spb/phd_thesis

Three article chapters (speculative trading & macro surprises; ETF iNAV
volatility transmission; FOMC tone & novelty) plus the assembled
Université Laval thesis document (these-ulaval/), with a full README.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

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	1	+# macOS
	2	+.DS_Store
	3	+
	4	+# Claude Code local settings
	5	+.claude/
	6	+
	7	+# Archive duplicate of these-ulaval/
	8	+these-ulaval.zip
	9	+
	10	+# LaTeX build artifacts (PDFs and .bbl are kept)
	11	+*.aux
	12	+*.log
	13	+*.blg
	14	+*.out
	15	+*.toc
	16	+*.lof
	17	+*.lot
	18	+*.fls
	19	+*.fdb_latexmk
	20	+*.synctex.gz

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	1	+.output
	2	+.log
	3	+.tmp

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	1	+name: PHD_chapitre3_theses_20260417

added PHD_chapitre3_theses_20260731/appendices/appendix_additional.tex +116 −0

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	1	+\section{Additional Tables and Figures}
	2	+\label{sec:app_additional}
	3	+
	4	+This appendix collects supplementary tables and figures that support the main results but are not essential for following the core argument.
	5	+
	6	+\subsection{Descriptive Figures}
	7	+
	8	+\begin{figure}[H]
	9	+\centering
	10	+\includegraphics[width=0.85\textwidth]{figures/figD1_return_density.pdf}
	11	+\caption{Distribution of 1-minute log returns on FOMC days. Winsorized at 0.5\% tails for display. The heavy tails and leptokurtic shape are consistent with the Jarque--Bera test rejections reported in Table~\ref{tab:desc_1min_ret}.}
	12	+\label{fig:D1}
	13	+\end{figure}
	14	+
	15	+\begin{figure}[H]
	16	+\centering
	17	+\includegraphics[width=0.85\textwidth]{figures/figD5_acf_returns.pdf}
	18	+\caption{Autocorrelation of 1-minute returns. Grey band shows 95\% confidence interval. Negative first-order autocorrelation reflects bid--ask bounce effects typical of high-frequency data.}
	19	+\label{fig:D5}
	20	+\end{figure}
	21	+
	22	+\begin{figure}[H]
	23	+\centering
	24	+\includegraphics[width=0.85\textwidth]{figures/figD8b_log_rv_distribution.pdf}
	25	+\caption{Distribution of $\log(\mathrm{RV})$. Near-Gaussian shape validates the use of $\log(\mathrm{RV})$ as the dependent variable in the panel regressions.}
	26	+\label{fig:D8b}
	27	+\end{figure}
	28	+
	29	+\subsection{Ensemble Model Diagnostics}
	30	+
	31	+\begin{figure}[H]
	32	+\centering
	33	+\includegraphics[width=0.6\textwidth]{figures/pca_axis_quality.png}
	34	+\caption{PCA axis assignment quality. Bar height shows $|\text{Corr}|$ between PC projection and keyword differential. All axes exceed the 0.04 minimum separation threshold.}
	35	+\label{fig:pca_quality}
	36	+\end{figure}
	37	+
	38	+\begin{figure}[H]
	39	+\centering
	40	+\begin{subfigure}[b]{0.48\textwidth}
	41	+\includegraphics[width=\textwidth]{figures/novelty_comparison.png}
	42	+\caption{Novelty: MiniLM vs BERT}
	43	+\end{subfigure}
	44	+\hfill
	45	+\begin{subfigure}[b]{0.48\textwidth}
	46	+\includegraphics[width=\textwidth]{figures/scatter_comparison.png}
	47	+\caption{Score scatter plots}
	48	+\end{subfigure}
	49	+\caption{Model comparison: MiniLM (384d) vs.\ BERT (768d). Novelty correlation $r = 0.72$; policy stance tone $r = 0.56$. The moderate inter-model correlation supports the use of an ensemble approach.}
	50	+\label{fig:model_comparison}
	51	+\end{figure}
	52	+
	53	+\begin{figure}[H]
	54	+\centering
	55	+\begin{subfigure}[b]{0.48\textwidth}
	56	+\includegraphics[width=\textwidth]{figures/tone_comparison.png}
	57	+\caption{Tone comparison across models}
	58	+\end{subfigure}
	59	+\hfill
	60	+\begin{subfigure}[b]{0.48\textwidth}
	61	+\includegraphics[width=\textwidth]{figures/confidence_distribution.png}
	62	+\caption{Ensemble confidence distribution}
	63	+\end{subfigure}
	64	+\caption{Tone model comparison and confidence diagnostics. The right panel shows that ensemble confidence is concentrated above 0.7, indicating strong inter-model agreement for most statements.}
	65	+\label{fig:tone_conf}
	66	+\end{figure}
	67	+
	68	+\subsection{Additional Panel Regression Tables}
	69	+
	70	+Tables~\ref{tab:panel_rv_stance}--\ref{tab:panel_return_novelty} report panel minute-level regressions for the remaining dependent variables (realized volatility in levels, realized beta, and returns), separately for stance and novelty.
	71	+
	72	+\input{tables/tableP_panel_rv_stance.tex}
	73	+\input{tables/tableP_panel_rv_novelty.tex}
	74	+\input{tables/tableP_panel_beta_stance.tex}
	75	+\input{tables/tableP_panel_beta_novelty.tex}
	76	+\input{tables/tableP_panel_return_stance.tex}
	77	+\input{tables/tableP_panel_return_novelty.tex}
	78	+
	79	+\subsection{Additional Event-Level Regression Tables}
	80	+
	81	+Tables~\ref{tab:rolling_rv_ratio_30min} and~\ref{tab:rolling_log_rv_ratio_30min} report the event-level RV-ratio specifications, which corroborate the pre/post difference results in the main text.
	82	+
	83	+\input{tables/tableR_rv_ratio_30min.tex}
	84	+\input{tables/tableR_log_rv_ratio_30min.tex}
	85	+
	86	+\subsection{Additional IRF and Drift Figures}
	87	+
	88	+\begin{figure}[H]
	89	+\centering
	90	+\includegraphics[width=0.85\textwidth]{figures/figR9_drift_by_novelty.pdf}
	91	+\caption{Cumulative return drift by novelty tercile. Unlike stance-based drift (Figure~\ref{fig:R8}), novelty terciles show less directional separation, consistent with novelty affecting volatility rather than returns.}
	92	+\label{fig:R9}
	93	+\end{figure}
	94	+
	95	+\begin{figure}[H]
	96	+\centering
	97	+\includegraphics[width=0.85\textwidth]{figures/figR10_irf_ret_h_novelty.pdf}
	98	+\caption{Impulse response: cumulative return to novelty. Effects are generally smaller and less significant than stance effects (Figure~\ref{fig:R10_stance}), supporting the hypothesis that novelty operates through volatility rather than returns.}
	99	+\label{fig:R10_novelty}
	100	+\end{figure}
	101	+
	102	+\begin{figure}[H]
	103	+\centering
	104	+\includegraphics[width=0.85\textwidth]{figures/figR10b_irf_placebo_novelty.pdf}
	105	+\caption{Pre-announcement placebo: IRF for novelty. All coefficients are near zero, corroborating the placebo results for stance (Figure~\ref{fig:placebo_stance}).}
	106	+\label{fig:placebo_novelty}
	107	+\end{figure}
	108	+
	109	+\subsection{Sub-Period Stability}
	110	+
	111	+\begin{figure}[H]
	112	+\centering
	113	+\includegraphics[width=0.85\textwidth]{figures/figRob_subperiod_heatmap.pdf}
	114	+\caption{Sub-period stability: regression coefficients across six Fed policy regimes. Coefficient signs are generally consistent across sub-periods, though magnitudes vary with the degree of policy uncertainty in each regime.}
	115	+\label{fig:rob_subperiod}
	116	+\end{figure}

