1\section{Mechanisms and pricing}2\label{sec:mechanisms}34\subsection{Where would one-minute information live? (H3)}56The pre-registered heterogeneity hypothesis holds that if fine-grained activity carries incremental information, it7should do so where information asymmetry and processing frictions are largest: small, illiquid and highly levered8firms. Table~\ref{tab:subgroups} and Figure~\ref{fig:heterogeneity} split the test period along these ex-ante terciles9(cut-points from training rows), by profitability, release timing, sector, bar density, and by whether the 20-day window10straddles the previous release. In no subgroup does the 1-minute set improve on the daily benchmark. The ordering is11nevertheless informative: the deterioration is smallest and statistically indistinguishable from zero for small,12illiquid and loss-making firms (\emph{e.g.}, small firms: within $\pm0.002$ of zero), and largest for large, liquid and13profitable firms, where the extra features add noise to an already accurate forecast. The sign of the H3 ordering is14therefore the one predicted by frictions, but the level is zero: the groups in which intraday activity would be most15informative are also those in which it is not informative \emph{enough} to help.1617\begin{table}[H]18\centering\footnotesize19\caption{The 1-minute increment by pre-specified subgroup (LightGBM, test period, $h=20$)}20\label{tab:subgroups}21\adjustbox{max width=\textwidth}{\input{tables/tab07b_subgroups}}22\begin{minipage}{\textwidth}\vspace{0.3em}\footnotesize23\emph{Notes.} Terciles of log market capitalisation, Amihud illiquidity and debt-to-assets are formed on training rows.24``Window straddles previous release'': the 20-session feature window contains $A_{q-1}$. ``Dense bars'': at least2598\% of expected 1-minute bars present. 95\% block-bootstrap CIs over calendar quarters; 2020 is in the validation26period and therefore absent from the test subgroups.27\end{minipage}28\end{table}2930\begin{figure}[H]31\centering32\includegraphics[width=0.9\textwidth]{figures/fig07_heterogeneity.pdf}33\caption{Change in test log loss from adding 1-minute families to the daily-and-accounting benchmark, by subgroup34(LightGBM). Negative values would indicate a gain.}35\label{fig:heterogeneity}36\end{figure}3738The panel regressions of Table~\ref{tab:panel} use the out-of-fold Latent Fundamental Deterioration Signal from the39expanding-window refits. The daily-benchmark signal $\LFDS^{\mathrm{B2}}$ is a powerful predictor of the40realised surprise with firm and sector-by-quarter fixed effects ($\beta=\panSonlfdsTwoanddlfdslfdsTwo$,41$t=\pantSonlfdsTwoanddlfdslfdsTwo$, two-way clustered): a one-point increase in the predicted probability of an adverse42quarter is associated with a surprise lower by 7.6\% of assets. The \emph{incremental} 1-minute component43$\LFDS^{\mathrm{B5}}-\LFDS^{\mathrm{B2}}$ has a coefficient of \panSonlfdsTwoanddlfdsdlfds{}44($t=\pantSonlfdsTwoanddlfdsdlfds$), one sixth of the benchmark's and marginal at conventional levels. Its interactions45with ex-ante terciles point in the direction \emph{opposite} to H3: the incremental component is less informative for46the smallest firms ($t=\pantdlfdsxsizedlfdsxsizeZero$ on the bottom-tercile interaction) and for the least levered47firms ($t=\pantdlfdsxlevdlfdsxlevZero$), and does not vary with illiquidity. Whatever small amount of information the481-minute features add is concentrated in large, levered firms, consistent with fine-grained activity reflecting the49trading of well-informed participants in liquid names rather than the slow processing of information in neglected ones;50in the forecasting exercise this amount is not large enough to survive the noise the features bring.5152\begin{table}[H]53\centering\footnotesize54\caption{Panel regressions of the realised surprise on out-of-fold deterioration signals}55\label{tab:panel}56\adjustbox{max width=\textwidth}{\input{tables/tab06_panel}}57\begin{minipage}{\textwidth}\vspace{0.3em}\footnotesize58\emph{Notes.} Dependent variable: $S_{i,q}$ winsorised at 1/99\% (specifications ``S\_on''), or the binary adverse outcome59(``y\_on''). $\mathrm{lfds2}$, $\mathrm{lfds5}$: out-of-fold predicted probabilities from LB2 and LB5 (expanding-window60annual refits, 2016--2026); $\mathrm{d\_lfds}=\mathrm{lfds5}-\mathrm{lfds2}$; interactions with within-quarter terciles61(0 = bottom, 2 = top). Controls: ROA, leverage, log market cap, 20-day return and volatility, last and mean surprise.62Firm and sector$\times$calendar-quarter fixed effects; standard errors two-way clustered by firm and calendar quarter.63$^{*}$, $^{**}$, $^{***}$: 10, 5, 1\%.64\end{minipage}65\end{table}6667\subsection{Is the signal in prices? (H5)}6869If the deterioration probability were news to the market, firms with a high ex-ante probability should experience70negative abnormal returns between the cutoff and the day after the release. Appendix Table~\ref{app:tables} shows that71the market-adjusted return from $c+1$ to $A_q+1$ is unrelated to $\LFDS^{\mathrm{B5}}$72($\beta=\carcaronlfdsFivelfdsFive$, $t=\cartcaronlfdsFivelfdsFive$) and to the daily benchmark signal: by the cutoff,73twenty trading days before the release, the information that the models extract is already in prices. The incremental741-minute component carries a positive coefficient ($\carcaronlfdsTwodlfdsdlfds$, $t=\cartcaronlfdsTwodlfdsdlfds$),75i.e., firms whose 1-minute features push the probability \emph{up} relative to daily data earn slightly \emph{higher}76announcement-window returns, the opposite of a deterioration signal; we read this as a partial reversal of recent77intraday selling pressure rather than as information, and note that it is one of several H5 tests.7879The secondary portfolio exercise confirms the absence of economic value (Table~\ref{tab:economic},80Figure~\ref{fig:economic}). Month-end decile sorts on the out-of-fold calendar-design scores, with positions taken at the81close of the following session and held one month, produce long-minus-short (low minus high deterioration probability)82FF5+momentum alphas of \alphaLBFivegross\% per month ($t=\alphatLBFivegross$) gross and \alphaLBFivenet\% net of8320 basis points per side for the 1-minute scores, and \alphaLBTwogross\% ($t=\alphatLBTwogross$) for the daily84scores; mean returns \emph{rise} with the deterioration decile, as expected if high-probability firms are small,85volatile and compensated for risk. A forecastable accounting deterioration is therefore not a tradable anomaly in86this sample, at any sampling frequency.8788\begin{table}[H]89\centering\footnotesize90\caption{Economic value: monthly decile portfolios on the ex-ante deterioration score, 2016--2026}91\label{tab:economic}92\adjustbox{max width=\textwidth}{\input{tables/tab11_economic}}93\begin{minipage}{\textwidth}\vspace{0.3em}\footnotesize94\emph{Notes.} Long decile 1 (lowest score), short decile 10; equal weights; entry at the close of the session after the95month-end cutoff, exit at the close of the session after the next cutoff; turnover is one-way; net returns deduct9620 bps per side. Alphas from a regression on FF5 and momentum factors compounded over the same holding windows, HAC97standard errors.98\end{minipage}99\end{table}100101\begin{figure}[H]102\centering103\includegraphics[width=0.6\textwidth]{figures/fig09_economic.pdf}104\caption{Mean monthly return by decile of the 1-minute deterioration score.}105\label{fig:economic}106\end{figure}107