spb/wp17_uqo

1\begin{table}[H]\centering2\caption{Event-Study Inference under Cross-Sectional Dependence}\label{tab:eventcda}3\small4\begin{tabular}{lrrrr}\toprule5& High$-$Low CAR & Welch \textit{t} & Portfolio \textit{t} & Portfolio \textit{t} \\6Horizon & (\%) & (independence) & (estimation-window SD) & (event-window SD) \\\midrule7+60 trading days & +2.93 & 1.77 & 1.35 & 1.54 \\8+6 months & +4.53 & 1.60 & 1.45 & 1.65 \\9+1 year & +10.08 & 1.97 & 2.28 & 2.60 \\10+18 months & +14.59 & 1.89 & 2.63 & 2.99 \\11\bottomrule12\end{tabular}13\tablelegend{All firms share the same event date, so firm-level abnormal returns are cross-sectionally correlated and the Welch $t$-test of Table~\ref{tab:event}, which treats the 160 High and 162 Low firms as independent draws, overstates precision: the average pairwise correlation of market-model residuals over the January--October 2022 estimation window is $\bar\rho=0.039$, and the deflation factor of Kolari and Pynn\"onen (2010) for a one-sample test, $\sqrt{(1-\bar\rho)/(1+(n-1)\bar\rho)}$, equals 0.27. The portfolio tests sidestep the problem by treating the daily High-minus-Low abnormal return as a single time series: its cumulative value over $T$ event days is divided by $\hat\sigma\sqrt{T}$, where $\hat\sigma$ is the daily standard deviation of the same portfolio series either in the estimation window (crude dependence adjustment of Brown and Warner, 1985; $\hat\sigma=0.279\%$) or in the event window itself (0.245\%). Source: \texttt{scripts/11\_review\_reanalysis.py}.}14\end{table}