added PHD_chapitre3_theses_20260731/appendices/appendix_proofs.tex +105 −0

		@@ -0,0 +1,105 @@
	1	+\section{Mathematical Proofs}
	2	+\label{sec:proofs}
	3	+
	4	+This appendix provides formal mathematical derivations for the key theoretical relationships presented in Section~\ref{sec:methodology}.
	5	+
	6	+\subsection{Derivation of Pure Stance Definitions}
	7	+
	8	+\begin{theorem}[Pure Stance Characterization]
	9	+The pure dovish and hawkish stance measures satisfy the relationships given in Definition~\ref{def:pure_stances}.
	10	+\end{theorem}
	11	+
	12	+\begin{proof}
	13	+\textbf{Case 1: Pure Dovish Statement.} Assume the Federal Reserve releases a statement that exactly matches the dovish counterfactual: $F_t = F_t^D$.
	14	+
	15	+The tone measure becomes:
	16	+\begin{align}
	17	+\text{Tone}_t &= \frac{\text{sim}(F_t, F_t^H) - \text{sim}(F_t, F_t^D)}{1 - \text{sim}(F_t^D, F_t^H)} \notag \\
	18	+&= \frac{\text{sim}(F_t^D, F_t^H) - \text{sim}(F_t^D, F_t^D)}{1 - \text{sim}(F_t^D, F_t^H)} \notag \\
	19	+&= \frac{\text{sim}(F_t^D, F_t^H) - 1}{1 - \text{sim}(F_t^D, F_t^H)} \notag \\
	20	+&= -1
	21	+\end{align}
	22	+
	23	+The novelty measure is:
	24	+\begin{equation}
	25	+\text{Novelty}_t = 1 - \text{sim}(F_t, F_{t-1}) = 1 - \text{sim}(F_t^D, F_{t-1})
	26	+\end{equation}
	27	+
	28	+Therefore, the stance measure is:
	29	+\begin{align}
	30	+\text{Stance}_t &= \text{Novelty}_t \times \text{Tone}_t \notag \\
	31	+&= \left(1 - \text{sim}(F_t^D, F_{t-1})\right) \times (-1) \notag \\
	32	+&= -\left(1 - \text{sim}(F_t^D, F_{t-1})\right) \notag \\
	33	+&= \text{Stance}_t^{dove}
	34	+\end{align}
	35	+
	36	+\textbf{Case 2: Pure Hawkish Statement.} Assume $F_t = F_t^H$:
	37	+
	38	+The tone measure becomes:
	39	+\begin{align}
	40	+\text{Tone}_t &= \frac{\text{sim}(F_t^H, F_t^H) - \text{sim}(F_t^H, F_t^D)}{1 - \text{sim}(F_t^D, F_t^H)} \notag \\
	41	+&= \frac{1 - \text{sim}(F_t^H, F_t^D)}{1 - \text{sim}(F_t^D, F_t^H)} \notag \\
	42	+&= 1
	43	+\end{align}
	44	+
	45	+Therefore:
	46	+\begin{align}
	47	+\text{Stance}_t &= \left(1 - \text{sim}(F_t^H, F_{t-1})\right) \times 1 = \text{Stance}_t^{hawk}
	48	+\end{align}
	49	+
	50	+This completes the proof. \hfill $\square$
	51	+\end{proof}
	52	+
	53	+\subsection{Derivation of Dovish Weight Parameter}
	54	+
	55	+\begin{theorem}[Dovish Weight Parameter Formula]
	56	+The weight parameter $w_t$ in the weighted stance representation has the form given in Definition~\ref{def:weighted_stance}.
	57	+\end{theorem}
	58	+
	59	+\begin{proof}
	60	+From the weighted stance equation:
	61	+\begin{equation}
	62	+\text{Stance}_t = w_t \cdot \text{Stance}_t^{dove} + (1 - w_t) \cdot \text{Stance}_t^{hawk}
	63	+\end{equation}
	64	+
	65	+Substituting the expressions for pure stances from Theorem 1:
	66	+\begin{align}
	67	+\text{Stance}_t &= -w_t\left(1 - \text{sim}(F_t^D, F_{t-1})\right) + (1 - w_t)\left(1 - \text{sim}(F_t^H, F_{t-1})\right) \notag \\
	68	+&= 1 - 2w_t + w_t\left(\text{sim}(F_t^D, F_{t-1}) + \text{sim}(F_t^H, F_{t-1})\right) - \text{sim}(F_t^H, F_{t-1})
	69	+\end{align}
	70	+
	71	+Collecting the terms in $w_t$, this reads
	72	+\begin{equation}
	73	+\text{Stance}_t = 1 - \text{sim}(F_t^H, F_{t-1}) - w_t\left(2 - \text{sim}(F_t^D, F_{t-1}) - \text{sim}(F_t^H, F_{t-1})\right).
	74	+\end{equation}
	75	+Equating with $\text{Stance}_t = \left(1 - \text{sim}(F_t, F_{t-1})\right) \times \text{Tone}_t$ and solving for $w_t$:
	76	+\begin{equation}
	77	+w_t = \frac{1 - \text{sim}(F_t^H, F_{t-1}) - \left(1 - \text{sim}(F_t, F_{t-1})\right) \times \text{Tone}_t}{2 - \text{sim}(F_t^D, F_{t-1}) - \text{sim}(F_t^H, F_{t-1})}
	78	+\end{equation}
	79	+
	80	+This establishes the formula. \hfill $\square$
	81	+\end{proof}
	82	+
	83	+\subsection{Proof of MPS Decomposition}
	84	+
	85	+\begin{theorem}[Policy Stance Surprise Decomposition]
	86	+The policy stance surprise admits the decomposition given in Proposition~\ref{prop:mps}.
	87	+\end{theorem}
	88	+
	89	+\begin{proof}
	90	+From the definitions:
	91	+\begin{align}
	92	+\text{MPS}_t &= \text{Stance}_t - \mathbb{E}_{t-\Delta}[\text{Stance}_t] \notag \\
	93	+&= \text{Novelty}_t \times \text{Tone}_t - (1 - 2p_{t-\Delta}) \cdot \overline{\text{Novelty}}_{t \mid t-\Delta} \notag \\
	94	+&= \left(\overline{\text{Novelty}}_{t \mid t-\Delta} + \varepsilon_t\right) \times \text{Tone}_t - (1 - 2p_{t-\Delta}) \cdot \overline{\text{Novelty}}_{t \mid t-\Delta} \notag \\
	95	+&= \overline{\text{Novelty}}_{t \mid t-\Delta} \times \text{Tone}_t - \overline{\text{Novelty}}_{t \mid t-\Delta} + 2p_{t-\Delta} \cdot \overline{\text{Novelty}}_{t \mid t-\Delta} + \varepsilon_t \times \text{Tone}_t \notag \\
	96	+&= \overline{\text{Novelty}}_{t \mid t-\Delta}(\text{Tone}_t + 2p_{t-\Delta} - 1) + \text{Tone}_t \cdot \varepsilon_t
	97	+\end{align}
	98	+
	99	+This establishes the decomposition. \hfill $\square$
	100	+\end{proof}
	101	+
	102	+\subsection{Economic Interpretation}
	103	+
	104	+The mathematical results provide several economic insights. First, the pure stance characterization shows that our measures correctly identify extreme policy communications, with dovish statements receiving negative stance values and hawkish statements receiving positive values. Second, the weight parameter derivation reveals how actual policy communications can be understood as weighted averages of extreme alternatives. Third, the MPS decomposition shows that policy surprises have two distinct sources: unexpected tone conditional on expected information content, and unexpected information content weighted by actual tone.
	105	+

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	172	+\newblock Monetary policy surprises and interest rates: Evidence from the fed
	173	+ funds futures market.
	174	+\newblock {\em Journal of Monetary Economics}, 47(3):523--544.
	175	+
	176	+\bibitem[Loughran and McDonald, 2011]{loughran2011}
	177	+Loughran, T. and McDonald, B. (2011).
	178	+\newblock When is a liability not a liability? textual analysis, dictionaries,
	179	+ and 10-ks.
	180	+\newblock {\em Journal of Finance}, 66(1):35--65.
	181	+
	182	+\bibitem[Lucca and Moench, 2015]{lucca2012}
	183	+Lucca, D.~O. and Moench, E. (2015).
	184	+\newblock The pre-fomc announcement drift.
	185	+\newblock {\em Journal of Finance}, 70(1):329--371.
	186	+
	187	+\bibitem[Manela and Moreira, 2017]{manela2017}
	188	+Manela, A. and Moreira, A. (2017).
	189	+\newblock News implied volatility and disaster concerns.
	190	+\newblock {\em Journal of Financial Economics}, 123(1):137--162.
	191	+
	192	+\bibitem[Muth, 1961]{muth1961}
	193	+Muth, J.~F. (1961).
	194	+\newblock Rational expectations and the theory of price movements.
	195	+\newblock {\em Econometrica}, 29(3):315--335.
	196	+
	197	+\bibitem[Nakamura and Steinsson, 2018]{nakamura2018}
	198	+Nakamura, E. and Steinsson, J. (2018).
	199	+\newblock High-frequency identification of monetary non-neutrality: The
	200	+ information effect.
	201	+\newblock {\em Quarterly Journal of Economics}, 133(3):1283--1330.
	202	+
	203	+\bibitem[Patton and Verardo, 2012]{patton2013}
	204	+Patton, A.~J. and Verardo, M. (2012).
	205	+\newblock Why do markets disagree? evidence from variation in opinion.
	206	+\newblock {\em Review of Financial Studies}, 25(12):3734--3773.
	207	+
	208	+\bibitem[Rosa, 2013]{rosa2013}
	209	+Rosa, C. (2013).
	210	+\newblock The high-frequency response of exchange rates and interest rates to
	211	+ macroeconomic announcements.
	212	+\newblock {\em Journal of Banking \& Finance}, 37(6):2162--2174.
	213	+
	214	+\bibitem[Savor and Wilson, 2014]{savor2014}
	215	+Savor, P. and Wilson, M. (2014).
	216	+\newblock Asset pricing: A tale of two days.
	217	+\newblock {\em Journal of Financial Economics}, 113(2):171--201.
	218	+
	219	+\bibitem[Schmeling and Wagner, 2019]{schmeling2019}
	220	+Schmeling, M. and Wagner, C. (2019).
	221	+\newblock Does central bank tone move asset prices?
	222	+\newblock {\em Review of Finance}, 23(5):933--972.
	223	+
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	225	+Shapiro, A.~H., Sudhof, M., and Wilson, D.~J. (2022).
	226	+\newblock Taking the fed at its word: A new approach to estimating central bank
	227	+ objectives using text analysis.
	228	+\newblock {\em Review of Economics and Statistics}, 104(4):768--784.
	229	+
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	231	+Swanson, E.~T. and Williams, J.~C. (2014).
	232	+\newblock Measuring the effect of the zero lower bound on medium- and
	233	+ longer-term interest rates.
	234	+\newblock {\em American Economic Review}, 104(10):3154--3185.
	235	+
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	237	+Veldkamp, L.~L. (2011).
	238	+\newblock {\em Information Choice in Macroeconomics and Finance}.
	239	+\newblock Princeton University Press.
	240	+
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	242	+Wang, K., Reimers, N., and Gurevych, I. (2021).
	243	+\newblock Tsdae: Using transformer-based sequential denoising auto-encoder for
	244	+ unsupervised sentence embedding learning.
	245	+\newblock In {\em Findings of the Association for Computational Linguistics:
	246	+ EMNLP 2021}, pages 671--688.
	247	+
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	249	+Wongswan, J. (2009).
	250	+\newblock The response of global equity indexes to u.s. monetary policy
	251	+ announcements.
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	253	+
	254	+\end{thebibliography}

