spb/wp17_uqo

1% ============================================================================2\section{Results}3\label{sec:results}4% ============================================================================56\subsection{Portfolio sorts: a weak unconditional relation}7Table~\ref{tab:sorts} reports the quintile sorts over the full sample of fifteen formation years.8The relation between AI language and future returns is positive and broadly monotone but modest.9The equal-weighted Q5$-$Q1 spread is $+4.6$ percentage points per year for AI adoption10\tstat{1.83}, $+3.9$ for AI infrastructure \tstat{1.58}, $+5.3$ for AI disruption risk11\tstat{2.27}, and $+4.9$ for the composite \tstat{1.88}. Value-weighting attenuates the adoption12and composite spreads, indicating that the relation is stronger among smaller index members. The13left panel of Figure~\ref{fig:quint} displays the full-sample pattern: returns rise gently from the14lowest to the highest AI quintile. By the standards of \citet{harveyliuzhu2016}, none of these15spreads would qualify as a discovery, and the averages blend two very different sub-periods.1617\input{tables/tab_sorts}1819\subsection{Does AI language earn risk-adjusted alpha unconditionally? (H1)}20Table~\ref{tab:alpha} reports CAPM and FF6 alphas of the monthly long--short portfolios over the21178 months for which the French factors are available. The composite earns a raw spread of about22$+2.3\%$ per year, of which the FF6 alpha is $+1.9\%$ and statistically insignificant23\tstat{1.24}. The adoption and infrastructure long--shorts are similarly insignificant. The one24exception is the disruption-risk spread, whose FF6 alpha of $+2.8\%$ per year is marginally25significant \tstat{2.10}. The factor loadings show that the long--shorts are roughly26market-neutral, with modest negative profitability (RMW) and investment (CMA) tilts consistent with27a growth-oriented long leg. Panel~C of Table~\ref{tab:postinf}, discussed below, adds the28technology-sector factor: its loading is 0.35 \tstat{11.1} and the full-sample FF6 alpha of the29composite falls to $+0.4\%$ per year \tstat{0.36}. The verdict on H1 is clear: unconditionally, AI30language is at best weakly priced, and what premium there is resembles a technology-sector tilt.3132\input{tables/tab_alpha}3334\subsection{Panel and Fama--MacBeth estimates}35Table~\ref{tab:panel} juxtaposes the two-way fixed-effects panel of equation~\eqref{eq:panel} with36the Fama--MacBeth estimator of equation~\eqref{eq:fm}. In the Fama--MacBeth regressions the AI37adoption and infrastructure premia are positive---$+1.3$ and $+1.6$ percentage points per standard38deviation when entered separately---with $t$-statistics of 1.5--1.6, a weak cross-sectional39premium on average; when the three collinear signals are entered jointly, only infrastructure40retains a positive coefficient. In the two-way fixed-effects panel every AI coefficient is41indistinguishable from zero. Because firm fixed effects remove permanent cross-firm differences,42the signal lives across firms, not within them: a given firm whose filings resemble the AI anchors43more closely from one year to the next does not earn a higher subsequent return. Throughout, size44carries a negative premium ($t\approx-8$) and volatility a positive one.4546\input{tables/tab_panel}4748\subsection{The post-ChatGPT change: large on average, concentrated in one cohort (H2)}49\label{subsec:break}50Splitting the sample at the ChatGPT launch, the centre and right panels of Figure~\ref{fig:quint}51show two different pictures. Before 2022 the relation between AI quintile and forward return is52nearly flat; after 2022 the schedule tilts upward, and the composite Q5$-$Q1 spread rises from53$+2.5$ percentage points per year to $+14.6$. Table~\ref{tab:break} quantifies the change for each54signal. In sub-period sorts the adoption spread rises from $+2.2\%$ to $+14.3\%$, the composite55from $+2.5\%$ to $+14.6\%$, and infrastructure from $+1.4\%$ to $+13.6\%$. In the pooled56interaction regressions of equation~\eqref{eq:break} the post-2022 increment is positive for all57three signals, between $+2.0$ and $+2.8$ percentage points per standard deviation, and58statistically significant only for AI infrastructure \tstat{2.63}, the facet most directly tied to59the chip, cloud, data-centre, and power firms that led the 2023--2025 rally.6061\begin{figure}[htbp]\centering62\includegraphics[width=\textwidth]{fig1_quintile_returns.png}63\caption{\textbf{Forward returns by AI-language quintile, before and after ChatGPT.} Each panel64plots the mean forward twelve-month return across quintiles of the AI composite: the left panel65pools the full sample, the centre panel the pre-ChatGPT formation years (2010--2021), and the right66panel the post-ChatGPT formation years (2022--2024). The Q5$-$Q1 spread rises from $+2.5$67percentage points per year before ChatGPT to $+14.6$ after; the post-period average rests on three68cohorts and is dominated by the 2024 cohort (Table~\ref{tab:postinf}).