spb/wp15_uqo

1\documentclass[12pt]{article}2\makeatletter\def\input@path{{../paper/}}\makeatother3\input{../paper/preamble}4\graphicspath{{figures/}{../paper/figures/}}56\title{Online Appendix for\\ ``Faster, Wider, More Fragile? The Evolution of7Intraday Shock Propagation in U.S.\ Equity Markets, 1992--2026''}8\author{}9\date{}1011\begin{document}12\maketitle13\tableofcontents14\clearpage1516\section{Extended data audit}17\label{app:audit}1819\paragraph{Provenance and snapshot.} The data are one-minute OHLCV bars20originally sourced from Finnhub.io and aggregated into 411 monthly files21(January 1992--March 2026). The exact byte-level snapshot is pinned: every22file's SHA-256 checksum was verified at download against the archive's23metadata and re-verified after the full download; the manifest (per-file24checksum, byte size, row count, column schema, timestamp bounds, symbol25count, duplicate count) accompanies the replication package.2627\paragraph{Calendar and timezone.} Observed trading dates match the official28XNYS calendar exactly over the full sample: zero missing sessions, zero dates29outside the calendar, zero weekend observations. Timestamps are UTC at30bar-start; mapping to Eastern Time was verified empirically on both sides of31every daylight-saving transition (the regular session opens at 13:30 UTC in32summer months and 14:30 UTC in winter months throughout). The regular-hours33share of bars by calendar month is flat (96.75\%--97.09\%), ruling out any34DST mishandling: an offset error would displace roughly 15\% of session rows35in March and November. Early-closing sessions are truncated at the true36exchange close; residual post-close prints (7.3\% of morning volume on372025-12-24 versus 60.4\% on the adjacent full day) are labelled after-hours.3839\paragraph{Integrity.} Across \DataRows{} bars: \DataOHLCViol{} OHLC-impossible40bars (1.3 per $10^8$, concentrated 1993--1995), zero non-positive prices, zero41zero-volume or negative-volume bars, \DataDupKeys{} duplicate ticker-minute42keys (1.3 per million; merged as open=first, high=max, low=min, close=last,43volume=sum). Prices are unadjusted for corporate actions; volumes are in44shares (verified against public daily volumes for benchmark securities).4546\paragraph{Identity and survivorship.} The panel spans \DataTickers{} tickers47forming \DataSpells{} continuous spells (a gap exceeding 30 calendar days48starts a new spell); \DataMultiSpellTickers{} tickers have multiple spells, so49all long-horizon statements operate within spells. Delisted securities are50present throughout (exits run 800--1,600 per year); the single discrete51coverage expansion (2020, over-the-counter names) is absorbed by fixed-rule52lagged universes.5354\paragraph{Corporate actions.} A conservative overnight-ratio screen55(canonical ratios $\{2,\dots,8,10,20,3/2\}$ and inverses, $\pm1.5\%$56tolerance, both-day dollar volume $\ge \$50{,}000$, prior close $\ge \$1$)57detects \NSplitEvents{} events (\NSplitFwd{} splits, \NSplitRev{} reverse58splits); event days $\pm1$ trading day are excluded from every return-based59statistic.6061\section{Additional descriptive evidence}62\label{app:descriptive}6364Figures~\ref{fig:app_survivorship}--\ref{fig:app_splits} complement the65descriptive results of the main text: universe entry/exit dynamics, dollar66volume concentration, the cross-section of realized volatility, the67stale-price share, and the time series of detected corporate-action events.68Table~\ref{tab:summary_by_decade} reports decade-level summary statistics for69the top-1000 universe.7071\begin{figure}[h]72\centering73\includegraphics[width=\textwidth]{figE2_survivorship.pdf}74\caption{\textbf{Universe dynamics.} (a) Active symbols per year; (b) entries75and exits. The shaded band marks the 2020 source-coverage expansion.}76\label{fig:app_survivorship}77\end{figure}7879\begin{figure}[h]80\centering81\includegraphics[width=\textwidth]{figE4_concentration.pdf}82\caption{\textbf{Concentration of trading.} (a) Share of aggregate dollar83volume of the top 1\% and 5\% of symbols; (b) Herfindahl index of dollar84volume.}85\label{fig:app_concentration}86\end{figure}8788\begin{figure}[h]89\centering90\includegraphics[width=.6\textwidth]{figE6_rv.pdf}91\caption{\textbf{Cross-section of realized volatility.} Median, interquartile92range, and 95th percentile of daily 5-minute realized volatility, lagged93top-1000 universe.}94\label{fig:app_rv}95\end{figure}9697\begin{figure}[h]98\centering99\includegraphics[width=.6\textwidth]{figE7_staleness.pdf}100\caption{\textbf{Stale-price share.} Percentage of one-minute returns exactly101zero, lagged top-1000 universe.}102\label{fig:app_staleness}103\end{figure}104105\begin{figure}[h]106\centering107\includegraphics[width=.6\textwidth]{figE9_splits.pdf}108\caption{\textbf{Detected corporate-action events per year.} Forward splits109(up) and reverse splits (down) from the overnight-ratio screen.}110\label{fig:app_splits}111\end{figure}112113\input{tables/table2_summary_by_decade}114115\clearpage116\section{Additional propagation results}117\label{app:propagation}118119Figure~\ref{fig:app_evolution} shows the year-by-year evolution of abnormal120market-wide breadth at $h=5$ and $h=30$ with 95\% day-block bootstrap bands:121the market-wide null holds in essentially every year, not merely on average.122Figure~\ref{fig:app_pilot} reproduces the pilot-sample intraday seasonality123used in the initial data audit.124125\begin{figure}[h]126\centering127\includegraphics[width=.62\textwidth]{figF2_evolution.pdf}128\caption{\textbf{Evolution of abnormal market-wide propagation.}129$\Delta\Delta$ breadth by year at $h=5$ and $h=30$ minutes, with 95\%130day-block bootstrap intervals.}131\label{fig:app_evolution}132\end{figure}133134\begin{figure}[h]135\centering136\includegraphics[width=\textwidth]{figP2_seasonality.pdf}137\caption{\textbf{Pilot-sample intraday seasonality} (June 1992, June 2009,138December 2025; top-500 by within-month dollar volume).}139\label{fig:app_pilot}140\end{figure}141142\input{tables/tabP1_pilot_summary}143144\clearpage145\section{Computational details and reproducibility}146\label{app:compute}147148The pipeline is deterministic end-to-end. All parameters live in versioned149configuration files; the global seed (20260713) governs placebo draws and150bootstrap resampling; every table and figure is generated by a numbered151script from machine-readable intermediate results, and every numerical claim152in the manuscript resolves to a macro generated from those results---no153number is typed by hand. The full run comprises: download and checksum154verification (411 files); per-month integrity audit and daily metadata155construction; clean-panel construction (duplicate resolution, session156labelling with true exchange closes, integrity and corporate-action flags);157universe construction with strictly lagged screens; descriptive aggregation;158shock detection and outcome measurement (\NEventsReal{} events,159\NEventsPlacebo{} placebos); network and co-jump measurement; and estimation.160End-to-end wall-clock time is approximately six hours on a single161consumer-grade machine (Apple Silicon, 4 parallel workers); peak memory is162below 8~GB per worker because every stage operates month-by-month on163partitioned columnar files.164165\end{document}166