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	1	+\documentclass[11pt,letterpaper]{article}
	2	+
	3	+% Essential packages
	4	+\usepackage[utf8]{inputenc}
	5	+\usepackage[T1]{fontenc}
	6	+\usepackage[english]{babel}
	7	+\usepackage{amsmath,amssymb,amsthm}
	8	+\usepackage{graphicx}
	9	+\usepackage{booktabs}
	10	+\usepackage{longtable}
	11	+\usepackage{setspace}
	12	+\usepackage{natbib}
	13	+\usepackage{hyperref}
	14	+\usepackage{geometry}
	15	+\usepackage{caption}
	16	+\usepackage{subcaption}
	17	+\usepackage{float}
	18	+\usepackage{pdflscape}
	19	+\usepackage{rotating}
	20	+\usepackage{adjustbox}
	21	+\usepackage{threeparttable}
	22	+\usepackage{enumitem}
	23	+
	24	+% Page geometry
	25	+\geometry{
	26	+ top=1in,
	27	+ bottom=1in,
	28	+ left=1in,
	29	+ right=1in
	30	+}
	31	+
	32	+% Hyperlink configuration
	33	+\hypersetup{
	34	+ colorlinks=true,
	35	+ linkcolor=blue,
	36	+ citecolor=blue,
	37	+ urlcolor=blue
	38	+}
	39	+
	40	+% Theorem definitions
	41	+\newtheorem{definition}{Definition}
	42	+\newtheorem{theorem}{Theorem}
	43	+\newtheorem{proposition}{Proposition}
	44	+\newtheorem{assumption}{Assumption}
	45	+
	46	+% Line spacing
	47	+\doublespacing
	48	+
	49	+% Begin document
	50	+\begin{document}
	51	+
	52	+% Title page
	53	+\begin{titlepage}
	54	+\begin{center}
	55	+\vspace*{1.5cm}
	56	+
	57	+{\LARGE \textbf{Returns and Volatility Around FOMC Announcements:}}\\[0.4cm]
	58	+{\LARGE \textbf{A High-Frequency Analysis of Policy Tone and Novelty}}\\[1.5cm]
	59	+
	60	+{\large Simon-Pierre Boucher\footnotemark[1] \qquad Marie-H\'el\`ene Gagnon\footnotemark[2] \qquad Gabriel J. Power\footnotemark[3]}\\[1cm]
	61	+
	62	+{\large 2026-03-06}\\[1cm]
	63	+
	64	+\end{center}
	65	+
	66	+\footnotetext[1]{PhD student in finance, Universit\'e Laval, Quebec City QC Canada G1V 0A6, email: simon-pierre.boucher.1@ulaval.ca}
	67	+\footnotetext[2]{Professor of Finance and Research Fellow, CRREP, Universit\'e Laval, email: marie-helene.gagnon@fsa.ulaval.ca}
	68	+\footnotetext[3]{IG Wealth Management Chairholder, Professor of Finance and Research Fellow, CRREP and CRIB, Universit\'e Laval, email: gabriel.power@fsa.ulaval.ca}
	69	+
	70	+\begin{abstract}
	71	+\noindent We decompose FOMC statements into policy tone (hawkish/dovish) and informational novelty (departure from previous messaging) and estimate their effects on high-frequency asset returns and volatility. Using 1-minute data for 7 futures contracts across 148 FOMC events (2008--2025), we find that tone predicts directional returns (a one-standard-deviation dovish shift is associated with equity gains that build to about 12 basis points within two hours) while novelty predicts volatility changes (the stance--novelty interaction on VIX persists from 5 to 120 minutes, $t = -5.06$). Policy stance is associated with realized volatility changes in 6 of 7 contracts ($p < 0.01$). Pre-announcement placebo tests and five independent inference methods validate these results. To construct our measures, we train a dual-model ensemble (MiniLM and BERT) on FOMC communications with data-driven PCA-based reference selection.
	72	+\end{abstract}
	73	+
	74	+\vspace{0.3cm}
	75	+
	76	+\noindent \textbf{JEL Classification:} E52, E58, G12, G14
	77	+
	78	+\noindent \textbf{Keywords:} Monetary policy, FOMC announcements, high-frequency data, textual analysis, market volatility
	79	+
	80	+\end{titlepage}
	81	+
	82	+\newpage
	83	+
	84	+% Include all sections
	85	+\input{sections/01_introduction}
	86	+\input{sections/02_data}
	87	+\input{sections/03_methodology}
	88	+\input{sections/04_results}
	89	+\input{sections/05_conclusion}
	90	+
	91	+% Tables
	92	+\input{tables/tables}
	93	+
	94	+% Figures
	95	+\input{figures/figures}
	96	+
	97	+% Appendices
	98	+\clearpage
	99	+\appendix
	100	+\input{appendices/appendix_proofs}
	101	+\clearpage
	102	+\input{appendices/appendix_additional}
	103	+
	104	+% Bibliography
	105	+\newpage
	106	+\bibliographystyle{apalike}
	107	+\bibliography{master}
	108	+
	109	+\end{document}

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		@@ -0,0 +1,74 @@
	1	+\section*{Figures}
	2	+\addcontentsline{toc}{section}{Figures}
	3	+
	4	+% Figure 1: Intraday Volatility Pattern
	5	+\begin{figure}[H]
	6	+\centering
	7	+\includegraphics[width=0.85\textwidth]{figures/figD3_intraday_vol_pattern.pdf}
	8	+\caption{Intraday volatility pattern on FOMC days. Red dashed line marks the 14:00~ET announcement. This figure documents the characteristic volatility spike at announcement time, motivating our high-frequency identification strategy. The pre-announcement period shows relatively stable volatility, while the post-announcement spike and gradual decay are consistent with information processing models.}
	9	+\label{fig:D3}
	10	+\end{figure}
	11	+
	12	+% Figure 2: Semantic Measures Scatter
	13	+\begin{figure}[H]
	14	+\centering
	15	+\includegraphics[width=0.75\textwidth]{figures/figD6_stance_novelty_scatter.pdf}
	16	+\caption{FOMC semantic measures: stance vs.\ novelty (z-scored). Points colored by stance tercile. The low correlation between stance and novelty ($r = 0.12$) supports the conditional independence assumption (Assumption~\ref{ass:indep}) and motivates the separate estimation of tone and novelty effects in our decomposition analysis.}
	17	+\label{fig:D6}
	18	+\end{figure}
	19	+
	20	+% Figure 3: Semantic Time Series
	21	+\begin{figure}[H]
	22	+\centering
	23	+\includegraphics[width=0.9\textwidth]{figures/figD7_semantic_timeseries.pdf}
	24	+\caption{Evolution of policy stance and novelty scores over time. Novelty peaks during the 2008 financial crisis and 2020 pandemic correspond to major policy regime changes. Stance shifts from dovish (2008--2015) to hawkish (2017--2019, 2022--2025) track well-known monetary policy cycles.}
	25	+\label{fig:D7}
	26	+\end{figure}
	27	+
	28	+% Figure 4: Heatmap of Event-Level Coefficients
	29	+\begin{figure}[H]
	30	+\centering
	31	+\includegraphics[width=0.85\textwidth]{figures/figR6a_rv_reg_heatmap_30min.pdf}
	32	+\caption{Heatmap of event-level $\Delta$RV regression coefficients by ticker. Darker shading indicates stronger effects. Stance effects are negative and significant across most contracts, while novelty effects are positive. The stance$\times$novelty interaction is concentrated in VIX and Treasury securities, suggesting that the joint impact of tone and information content operates primarily through the uncertainty channel.}
	33	+\label{fig:R6a}
	34	+\end{figure}
	35	+
	36	+% Figure 5: Cumulative Drift by Stance
	37	+\begin{figure}[H]
	38	+\centering
	39	+\includegraphics[width=0.85\textwidth]{figures/figR8_drift_by_stance.pdf}
	40	+\caption{Cumulative return drift by stance tercile. Dovish announcements generate positive equity drift that strengthens over 45 minutes, while hawkish announcements produce symmetric negative drift. The monotonic separation between terciles and gradual strengthening over time support H1c (tone effects increasing in magnitude) and the fundamental repricing interpretation.}
	41	+\label{fig:R8}
	42	+\end{figure}
	43	+
	44	+% Figure 6: IRF - Stance on Cumulative Returns
	45	+\begin{figure}[H]
	46	+\centering
	47	+\includegraphics[width=0.85\textwidth]{figures/figR10_irf_ret_h_stance.pdf}
	48	+\caption{Impulse response: cumulative return to policy stance (post-announcement, Newey--West SE). The equity (ES) response builds gradually over the 120-minute window, consistent with slow fundamental repricing by heterogeneous investors (H1c). The VIX response is negative and peaks within 30 minutes, consistent with directionally clear statements resolving uncertainty quickly.}
	49	+\label{fig:R10_stance}
	50	+\end{figure}
	51	+
	52	+% Figure 7: IRF - Abnormal Return to Stance x Novelty
	53	+\begin{figure}[H]
	54	+\centering
	55	+\includegraphics[width=0.85\textwidth]{figures/figR10_irf_abn_h_stance_x_novelty.pdf}
	56	+\caption{Impulse response: abnormal cumulative return to stance $\times$ novelty interaction. VIX shows persistent, significant effects from 5 to 120 minutes ($t = -5.06$ at peak), representing the most robust finding in our analysis. This confirms that the joint impact of tone and novelty on uncertainty is both economically large and statistically robust across the full post-announcement window.}
	57	+\label{fig:R10_abn_interaction}
	58	+\end{figure}
	59	+
	60	+% Figure 8: Placebo Tests
	61	+\begin{figure}[H]
	62	+\centering
	63	+\includegraphics[width=0.85\textwidth]{figures/figR10b_irf_placebo_stance.pdf}
	64	+\caption{Pre-announcement placebo: IRF for stance. All coefficients are near zero and statistically insignificant across all tickers and horizons, validating our event study design. The absence of pre-announcement effects rules out information leakage and confirms that our identification strategy successfully isolates the causal impact of FOMC statement content.}
	65	+\label{fig:placebo_stance}
	66	+\end{figure}
	67	+
	68	+% Figure 9: Multi-Method Robustness Heatmap
	69	+\begin{figure}[H]
	70	+\centering
	71	+\includegraphics[width=0.85\textwidth]{figures/figRob2_multimethod_heatmap.pdf}
	72	+\caption{Multi-method robustness heatmap: number of methods (out of 5) yielding $p < 0.10$ for each ticker--variable combination. Darker cells indicate more robust results. Stance effects on $\Delta$RV and $\Delta\log$RV are the most robust, with 3--4 methods confirming significance for ES, CL, and Treasury contracts. The interaction term is most robust for VIX, consistent with the uncertainty channel interpretation.}
	73	+\label{fig:rob_heatmap}
	74	+\end{figure}

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added PHD_chapitre3_theses_20260731/master.bib +430 −0