}\label{fig:quint}69\end{figure}7071\input{tables/tab_break}7273The Newey--West $t$-statistics of Table~\ref{tab:break} are computed on three post-period74observations and carry little information. Table~\ref{tab:postinf} asks directly how much evidence75the post-period contains. Panel~A lists the three post-launch cohorts: the 2022 cohort (held from76July 2023 to June 2024) earned a composite spread of $+9.3$ points, the 2023 cohort $-4.0$, and the772024 cohort (held from July 2025 to June 2026) $+38.4$. Two pre-launch cohorts, 2012 and 2015,78earned more than the 2022 cohort, and nine of the twelve pre-launch spreads are positive. The79post-period average therefore owes its size to a single cohort: dropping 2024 leaves a post-period80mean of $+2.6$ points, essentially the pre-period value of $+2.4$, whereas dropping either of the81other two cohorts raises the mean. Figure~\ref{fig:spread}, which plots the annual spreads, makes82the same point visually; the first version of this paper described the post-2022 cohorts as83``uniformly and substantially positive,'' which the figure does not support.8485\begin{figure}[htbp]\centering86\includegraphics[width=0.9\textwidth]{fig3_annual_spread.png}87\caption{\textbf{Annual AI-language return spreads by cohort.} The figure plots the annual88high-minus-low (Q5$-$Q1) forward-return spread on the AI composite by formation year (the filing89year of the signal). Spreads are of mixed sign through 2021; among the post-ChatGPT cohorts (in90red) the 2022 spread is positive, the 2023 spread negative, and the 2024 spread, whose holding91period is July 2025--June 2026, far larger than any other. The post-period average of92Table~\ref{tab:break} is driven by the 2024 cohort.}93\label{fig:spread}94\end{figure}9596Panel~B of Table~\ref{tab:postinf} pools the firm-years in the top and bottom quintiles of the three97post-launch cohorts and regresses the forward return on a top-quintile indicator with year dummies98and standard errors clustered by firm. The post-period spread is $+14.7$ points \tstat{2.18} on raw99returns but $+7.2$ points \tstat{2.21} on returns winsorized at the first and ninety-ninth100percentiles: half of the raw spread comes from a handful of extreme winners in the top quintile of101the 2024 cohort, among them Western Digital ($+969\%$), Micron ($+730\%$), and Seagate ($+624\%$),102the memory and storage manufacturers whose prices rose with AI-related demand in 2025--2026.103Restricting the pooled test to the 2022 and 2023 cohorts gives $+2.6$ points \tstat{0.46}, and the104difference between the post- and pre-period spreads in the pooled sample is $+12.1$ points105\tstat{1.79}. Panel~C turns to the monthly long--short series, which has 36 post-period106observations. The composite portfolio earned 7.5\% per year after July 2023 with an annualized107Sharpe ratio of 1.32 and a HAC $t$-statistic of 2.20, against 1.1\% per year and a Sharpe ratio108of 0.22 before; its FF6 alpha is $+5.2\%$ per year \tstat{1.72}. The monthly mean is about half109the annual spread because the monthly portfolio rebalances equal weights every month, which caps110the contribution of stocks that multiply in value within the year, whereas the annual buy-and-hold111spread lets them run. Adding the technology-sector factor, on which the post-period loading is 0.47112\tstat{6.53}, reduces the alpha to $+1.9\%$ per year \tstat{0.86}. The monthly evidence thus113supports a post-2022 increase in the return to AI language that is statistically detectable, but114it is largely spanned by the technology sector's own outperformance over the same months, which115averaged 15.8\% per year in our equal-weighted sector factor.116117\input{tables/tab_postinference}118119Two further lenses show the same regime change and the same concentration. Figure~\ref{fig:cum}120plots the cumulative value of one dollar in the equal-weighted, annually rebalanced long--short121portfolio: it drifts sideways for a decade and rises after the dashed ChatGPT line, with most of122the rise in the last year. Figure~\ref{fig:fmyear} plots the year-by-year Fama--MacBeth slope on123the composite with controls: it fluctuates around zero through 2021, is positive in 2022124($+2.9$ points per standard deviation), negative in 2023 ($-1.1$), and large in 2024 ($+14.3$).125With sector dummies (Table~\ref{tab:reviewrobust}, Panel~D) the 2024 slope falls to $+10.2$ and the126post-period average from $+5.5$ \tstat{2.00} to $+2.9$ \tstat{1.36}.127128\begin{figure}[htbp]\centering129\includegraphics[width=0.86\textwidth]{fig2_cumulative_ls.png}130\caption{\textbf{Cumulative performance of the AI long--short portfolio.