumThirtySE$\times10^{-4}$, against a base rate near110\CumBaseFifteen\% at fifteen minutes). The market-wide bound is therefore not111an artifact of sampling the response at isolated instants; transient112market-wide cascades after isolated idiosyncratic extremes are absent as113well.114115\subsection{Systemic co-jump minutes}116117The isolation filters exclude minutes in which more than 2\% of the universe118moves beyond four robust standard deviations simultaneously. These minutes119are the natural home of the fragility hypothesis, and their time series120(Figure~\ref{fig:cojumps}) delivers two messages, each with a comparability121limit. First, the ordinary cross-section de-synchronized secularly: with122idiosyncratic tail activity two orders of magnitude rarer, minutes breaching123the fixed 2\% threshold fell from near-ubiquity in the sparse, wide-tick1241990s to about \CoJumpPerThousandRecent{} per 1,000, roughly one minute in125eight, in 2021--2025. Under the same standardization the early 1990s also126produce \SevereEarlyNineties{} severe minutes per 1,000 and a mean affected127share of \CoJumpSevEarlyNineties\% within co-jump minutes---both above1282008---which we read as discreteness rather than fragility: when most minute129returns are zero or one tick, a two-tick move in many names at once breaches130a four-MAD threshold without any economic synchronization. The fixed-threshold131count and the pre-2001 severity series are therefore not fragility measures,132and no claim in this paper compares synchronization across the133decimalization boundary.134135Second, within the post-decimalization era, conditional severity moves136sharply in stress. Within co-jump minutes, the mean share of names beyond137$4\sigma$ averages \CoJumpSevCalm\% in calm recent years but reaches138\CoJumpSevGFC\% in 2008 and \CoJumpSevCovid\% in 2020, and139severe-synchronization minutes (more than 10\% of the universe moving140together) rise from \SeverePreCovid{} per 1,000 in 2017--2019 to141\SevereCovid{} per 1,000 in 2020, with \SevereGFC{} per 1,000 in 2008142against fewer than 6 per 1,000 in 2006 and 2019: an increase of roughly an143order of magnitude in both crises. Combined with the144evidence of Figure~\ref{fig:extreme_minutes} that $|r|>5\%$ minutes rose by a145factor of \ExtremeCovidFactor{} in 2020, the pattern is consistent across146measures and with the collective-synchronization events documented by147\citet{calcagnile2018collective} on a shorter sample: modern stress arrives148as market-wide synchronized minutes, not as single-name events. Whether those149minutes are common news arrivals or endogenous synchronization of the kind150modelled by \citet{bormetti2015modelling} is not identified by bars alone.151152\begin{figure}[t]153\centering154\includegraphics[width=\textwidth]{figF5_cojumps.pdf}155\caption{\textbf{Systemic co-jump minutes, 1992--2026.} (a) Minutes per 1,000156in which more than 10\% of observable top-500 names exceed $|z|>4$157simultaneously (log scale). (b) Mean affected share within co-jump minutes158($>$2\% threshold). Pre-2001 levels are inflated by price discreteness and159are not comparable with later years.}160\label{fig:cojumps}161\end{figure}162163Taken together, the mechanism evidence sharpens the baseline into a bounded164statement: idiosyncratic extremes propagate narrowly along the lagged165correlation network, that measured channel at least tripled in the166algorithmic era, and market-wide tail risk in the post-decimalization era is167the province of common-shock minutes whose severity in crises, not their168frequency in calm times, is the binding object.169