		@@ -0,0 +1,430 @@
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	9	+ publisher={Oxford University Press}
	10	+}
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	24	+ journal={Review of Financial Studies},
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	42	+ author={Kuttner, Kenneth N},
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	48	+ publisher={Elsevier}
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	78	+ publisher={Wiley Online Library}
	79	+}
	80	+@article{wongswan2009,
	81	+ title={The Response of Global Equity Indexes to U.S. Monetary Policy Announcements},
	82	+ author={Wongswan, Jon},
	83	+ journal={Journal of International Money and Finance},
	84	+ volume={28},
	85	+ number={2},
	86	+ pages={344--365},
	87	+ year={2009},
	88	+ publisher={Elsevier}
	89	+}
	90	+@article{lucca2012,
	91	+ title={The Pre-FOMC Announcement Drift},
	92	+ author={Lucca, David O and Moench, Emanuel},
	93	+ journal={Journal of Finance},
	94	+ volume={70},
	95	+ number={1},
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	98	+ publisher={Wiley Online Library}
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	178	+ title={FinBERT: Financial Sentiment Analysis with Pre-trained Language Models},
	179	+ author={Araci, Dogu},
	180	+ journal={arXiv preprint arXiv:1908.10063},
	181	+ year={2019}
	182	+}
	183	+@article{bligh2008,
	184	+ title={The Decline of Symbolic Politics: Federal Reserve Communications},
	185	+ author={Bligh, Michelle C and Hess, Gregory D},
	186	+ journal={Journal of Economic Psychology},
	187	+ volume={29},
	188	+ number={4},
	189	+ pages={535--559},
	190	+ year={2008},
	191	+ publisher={Elsevier}
	192	+}
	193	+@article{shapiro2019,
	194	+ title={Taking the Fed at its Word: A New Approach to Estimating Central Bank Objectives using Text Analysis},
	195	+ author={Shapiro, Adam Hale and Sudhof, Moritz and Wilson, Daniel J},
	196	+ journal={Review of Economics and Statistics},
	197	+ volume={104},
	198	+ number={4},
	199	+ pages={768--784},
	200	+ year={2022},
	201	+ publisher={MIT Press}
	202	+}
	203	+@article{campbell2012,
	204	+ title={Macroeconomic Effects of Federal Reserve Forward Guidance},
	205	+ author={Campbell, Jeffrey R and Evans, Charles L and Fisher, Jonas DM and Justiniano, Alejandro},
	206	+ journal={Brookings Papers on Economic Activity},
	207	+ volume={2012},
	208	+ number={1},
	209	+ pages={1--80},
	210	+ year={2012},
	211	+ publisher={Brookings Institution Press}
	212	+}
	213	+@article{hansen2017,
	214	+ title={Transparency and Deliberation within the FOMC: A Computational Linguistics Approach},
	215	+ author={Hansen, Stephen and McMahon, Michael and Prat, Andrea},
	216	+ journal={Quarterly Journal of Economics},
	217	+ volume={133},
	218	+ number={2},
	219	+ pages={801--870},
	220	+ year={2018},
	221	+ publisher={Oxford University Press}
	222	+}
	223	+@article{nakamura2018,
	224	+ title={High-Frequency Identification of Monetary Non-neutrality: The Information Effect},
	225	+ author={Nakamura, Emi and Steinsson, J{\'o}n},
	226	+ journal={Quarterly Journal of Economics},
	227	+ volume={133},
	228	+ number={3},
	229	+ pages={1283--1330},
	230	+ year={2018},
	231	+ publisher={Oxford University Press}
	232	+}
	233	+@article{jarocinski2020,
	234	+ title={Deconstructing Monetary Policy Surprises—The Role of Information Shocks},
	235	+ author={Jaro{\'c}inski, Marek and Kar{\'a}di, Peter},
	236	+ journal={American Economic Journal: Macroeconomics},
	237	+ volume={12},
	238	+ number={2},
	239	+ pages={1--43},
	240	+ year={2020},
	241	+ publisher={American Economic Association}
	242	+}
	243	+@article{grossman1980,
	244	+ title={On the Impossibility of Informationally Efficient Markets},
	245	+ author={Grossman, Sanford J and Stiglitz, Joseph E},
	246	+ journal={American Economic Review},
	247	+ volume={70},
	248	+ number={3},
	249	+ pages={393--408},
	250	+ year={1980},
	251	+ publisher={American Economic Association}
	252	+}
	253	+@book{veldkamp2011,
	254	+ title={Information Choice in Macroeconomics and Finance},
	255	+ author={Veldkamp, Laura L},
	256	+ year={2011},
	257	+ publisher={Princeton University Press}
	258	+}
	259	+@article{patton2013,
	260	+ title={Why Do Markets Disagree? Evidence from Variation in Opinion},
	261	+ author={Patton, Andrew J and Verardo, Michela},
	262	+ journal={Review of Financial Studies},
	263	+ volume={25},
	264	+ number={12},
	265	+ pages={3734--3773},
	266	+ year={2012},
	267	+ publisher={Oxford University Press}
	268	+}
	269	+@article{manela2017,
	270	+ title={News Implied Volatility and Disaster Concerns},
	271	+ author={Manela, Asaf and Moreira, Alan},
	272	+ journal={Journal of Financial Economics},
	273	+ volume={123},
	274	+ number={1},
	275	+ pages={137--162},
	276	+ year={2017},
	277	+ publisher={Elsevier}
	278	+}
	279	+@article{andersen2003,
	280	+ title={Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange},
	281	+ author={Andersen, Torben G and Bollerslev, Tim and Diebold, Francis X and Vega, Clara},
	282	+ journal={American Economic Review},
	283	+ volume={93},
	284	+ number={1},
	285	+ pages={38--62},
	286	+ year={2003},
	287	+ publisher={American Economic Association}
	288	+}
	289	+ @article{benjamini1995controlling,
	290	+ title={Controlling the false discovery rate: a practical and powerful approach to multiple testing},
	291	+ author={Benjamini, Yoav and Hochberg, Yosef},
	292	+ journal={Journal of the Royal Statistical Society: Series B (Methodological)},
	293	+ volume={57},
	294	+ number={1},
	295	+ pages={289--300},
	296	+ year={1995},
	297	+ publisher={Wiley Online Library}
	298	+ }
	299	+@article{gurkaynak2005,
	300	+ title={Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements},
	301	+ author={G{\"u}rkaynak, Refet S and Sack, Brian P and Swanson, Eric T},
	302	+ journal={International Journal of Central Banking},
	303	+ volume={1},
	304	+ number={1},
	305	+ pages={55--93},
	306	+ year={2005}
	307	+}
	308	+@article{swanson2014,
	309	+ title={Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates},
	310	+ author={Swanson, Eric T and Williams, John C},
	311	+ journal={American Economic Review},
	312	+ volume={104},
	313	+ number={10},
	314	+ pages={3154--3185},
	315	+ year={2014},
	316	+ publisher={American Economic Association}
	317	+}
	318	+@article{gorodnichenko2023,
	319	+ title={The Voice of Monetary Policy},
	320	+ author={Gorodnichenko, Yuriy and Pham, Tho and Talavera, Oleksandr},
	321	+ journal={American Economic Review},
	322	+ volume={113},
	323	+ number={2},
	324	+ pages={548--584},
	325	+ year={2023},
	326	+ publisher={American Economic Association}
	327	+}
	328	+@article{schmeling2019,
	329	+ title={Does Central Bank Tone Move Asset Prices?},
	330	+ author={Schmeling, Maik and Wagner, Christian},
	331	+ journal={Review of Finance},
	332	+ volume={23},
	333	+ number={5},
	334	+ pages={933--972},
	335	+ year={2019},
	336	+ publisher={Oxford University Press}
	337	+}
	338	+@article{hayo2010,
	339	+ title={Do Federal Reserve Communications Help Predict Federal Funds Target Rate Decisions?},
	340	+ author={Hayo, Bernd and Neuenkirch, Matthias},
	341	+ journal={Journal of Macroeconomics},
	342	+ volume={32},
	343	+ number={4},
	344	+ pages={1014--1024},
	345	+ year={2010},
	346	+ publisher={Elsevier}
	347	+}
	348	+@techreport{apel2012,
	349	+ title={The Information Content of Central Bank Minutes},
	350	+ author={Apel, Mikael and Grimaldi, Marianna Blix},
	351	+ institution={Sveriges Riksbank},
	352	+ type={Working Paper Series},
	353	+ number={261},
	354	+ year={2012}
	355	+}
	356	+@article{fleming1999,
	357	+ title={Price Formation and Liquidity in the US Treasury Market: The Response to Public Information},
	358	+ author={Fleming, Michael J and Remolona, Eli M},
	359	+ journal={Journal of Finance},
	360	+ volume={54},
	361	+ number={5},
	362	+ pages={1901--1915},
	363	+ year={1999},
	364	+ publisher={Wiley Online Library}
	365	+}
	366	+@article{blinder2008,
	367	+ title={Central Bank Communication and Monetary Policy: A Survey of Theory and Evidence},
	368	+ author={Blinder, Alan S and Ehrmann, Michael and Fratzscher, Marcel and De Haan, Jakob and Jansen, David-Jan},
	369	+ journal={Journal of Economic Literature},
	370	+ volume={46},
	371	+ number={4},
	372	+ pages={910--945},
	373	+ year={2008},
	374	+ publisher={American Economic Association}
	375	+}
	376	+@article{barndorff2002,
	377	+ title={Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models},
	378	+ author={Barndorff-Nielsen, Ole E and Shephard, Neil},
	379	+ journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	380	+ volume={64},
	381	+ number={2},
	382	+ pages={253--280},
	383	+ year={2002},
	384	+ publisher={Wiley Online Library}
	385	+}
	386	+@article{fama1970,
	387	+ title={Efficient Capital Markets: A Review of Theory and Empirical Work},
	388	+ author={Fama, Eugene F},
	389	+ journal={Journal of Finance},
	390	+ volume={25},
	391	+ number={2},
	392	+ pages={383--417},
	393	+ year={1970},
	394	+ publisher={Wiley Online Library}
	395	+}
	396	+@article{muth1961,
	397	+ title={Rational Expectations and the Theory of Price Movements},
	398	+ author={Muth, John F},
	399	+ journal={Econometrica},
	400	+ volume={29},
	401	+ number={3},
	402	+ pages={315--335},
	403	+ year={1961},
	404	+ publisher={JSTOR}
	405	+}
	406	+@inproceedings{wang2021tsdae,
	407	+ title={TSDAE: Using Transformer-based Sequential Denoising Auto-Encoder for Unsupervised Sentence Embedding Learning},
	408	+ author={Wang, Kexin and Reimers, Nils and Gurevych, Iryna},
	409	+ booktitle={Findings of the Association for Computational Linguistics: EMNLP 2021},
	410	+ pages={671--688},
	411	+ year={2021}
	412	+}
	413	+@article{andersen1997,
	414	+ title={Intraday Periodicity and Volatility Persistence in Financial Markets},
	415	+ author={Andersen, Torben G. and Bollerslev, Tim},
	416	+ journal={Journal of Empirical Finance},
	417	+ volume={4},
	418	+ number={2--3},
	419	+ pages={115--158},
	420	+ year={1997}
	421	+}
	422	+@article{jorda2005,
	423	+ title={Estimation and Inference of Impulse Responses by Local Projections},
	424	+ author={Jord{\`a}, {\`O}scar},
	425	+ journal={American Economic Review},
	426	+ volume={95},
	427	+ number={1},
	428	+ pages={161--182},
	429	+ year={2005}
	430	+}
		\ No newline at end of file