} The figure plots the131cumulative value of \$1 invested in the equal-weighted, annually rebalanced, self-financing132high-minus-low portfolio, for the AI composite and the AI disruption-risk signal. Both curves drift133sideways for a decade and rise after the dashed ChatGPT line, with most of the increase during the134holding period of the 2024 cohort.}135\label{fig:cum}136\end{figure}137138\begin{figure}[htbp]\centering139\includegraphics[width=0.9\textwidth]{fig6_fm_byyear.png}140\caption{\textbf{Year-by-year Fama--MacBeth slopes on the AI composite.} The figure plots the141annual cross-sectional slope on the composite---the forward return per cross-sectional standard142deviation---controlling for size, momentum, and volatility, with error bars of $\pm1$ standard143error (heteroskedasticity-robust, within year). The slope fluctuates around zero through 2021 and144is large only in the 2024 cohort.}\label{fig:fmyear}145\end{figure}146147Figure~\ref{fig:bin} shows that, within the post-period, the relation is not confined to the148extreme quintiles: the binned relation between the composite and forward returns is flat before149ChatGPT and upward-sloping afterward across the distribution of the signal. The binned means are150averages over the three post-period cohorts, so the slope inherits the weight of the 2024 cohort.151152\begin{figure}[htbp]\centering153\includegraphics[width=\textwidth]{fig5_binscatter.png}154\caption{\textbf{Binned relation between AI language and returns, by sub-period.} Binned scatter of155the forward twelve-month return against the AI composite, separately for the pre- and post-ChatGPT156formation years. Each point is the mean within a bin of the signal and the line is an OLS fit. The157relation is flat before ChatGPT and upward-sloping afterward across the distribution of the signal;158the post-period bins average the 2022--2024 cohorts.}\label{fig:bin}159\end{figure}160161\subsection{The anatomy of the post-period spread: size and sector}162Where in the cross-section does the post-2022 spread concentrate? Table~\ref{tab:doublesort} and163Figure~\ref{fig:double} report an AI~$\times$~size double sort. Before 2022 the AI gradient is flat164within both size halves. After 2022 it is steep, and markedly so among smaller firms: small,165high-AI firms earned a mean forward return of 34.6\%, against 19.5\% for small, low-AI firms, a16615-point gap, while the gap among large firms is 7 points. The post-period spread is thus not a167mega-cap phenomenon, a point reinforced in Section~\ref{sec:robustness}; it is strongest among the168smaller, less-followed index members, which is consistent with an attention-based mechanism but169also with the fact that the memory and storage manufacturers of the 2024 cohort were mid-sized170index members at formation.171172\input{tables/tab_doublesort}173174\begin{figure}[htbp]\centering175\includegraphics[width=\textwidth]{fig9_double_sort.png}176\caption{\textbf{AI language $\times$ firm-size double sort.} Mean forward twelve-month return by AI177tercile within small and large firms, separately for the pre- and post-ChatGPT formation years. The178post-2022 AI gradient is steeper among small firms, where high-AI firms outperform low-AI firms by179about 15 percentage points; the post-period cells average three cohorts.}\label{fig:double}180\end{figure}181182\subsection{Economic significance}183The Sharpe ratio of the equal-weighted composite long--short portfolio rises from 0.22 in the184pre-ChatGPT period to 1.32 afterward (Table~\ref{tab:postinf}, Panel~C); for the disruption-risk185spread it rises from 0.41 to 1.09. The broad U.S.\ equity market has historically delivered a186Sharpe ratio in the neighbourhood of 0.4, so a value above one for a single-characteristic187strategy is large. Three qualifications keep the magnitude in proportion. First, the ratio is188estimated on 36 months and its standard error is roughly $1/\sqrt{3}\approx0.58$ in annual units,189so it is distinguishable from the pre-period value but not precisely measured. Second, the190portfolio's post-period return is largely explained by its technology-sector loading, so the191Sharpe ratio is in part that of a sector bet during a sector boom. Third, the annual spreads that192produce the ``$+14.6$ points per year'' headline are dominated by one cohort and by extreme193winners within it; the winsorized pooled spread of $+7.2$ points is the better summary of what a194typical top-quintile firm earned over a typical bottom-quintile firm. The first version of this195paper described the post-2022 re-rating as ``among the largest single-theme cross-sectional effects196in the recent asset-pricing record''; the evidence supports a weaker statement, namely that AI197language, which was unrelated to returns for a decade, became strongly related to them in the1982024 cohort and modestly related in the 2022 cohort.199