added PHD_chapitre3_theses_20260731/sections/01_introduction.tex +21 −0

		@@ -0,0 +1,21 @@
	1	+\section{Introduction}
	2	+
	3	+We study how the textual content of Federal Reserve communications affects asset returns and market volatility at high frequency. The Federal Open Market Committee (FOMC)---composed of the seven members of the Board of Governors, the president of the Federal Reserve Bank of New York, and four of the remaining eleven Reserve Bank presidents on a rotating basis---meets eight times per year to set the target federal funds rate. Since 1994, the Committee has released a public statement after each meeting; since 2011, the Chair has also held post-meeting press conferences. Other communications include meeting minutes (released three weeks later) and the Summary of Economic Projections with individual rate forecasts (the ``dot plot''). Our analysis focuses exclusively on post-meeting statements, which are the first piece of information available to market participants at a precise, scheduled time. These statements affect U.S. asset prices, global capital flows, and exchange rates \citep{blinder2008,campbell2012,wongswan2009,ehrmann2011}.
	4	+
	5	+Our central research question is: \textit{Do different semantic dimensions of FOMC communications---specifically policy tone and informational novelty---affect financial market returns and volatility through distinct economic channels?} If tone captures the directional policy signal (hawkish vs.\ dovish) while novelty captures how much genuinely new information the statement contains, standard asset pricing theory predicts that these dimensions should have different effects. In the standard framework, asset prices equal expected future cash flows discounted at a rate that reflects policy expectations \citep{fama1970,bernanke2005}, so the directional content of the statement---tone---should move expected cash flows and discount rates, and hence returns. Volatility, by contrast, reflects uncertainty and disagreement about how to interpret new information \citep{veldkamp2011,patton2013}, so the amount of new language---novelty---should affect information processing complexity and interpretive uncertainty, and hence volatility. We test this prediction using 1-minute price data for 7 futures contracts---the E-mini S\&P 500 (ES), futures on the Chicago Board Options Exchange Volatility Index (VIX futures, VX), the 10-year (ZN) and 5-year (ZF) Treasury notes, the U.S. Dollar Index (DX), crude oil (CL), and gold (GC)---across 148 FOMC events from 2008 to 2025, estimating panel minute-level regressions, event-level regressions, and local projection impulse response functions \citep{jorda2005}. Our identification strategy exploits the exogenous timing of announcements and is validated by pre-announcement placebo tests \citep{andersen2003,andersen2007}.
	6	+
	7	+To measure these dimensions, we construct two primary variables: (1) a tone measure capturing the hawkish-dovish spectrum, and (2) a novelty measure quantifying the semantic distance between consecutive FOMC communications. Concretely, we proceed in three steps. First, we convert each statement into a numerical vector (an \textit{embedding}) using two language models of different sizes---MiniLM (which produces 384-dimensional vectors) and BERT (768-dimensional vectors)---and combine their outputs; using two architecturally distinct models guards against findings that are artifacts of a single model. Second, because generic language models are not trained on central bank language, we adapt both models to the corpus of FOMC statements in two stages: an unsupervised stage based on the Transformer-based Sequential Denoising Auto-Encoder (TSDAE) of \citet{wang2021tsdae}, which teaches the models Fed-specific vocabulary, followed by a supervised contrastive learning stage on pairs of statements with known relationships. Third, we locate each statement on the hawkish-dovish axis by measuring its proximity to reference statements at the two extremes of the spectrum. Whereas previous studies select these reference statements by hand---introducing researcher degrees of freedom, since results may depend on which dates the researcher chooses---we select them algorithmically using principal component analysis (PCA), making the construction of the semantic axes fully reproducible. Novelty is then measured as the distance between the embeddings of consecutive statements.
	8	+
	9	+FOMC announcements are widely seen as the most important scheduled monetary policy events in global financial markets, as they contribute substantially to shaping expectations about the future path of the U.S. economy. Because markets are forward-looking, surprising announcements are typically followed by sizable adjustments across several markets \citep{bernanke2005,blinder2008}. \citet{savor2014} show that a disproportionate share of the equity risk premium is earned on macroeconomic announcement days, with FOMC days being particularly important. \citet{brusa2015,brusa2019} find that average stock returns and Sharpe ratios on FOMC days are 20--40 times higher than on non-announcement days. \citet{lucca2012} document a systematic pre-FOMC drift in equity prices. \citet{nakamura2018} and \citet{jarocinski2020} decompose FOMC surprises into policy shocks and information shocks and show that these have different effects on asset prices.
	10	+
	11	+While earlier research focuses exclusively on the measurable policy surprise content of FOMC announcements, typically extracted from federal funds futures \citep{kuttner2001,bernanke2005}, a more recent strand of literature has begun to apply textual analysis to extract subtler information from the language itself \citep{hansen2017,shapiro2019,schmeling2019,gorodnichenko2023}. This is an important step forward, given that the early contributions identify the effect of unexpected rate changes but ignore the qualitative content of the accompanying statement---forward guidance, risk assessments, and descriptions of economic conditions---which \citet{gurkaynak2005} show can move long-term yields even when the rate decision is fully anticipated. Within this new strand of literature, however, most studies use daily data \citep{shapiro2019,schmeling2019,eklund2024}, which cannot separate the immediate market reaction to the statement from confounding information that arrives later in the day. Furthermore, the standard approach treats the statement as a one-dimensional object (hawkish vs.\ dovish), ignoring other dimensions such as how much the statement departs from prior language. In this paper, we address both limitations by using 1-minute data and by decomposing statements into two distinct dimensions: directional tone and informational novelty.
	12	+
	13	+Textual analysis of financial communications has progressed from keyword counting \citep{bligh2008} and dictionary-based sentiment scoring \citep{loughran2011} to transformer-based language models that capture context and word order \citep{gentzkow2019,kenton2019,araci2019}. Within central bank communication, \citet{hayo2010,apel2012} develop systematic measures of FOMC tone and show that these predict monetary policy expectations. \citet{shapiro2019,hansen2017} use natural language processing (NLP) classifiers to place FOMC statements on the hawkish-dovish spectrum, and \citet{eklund2024} find that hawkish sentiment measures predict subsequent realizations of the consumer price index (CPI). However, this literature treats FOMC communication as essentially one-dimensional---hawkish versus dovish---and has not examined whether other dimensions of the text, such as how much the language departs from the prior statement, have independent effects on asset prices.
	14	+
	15	+We define informational novelty as the degree to which a new FOMC statement departs from the previous one, measured as the cosine distance between their sentence-transformer embeddings. It is useful to distinguish this concept from three related constructs. \textit{Tone} or \textit{sentiment} refers to the directional content of text (hawkish vs.\ dovish) and has been studied using dictionaries \citep{loughran2011} and classifiers \citep{shapiro2019}. \textit{Economic policy uncertainty} (EPU), as measured by \citet{baker2016}, is a macro-level index based on newspaper coverage, tax code provisions, and forecaster disagreement. \textit{Monetary policy surprises}, in the tradition of \citet{kuttner2001}, are the unexpected component of the rate decision itself. Our novelty measure differs from all three: it captures changes in \textit{how} information is presented between consecutive statements, independent of both directional stance and the rate decision. A statement can be highly novel yet neutral in tone (e.g., introducing new forward guidance language), or low in novelty yet accompanied by a large rate surprise.
	16	+
	17	+Why should novelty matter for asset prices? Under rational expectations \citep{muth1961,fama1970}, only genuinely new information should move prices; repetitive content should already be priced in. But theory also suggests that novel and familiar information may affect returns and volatility differently. Returns respond to revisions in expected cash flows and discount rates---that is, to directional content. Volatility may respond more to disagreement among market participants about the interpretation of new language or to the processing cost of unfamiliar information \citep{patton2013,hu2019,veldkamp2011}. Consistent with this distinction, \citet{manela2017} show that their news-based implied volatility index (NVIX) predicts future market volatility.
	18	+
	19	+Our principal finding is that tone is associated with directional asset returns while novelty is associated with volatility, consistent with two distinct transmission channels. We make two main contributions. First, we develop a decomposition framework for FOMC statements based on a dual-model ensemble (MiniLM and BERT) fine-tuned on the FOMC corpus with data-driven PCA-based reference selection. Second, we provide the first high-frequency evidence on the differential effects of tone versus novelty, using local projection impulse response functions across 7 futures contracts and 148 FOMC events. In addition, we show that these two dimensions operate through distinct channels: tone is associated with fundamental valuations (equity returns building to about 12 basis points per standard deviation within two hours), while novelty is associated with uncertainty resolution (the stance--novelty interaction on VIX futures has a $t$-statistic of $-5.06$ and persists from 5 to 120 minutes). Our results are robust to five independent inference methods (Newey--West, wild bootstrap, clustered standard errors, quantile regression, and permutation tests) and are validated through pre-announcement placebo tests.
	20	+
	21	+The remainder of this paper proceeds as follows. Section~\ref{sec:data} describes data construction and processing. Section~\ref{sec:methodology} presents our theoretical framework, propositions, and empirical methodology, including our identification strategy and econometric specifications. Section~\ref{sec:results} reports our main empirical findings. Section~\ref{sec:conclusion} concludes with implications for monetary policy transmission and central bank communication strategy.

added PHD_chapitre3_theses_20260731/sections/02_data.tex +66 −0

		@@ -0,0 +1,66 @@
	1	+\section{Data}
	2	+\label{sec:data}
	3	+
	4	+\subsection{FOMC Statement Collection}
	5	+
	6	+We collect 451 FOMC communications from the Federal Reserve Board website, spanning 2000--2025. After filtering to policy statements only, our textual corpus contains $N = 217$ FOMC statements, each averaging 3,840 characters. We use the broader 2000--2025 textual sample to train the embedding models and construct the semantic axes, which requires examples spanning multiple policy regimes. For the high-frequency event study, we focus on 148 FOMC events from 2008 to 2025. The 2008 start date reflects two considerations. First, reliable 1-minute futures data became consistently available following the shift to predominantly electronic trading on CME Globex in 2006--2007; pre-2008 high-frequency data for several of our contracts contains gaps and timing errors that would compromise our minute-level identification. Second, the 2008--2025 window encompasses sufficient variation in monetary policy regimes---the zero lower bound (2008--2015), quantitative easing programs, post-crisis normalization (2016--2019), the pandemic response (2020--2021), and the inflation-driven tightening cycle (2022--2025)---across three Fed Chairs (Bernanke, Yellen, Powell) to identify communication effects without sacrificing data quality \citep{swanson2014,gurtler2010,blinder2008}. The broader 2000--2025 textual sample used for model fine-tuning starts in 2000 because the FOMC adopted its current practice of issuing post-meeting statements with substantive policy language beginning in 1999--2000; earlier statements were shorter and formulaic, providing too little variation for our NLP models to learn from.
	7	+
	8	+All statements are obtained directly from Federal Reserve official releases archived on the Board of Governors website. We focus exclusively on post-meeting statements rather than meeting minutes, transcripts, or other Fed communications because these statements represent the information that is immediately available to market participants at precise announcement times \citep{gurkaynak2005}. This temporal precision is necessary for high-frequency identification \citep{andersen2003,rosa2013}.
	9	+
	10	+We preprocess statements following \citet{gentzkow2019}: we remove headers, footers, voting records, and administrative content, keeping only policy-relevant text. We account for structural breaks in statement format (e.g., the lengthening of statements post-2008) to avoid introducing spurious variation in our semantic measures \citep{hansen2017}. We cross-reference all statements with the Fed's public archives to verify completeness.
	11	+
	12	+\subsection{Dual-Model Embedding Generation}
	13	+
	14	+We convert each FOMC statement into a numerical vector using two sentence transformer models, adapted to the FOMC corpus through the training procedure described in Section~\ref{sec:nlp_framework}.
	15	+
	16	+\subsubsection{Model Architectures}
	17	+
	18	+\begin{enumerate}
	19	+\item \textbf{MiniLM} (\texttt{all-MiniLM-L6-v2}): 33M parameters, 384-dimensional embeddings.
	20	+\item \textbf{BERT} (\texttt{bert-base-uncased} with mean pooling): 110M parameters, 768-dimensional embeddings. A larger model that captures finer contextual distinctions in policy language \citep{kenton2019}.
	21	+\end{enumerate}
	22	+
	23	+We train both models on the FOMC corpus using the two-stage procedure (TSDAE domain adaptation, then MNRL contrastive learning) described in Section~\ref{sec:nlp_framework}. The training hyperparameters are: batch size 32 (MiniLM) / 16 (BERT), learning rate $1 \times 10^{-5}$, 5 (MiniLM) / 4 (BERT) supervised epochs with cosine warmup schedule (10\% warmup ratio), and approximately 4,000 training examples per model from six pairing strategies.
	24	+
	25	+\subsubsection{Construction of Training Pairs}
	26	+
	27	+We construct training pairs using six strategies: (1) overlapping text segments from the same document; (2) consecutive sentence pairs within a document; (3) hawk--dove contrastive pairs classified through keyword banks; (4) temporal proximity pairs from consecutive FOMC meetings; (5) topic-based pairs sharing the same Fed topic (monetary policy, inflation, employment, etc.); and (6) key phrase paraphrases containing identical policy phrases (\textit{``maintain the target range''}, \textit{``decided to raise''}, etc.). The diversity of pairing strategies prevents the trained models from learning only a single sentiment dimension.
	28	+
	29	+\subsubsection{Data-Driven Reference Selection}
	30	+
	31	+Previous studies select reference dates manually or construct counterfactual statements by hand. We instead use the hybrid PCA--percentile approach described in Definition~\ref{def:pca_axes} to identify semantically extreme statements algorithmically. This procedure eliminates researcher degrees of freedom and produces more stable centroids (5 reference statements per pole versus 2 in typical manual selection). All semantic axes exceed the 0.04 minimum separation threshold. Ensemble separations are: total policy stance (0.302), risk assessment (0.274), policy communication (0.248), and economic priority (0.252).
	32	+
	33	+We validate the embeddings in three ways. First, we compare embedding-based tone rankings with expert classifications and verify that known dovish and hawkish statements sort correctly. Second, we measure inter-model agreement: mean ensemble confidence is 0.837 for novelty and 0.562--0.806 for tone across axes. Third, we verify that the PCA axis assignments produce intuitive orderings.
	34	+
	35	+\subsection{High-Frequency Financial Data Construction}
	36	+
	37	+We use 1-minute OHLCV data for seven futures contracts spanning the major asset classes relevant to monetary policy transmission:
	38	+
	39	+\begin{itemize}
	40	+\item \textbf{ES}: E-mini S\&P 500 (equity benchmark)---responds to policy communications through discount rate effects, growth expectations, and risk premium adjustments.
	41	+\item \textbf{VX}: VIX Futures (volatility)---captures implied volatility and uncertainty resolution, providing the most direct measure of information processing effects.
	42	+\item \textbf{ZN}: 10-Year Treasury Note---reflects the interaction between policy expectations and term premium effects.
	43	+\item \textbf{ZF}: 5-Year Treasury Note---primarily captures expectations about near-term policy rate changes.
	44	+\item \textbf{DX}: Dollar Index---reflects relative monetary policy stances and international spillover effects.
	45	+\item \textbf{CL}: Crude Oil WTI---reflects both inflation expectations and growth concerns influenced by monetary policy.
	46	+\item \textbf{GC}: Gold---a safe-haven asset whose demand falls when accommodative communication triggers a rotation toward risk assets, and rises with policy-induced uncertainty.
	47	+\end{itemize}
	48	+
	49	+The data span 148 FOMC events (approximately 8 per year from 2008 to 2025). For each event, we extract a $\pm 120$ minute window around the 14:00~ET announcement time. We interpolate the raw data to a regular 1-minute grid with forward-filling of short gaps ($\leq 5$ minutes) and returns recomputed on the regularized grid. We require at least 80\% valid observations per rolling window.
	50	+
	51	+For each instrument, we construct minute-by-minute log returns as:
	52	+\begin{equation}
	53	+r_{i,m}^{(j)} = \log\left(P_{i,m}^{(j)}\right) - \log\left(P_{i,m-1}^{(j)}\right)
	54	+\end{equation}
	55	+where $P_{i,m}^{(j)}$ is the price of asset $i$ at minute $m$ relative to FOMC event $j$. We align timestamps across instruments and exchanges, handle market closures and trading halts, and filter outliers following standard microstructure procedures.
	56	+
	57	+\subsection{Event Window Specification and Temporal Alignment}
	58	+
	59	+Our primary analysis employs a 45-minute event window following each FOMC announcement, spanning from the announcement time ($t=0$) to 45 minutes after ($t=+45$). We choose this window length for two reasons.
	60	+
	61	+First, most of the announcement effect occurs within 15 minutes of the release, but equity responses to tone continue to develop through 45 minutes post-announcement. Second, press conferences typically begin 30 minutes after the statement, so a 45-minute window includes only the first 15 minutes of the press conference, limiting contamination.
	62	+
	63	+We also implement several alternative window specifications as robustness checks. A narrow 15-minute post-announcement window provides very clean identification but with reduced statistical power. An extended 60-minute post-announcement window captures longer adjustment dynamics but with increased contamination risk, particularly from press conferences that typically begin 30 minutes after the statement release.
	64	+
	65	+FOMC statements are typically released at 2:00 PM Eastern Time. We verify actual release times using Federal Reserve timestamps, news services, and market data providers, and correct any timing discrepancies before aligning with price data.
	66	+

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	1	+\section{Methodology}
	2	+\label{sec:methodology}
	3	+
	4	+This section describes our NLP framework for measuring tone and novelty (Section~\ref{sec:nlp_framework}), presents the econometric specifications we use to estimate the effects of these measures on asset returns and volatility (Section~\ref{sec:econometric}), and states the testable hypotheses together with the specific coefficient restrictions that each one implies (Section~\ref{sec:hypotheses}).
	5	+
	6	+\subsection{Theoretical Framework}
	7	+\label{sec:nlp_framework}
	8	+
	9	+\subsubsection{Conceptual Foundation}
	10	+
	11	+We decompose each FOMC statement into two dimensions: policy tone (hawkish vs.\ dovish) and informational novelty (distance from the previous statement). To illustrate why context-aware methods are needed for this decomposition, consider the difference between dictionary-based and machine learning approaches. A dictionary approach aggregates sentiment as:
	12	+\begin{equation}
	13	+S_{\text{dict}} = \frac{1}{N} \sum_{i=1}^{N} \mathbb{1}_{[\text{word}_i \in D_{\text{pos}}]} - \mathbb{1}_{[\text{word}_i \in D_{\text{neg}}]}
	14	+\end{equation}
	15	+where $D_{\text{pos}}$ and $D_{\text{neg}}$ are predetermined word lists. The dictionary approach counts words one at a time, without regard to their position or neighbors. A transformer-based model instead produces $S_{\text{ML}} = f_{\theta}(x_1, x_2, \ldots, x_N; C)$, where $f_{\theta}$ is a neural network with learned parameters $\theta$, and $x_i$ are token representations that depend on surrounding words and document-level context $C$. To see why context matters, note that ``the policy remains accommodative'' and ``the policy is no longer accommodative'' contain the same keyword (``accommodative'') but have opposite meanings; a dictionary assigns similar scores to both, while a transformer assigns opposite scores.
	16	+
	17	+Our approach builds on three literatures. The information processing literature predicts that markets react more strongly to genuinely new information than to repetition \citep{grossman1980,fama1970}. The central bank communication literature shows that policy statements move asset prices independently of rate decisions \citep{gurkaynak2005,campbell2012}. The market microstructure literature demonstrates that high-frequency data can isolate the real-time incorporation of new information into prices \citep{andersen2003,rosa2013}.
	18	+
	19	+\begin{definition}[FOMC Statement Representation]
	20	+Each FOMC statement $F_t$ released at time $t$ is mapped to a vector $\mathbf{f}_t \in \mathbb{R}^d$ in $d$-dimensional semantic space through domain-specific transformer embeddings. We employ two architecturally distinct models: MiniLM ($d = 384$) and BERT ($d = 768$), combined into a separation-weighted ensemble.
	21	+\end{definition}
	22	+
	23	+Each model maps a statement to a real-valued vector in which semantically similar texts (e.g., ``accommodative'' and ``easy policy'') are represented by nearby points, enabling cosine similarity comparisons and PCA. Unlike bag-of-words representations, where each coordinate is a word count and most are zero, these vectors are dense: every coordinate carries information. The output dimensionality ($d = 384$ for MiniLM, $d = 768$ for BERT) is fixed by the model architecture---MiniLM-L6-v2 has 6 layers and 384 hidden units per layer; BERT-base has 12 layers and 768 hidden units \citep{kenton2019}---and is not a hyperparameter we select. We adapt both architectures to the FOMC domain using a two-stage training procedure.
	24	+
	25	+\paragraph{Stage 1: TSDAE Unsupervised Pre-Training.} We first apply Transformer-based Sequential Denoising Auto-Encoder (TSDAE) \citep{wang2021tsdae} to adapt each model to the FOMC domain vocabulary:
	26	+\begin{equation}
	27	+\mathcal{L}_{\text{TSDAE}} = - \sum_{i=1}^{N} \log P\bigl(x_i \mid \tilde{x}_i; \theta_{\text{enc}}, \theta_{\text{dec}}\bigr),
	28	+\end{equation}
	29	+where $\tilde{x}_i$ is a corrupted version of sentence $x_i$ (token deletion with probability 0.6). This unsupervised stage teaches domain-specific vocabulary and structure without requiring labeled pairs, training for 3 epochs (MiniLM) or 2 epochs (BERT) with learning rate $3 \times 10^{-5}$.
	30	+
	31	+\paragraph{Stage 2: Supervised Contrastive Learning with MNRL.} We then fine-tune using Multiple Negatives Ranking Loss (MNRL):
	32	+\begin{equation}
	33	+\mathcal{L}_{\text{MNRL}} = - \frac{1}{B} \sum_{i=1}^{B} \log \frac{\exp\bigl(\text{sim}(a_i, p_i) / \tau\bigr)}{\sum_{j=1}^{B} \exp\bigl(\text{sim}(a_i, p_j) / \tau\bigr)},
	34	+\end{equation}
	35	+where $(a_i, p_i)$ are positive pairs, $\text{sim}(\cdot, \cdot)$ denotes cosine similarity, $\tau$ is the temperature parameter, and $B$ is the batch size. In-batch negatives provide contrastive signal without explicit negative sampling. We construct approximately 4,000 training pairs per model using the six pairing strategies described in Section~\ref{sec:data}.
	36	+
	37	+\paragraph{Dual-Model Ensemble.} The two models are combined using separation-weighted averaging:
	38	+\begin{equation}
	39	+\widehat{\text{Tone}}_{t,k}^{\text{ens}} = w_k^{\text{MiniLM}} \cdot \text{Tone}_{t,k}^{\text{MiniLM}} + w_k^{\text{BERT}} \cdot \text{Tone}_{t,k}^{\text{BERT}},
	40	+\end{equation}
	41	+where the weights are proportional to axis separation quality:
	42	+\begin{equation}
	43	+w_k^{m} = \frac{\text{Sep}_k^{m}}{\text{Sep}_k^{\text{MiniLM}} + \text{Sep}_k^{\text{BERT}}}, \quad m \in \{\text{MiniLM}, \text{BERT}\}.
	44	+\end{equation}
	45	+For each statement, we measure inter-model confidence as:
	46	+\begin{equation}
	47	+\text{Conf}_{t,k} = \frac{1}{2}\bigl[\mathbb{1}[\text{sign}(\text{Tone}_{t,k}^{\text{M}}) = \text{sign}(\text{Tone}_{t,k}^{\text{B}})] + (1 - |\text{Tone}_{t,k}^{\text{M}} - \text{Tone}_{t,k}^{\text{B}}| / \max_j |\text{Tone}_{j,k}^{\text{M}} - \text{Tone}_{j,k}^{\text{B}}|)\bigr].
	48	+\end{equation}
	49	+Mean ensemble confidence is 0.837 for novelty and ranges from 0.562 to 0.806 for tone across axes. This dual-model approach reduces model-specific biases: MiniLM (33M parameters, 384 dimensions) provides computational efficiency and strong separation on policy stance, while BERT (110M parameters, 768 dimensions) captures richer contextual relationships. The ensemble achieves balanced performance across all semantic dimensions.
	50	+
	51	+\subsubsection{Semantic Dimensions}
	52	+
	53	+\begin{definition}[Semantic Similarity Measure]
	54	+The semantic similarity between text vectors $\mathbf{u}$ and $\mathbf{v}$ is quantified using cosine similarity:
	55	+\begin{equation}
	56	+\text{sim}(\mathbf{u}, \mathbf{v}) = \frac{\mathbf{u} \cdot \mathbf{v}}{||\mathbf{u}||_2 \cdot ||\mathbf{v}||_2} = \frac{\sum_{i=1}^{d} u_i v_i}{\sqrt{\sum_{i=1}^{d} u_i^2} \cdot \sqrt{\sum_{i=1}^{d} v_i^2}}
	57	+\end{equation}
	58	+\end{definition}
	59	+
	60	+The cosine similarity measure ranges from $-1$ to $1$, where values approaching $1$ indicate high semantic similarity, values near $0$ indicate orthogonal or unrelated content, and values approaching $-1$ indicate semantic opposition. This metric is particularly well-suited for high-dimensional text embeddings because it captures angular distance between vectors while being invariant to vector magnitude differences that might arise from statement length variations.
	61	+
	62	+\begin{definition}[Statement Novelty]
	63	+The informational novelty of statement $F_t$ relative to the immediately preceding statement is defined as:
	64	+\begin{equation}
	65	+\text{Novelty}_t = 1 - \text{sim}(\mathbf{f}_t, \mathbf{f}_{t-1})
	66	+\end{equation}
	67	+\end{definition}
	68	+
	69	+This novelty measure captures the degree to which current policy communications represent genuine departures from recent messaging patterns. Higher novelty values indicate statements containing substantively new informational content relative to recent communications, while lower values suggest continuity with established messaging. The measure is bounded between $0$ and $2$, where $0$ indicates identical statements and $2$ indicates maximally opposed statements.
	70	+
	71	+To construct our policy tone measure, we develop a data-driven approach based on PCA-based semantic axis construction that replaces manually selected reference dates with an algorithmic procedure, eliminating researcher degrees of freedom.
	72	+
	73	+\begin{definition}[Data-Driven Semantic Axis Construction]
	74	+\label{def:pca_axes}
	75	+Let $\mathbf{E} \in \mathbb{R}^{N \times d}$ be the L2-normalized embedding matrix. We compute the first $K = 8$ principal components:
	76	+\begin{equation}
	77	+\mathbf{E} = \mathbf{U} \boldsymbol{\Sigma} \mathbf{V}^\top + \boldsymbol{\epsilon}.
	78	+\end{equation}
	79	+For each semantic dimension $k \in \{1, \ldots, 4\}$ (policy stance, risk assessment, policy communication, economic priority), we define keyword banks $\mathcal{K}_k^+$ (positive pole) and $\mathcal{K}_k^-$ (negative pole), and compute a keyword differential score:
	80	+\begin{equation}
	81	+\Delta_i^{(k)} = \sum_{w \in \mathcal{K}_k^+} \mathbb{1}[w \in \text{text}_i] - \sum_{w \in \mathcal{K}_k^-} \mathbb{1}[w \in \text{text}_i].
	82	+\end{equation}
	83	+We match each semantic axis to the PC maximizing the absolute Pearson correlation:
	84	+\begin{equation}
	85	+j^*(k) = \arg\max_{j \in \{1,\ldots,K\}} \bigl|\text{Corr}(\mathbf{v}_j, \boldsymbol{\Delta}^{(k)})\bigr|.
	86	+\end{equation}
	87	+\end{definition}
	88	+
	89	+The reference selection uses a hybrid seed-and-percentile approach: (1) use 3 expert-selected dates per pole to define an initial axis direction $\hat{\mathbf{d}}_k = \bar{\mathbf{e}}_{\text{pos}} - \bar{\mathbf{e}}_{\text{neg}}$; (2) project all embeddings onto this direction: $s_i = \mathbf{e}_i^\top \hat{\mathbf{d}}_k / \|\hat{\mathbf{d}}_k\|$; (3) select $M = 5$ statements with highest and lowest projection scores; (4) iteratively refine by recomputing the axis direction from selected references and re-selecting. This yields 5 reference statements per pole (compared to 2 in manual selection), producing more stable centroids.
	90	+
	91	+For each axis $k$, we measure discrimination quality using the separation metric:
	92	+\begin{equation}
	93	+\text{Sep}_k = 1 - \cos(\bar{\mathbf{c}}_k^+, \bar{\mathbf{c}}_k^-),
	94	+\end{equation}
	95	+where $\bar{\mathbf{c}}_k^+, \bar{\mathbf{c}}_k^-$ are the L2-normalized positive and negative centroids. All axes achieve separations well above the 0.04 minimum threshold, with ensemble separations ranging from 0.248 to 0.302.
	96	+
	97	+\begin{definition}[Policy Tone]
	98	+The directional tone of statement $F_t$ on semantic axis $k$ is measured as:
	99	+\begin{equation}
	100	+\text{Tone}_{t,k} = \frac{\cos(\mathbf{f}_t, \bar{\mathbf{c}}_k^+) - \cos(\mathbf{f}_t, \bar{\mathbf{c}}_k^-)}{\text{Sep}_k}, \quad \text{clipped to } [-1, +1].
	101	+\end{equation}
	102	+\end{definition}
	103	+
	104	+This tone measure captures the relative proximity of actual statements to the positive (hawkish) and negative (dovish) reference centroids for each semantic axis, normalized by the axis separation. The primary variable used in regressions is the \emph{total policy stance tone}. In the regression tables, the z-scored stance variable is oriented so that positive values indicate more accommodative (dovish) communication; positive coefficients therefore measure the response to a one-standard-deviation dovish shift. The composite MPS measure defined below retains the hawkish-positive orientation. Relative to counterfactual-based methods, this approach is reproducible, does not depend on particular date choices, and extends to semantic dimensions other than the hawkish-dovish spectrum.
	105	+
	106	+\subsubsection{Integrated Policy Stance Measurement}
	107	+
	108	+\begin{definition}[Monetary Policy Stance]
	109	+The overall monetary policy stance is defined as:
	110	+\begin{equation}
	111	+\text{Stance}_t = \text{Novelty}_t \times \text{Tone}_t
	112	+\end{equation}
	113	+\end{definition}
	114	+
	115	+\textbf{Note on originality:} Definitions 1--11 and Proposition~\ref{prop:mps} are our own contributions. They apply the standard sentence-embedding framework from the NLP literature to monetary policy communications with a new decomposition structure.
	116	+
	117	+The multiplicative form means that stance is large only when a statement is both novel \textit{and} directionally clear. We adopt a multiplicative rather than additive form for two reasons. First, it ensures that Stance is zero whenever either component is zero: repetitive content has no impact regardless of its tone, and novel but directionally neutral content has none either. Second, it captures the reinforcing interaction between the two dimensions: novel information amplifies the impact of tone, and clear directional tone amplifies the impact of novelty.
	118	+
	119	+In the following two definitions, $\mathbf{f}_t^D$ and $\mathbf{f}_t^H$ denote the embeddings of counterfactual statements located at the dovish and hawkish reference centroids of the policy stance axis, $\bar{\mathbf{c}}^-$ and $\bar{\mathbf{c}}^+$; they represent what the Fed would have released had it issued a maximally dovish or maximally hawkish statement at meeting $t$.
	120	+
	121	+\begin{definition}[Pure Dovish and Hawkish Stances]
	122	+\label{def:pure_stances}
	123	+The extreme stance scenarios are defined as:
	124	+\begin{align}
	125	+\text{Stance}_t^{dove} &= -\left(1 - \text{sim}(\mathbf{f}_t^D, \mathbf{f}_{t-1})\right) \\
	126	+\text{Stance}_t^{hawk} &= 1 - \text{sim}(\mathbf{f}_t^H, \mathbf{f}_{t-1})
	127	+\end{align}
	128	+\end{definition}
	129	+
	130	+\begin{definition}[Weighted Policy Stance Representation]
	131	+\label{def:weighted_stance}
	132	+The overall stance can be expressed as a convex combination of extreme stances:
	133	+\begin{equation}
	134	+\text{Stance}_t = w_t \cdot \text{Stance}_t^{dove} + (1 - w_t) \cdot \text{Stance}_t^{hawk}
	135	+\end{equation}
	136	+where the dovish weight parameter $w_t$ is computed (not estimated) as a deterministic function of the observed similarities:
	137	+\begin{equation}
	138	+w_t = \frac{1 - \text{sim}(\mathbf{f}_t^H, \mathbf{f}_{t-1}) - \left(1 - \text{sim}(\mathbf{f}_t, \mathbf{f}_{t-1})\right) \cdot \text{Tone}_t}{2 - \text{sim}(\mathbf{f}_t^D, \mathbf{f}_{t-1}) - \text{sim}(\mathbf{f}_t^H, \mathbf{f}_{t-1})}
	139	+\end{equation}
	140	+\end{definition}
	141	+
	142	+This weighted representation provides an alternative interpretation of policy stance as a position along the spectrum between extreme dovish and hawkish alternatives. The weight parameter $w_t$ is not a free parameter to be estimated; rather, it is algebraically derived from the observed textual similarities.
	143	+
	144	+\subsubsection{Market Surprise Identification}
	145	+
	146	+\begin{definition}[Novelty Decomposition]
	147	+The total novelty can be decomposed into predictable and unpredictable components:
	148	+\begin{equation}
	149	+\text{Novelty}_t = \overline{\text{Novelty}}_{t \mid t-\Delta} + \varepsilon_t
	150	+\end{equation}
	151	+where $\overline{\text{Novelty}}_{t \mid t-\Delta} \equiv \mathbb{E}_{t-\Delta}[\text{Novelty}_t]$ represents the expected novelty based on information available $\Delta$ periods before the announcement, and $\varepsilon_t$ represents the novelty surprise component with $\mathbb{E}_{t-\Delta}[\varepsilon_t] = 0$ and $\text{Var}(\varepsilon_t) = \sigma_{\varepsilon}^2 < \infty$. We assume $\varepsilon_t$ is covariance-stationary with $\text{Cov}(\varepsilon_t, \varepsilon_{t-j}) \to 0$ as $j \to \infty$.
	152	+\end{definition}
	153	+
	154	+\begin{definition}[Expected Policy Stance]
	155	+Under rational expectations, the expected policy stance is:
	156	+\begin{equation}
	157	+\mathbb{E}_{t-\Delta}[\text{Stance}_t] = \mathbb{E}_{t-\Delta}\left[\text{Novelty}_t \times \text{Tone}_t\right]
	158	+\end{equation}
	159	+\end{definition}
	160	+
	161	+\begin{assumption}[Conditional Independence or Zero Covariance]
	162	+\label{ass:indep}
	163	+We assume either (i) conditional independence: $\text{Novelty}_t \perp \text{Tone}_t | \mathcal{I}_{t-\Delta}$, where $\mathcal{I}_{t-\Delta}$ is the information set at time $t - \Delta$, or (ii) the weaker condition of zero conditional covariance:
	164	+\begin{equation}
	165	+\text{Cov}_{t-\Delta}(\text{Novelty}_t, \text{Tone}_t) = 0
	166	+\end{equation}
	167	+\end{assumption}
	168	+
	169	+This assumption is plausible because novelty captures whether the Fed changes its messaging structure (how information is presented), while tone captures the directional policy stance (hawkish/dovish). Empirically, the correlation between novelty and tone in our sample is 0.12 (Figure~\ref{fig:D6}), supporting the assumption that these are largely independent dimensions. Under this assumption:
	170	+\begin{equation}
	171	+\mathbb{E}_{t-\Delta}[\text{Stance}_t] = \mathbb{E}_{t-\Delta}[\text{Novelty}_t] \times \mathbb{E}_{t-\Delta}[\text{Tone}_t]
	172	+\end{equation}
	173	+
	174	+Further assuming, for tractability, that tone is binary ($\text{Tone}_t \in \{-1, +1\}$, taking the dovish value $-1$ with probability $p_{t-\Delta}$), so that $\mathbb{E}_{t-\Delta}[\text{Tone}_t] = 1 - 2p_{t-\Delta}$:
	175	+\begin{equation}
	176	+\mathbb{E}_{t-\Delta}[\text{Stance}_t] = (1 - 2p_{t-\Delta}) \cdot \overline{\text{Novelty}}_{t \mid t-\Delta}
	177	+\end{equation}
	178	+
	179	+\begin{definition}[Policy Stance Surprise]
	180	+The communication-based policy stance surprise is defined as:
	181	+\begin{equation}
	182	+\text{MPS}_t = \text{Stance}_t - \mathbb{E}_{t-\Delta}[\text{Stance}_t]
	183	+\end{equation}
	184	+\end{definition}
	185	+
	186	+We use the abbreviation MPS (monetary policy surprise) for brevity, but emphasize that this measure is conceptually distinct from the traditional rate-based monetary policy surprise of \citet{kuttner2001}, which measures the unexpected component of the federal funds rate decision using futures prices. Our MPS is a \textit{communication} surprise---it captures unexpected variation in the textual content of FOMC statements, not in the quantitative rate decision. The two measures are complementary and potentially orthogonal: a meeting can produce a large rate surprise with a routine statement, or a novel and directional statement with a fully anticipated rate decision. Our measure captures the latter dimension, which has become increasingly important as forward guidance and qualitative communication have gained prominence in the monetary policy toolkit.
	187	+
	188	+\begin{proposition}[MPS Decomposition Structure]
	189	+\label{prop:mps}
	190	+The monetary policy surprise admits the following decomposition:
	191	+\begin{equation}
	192	+\text{MPS}_t = \overline{\text{Novelty}}_{t \mid t-\Delta}(\text{Tone}_t + 2p_{t-\Delta} - 1) + \text{Tone}_t \cdot \varepsilon_t
	193	+\end{equation}
	194	+\end{proposition}
	195	+
	196	+This decomposition reveals that policy surprises consist of two distinct components: (1) surprises arising from unexpected tone conditional on expected novelty, and (2) surprises arising from unexpected novelty, weighted by the actual tone of the communication. The proof of Proposition~\ref{prop:mps}, together with the derivations underlying Definitions~\ref{def:pure_stances} and~\ref{def:weighted_stance}, is in Appendix~\ref{sec:proofs}.
	197	+
	198	+\subsection{Econometric Framework}
	199	+\label{sec:econometric}
	200	+
	201	+\subsubsection{Panel Data Structure}
	202	+
	203	+The data are organized as a three-dimensional panel structure with observations indexed along three dimensions:
	204	+\begin{itemize}
	205	+\item Asset identifier $i \in \{1, 2, \ldots, I\}$ where $I$ represents the total number of financial instruments
	206	+\item Event identifier $j \in \{1, 2, \ldots, J\}$ corresponding to FOMC announcement dates where $J = 148$
	207	+\item Relative minute $m \in \{-120, \ldots, +120\}$ measured from announcement time, with the primary post-announcement window covering $m \in \{0, \ldots, +45\}$
	208	+\end{itemize}
	209	+
	210	+\subsubsection{Identification Strategy}
	211	+
	212	+Our identification relies on the fact that FOMC statements are drafted and finalized before the announcement and released at a scheduled time (typically 2:00 PM ET). The text at $t=0$ therefore cannot be influenced by market reactions at $t>0$, satisfying the timing restriction for causal interpretation.
	213	+
	214	+Our identification relies on three core conditions:
	215	+
	216	+\textbf{Identification Condition 1 (Exogenous Timing).} The precise minute-by-minute timing of FOMC announcements is predetermined and exogenous to short-term market movements within our event windows.
	217	+
	218	+\textbf{Identification Condition 2 (Information Concentration).} Within our 45-minute post-announcement event windows, FOMC statements represent the dominant source of monetary policy-relevant information, with minimal contamination from other systematic news sources.
	219	+
	220	+\textbf{Identification Condition 3 (Market Efficiency).} Financial markets rapidly incorporate new information from FOMC statements into prices, enabling causal interpretation of immediate price movements following announcements.
	221	+
	222	+We acknowledge two potential threats to this identification strategy. First, the Federal Reserve may adjust its communication in response to broader financial conditions observed before the meeting. We mitigate this concern by including event fixed effects $\delta_j$ that absorb all meeting-level heterogeneity. Second, FOMC announcements may coincide with other information releases (e.g., Summary of Economic Projections, press conference expectations). Our focus on the immediate post-announcement window limits contamination from subsequent press conference content, which typically begins 30 minutes after the statement release.
	223	+
	224	+\subsubsection{Dynamic Response Function Estimation}
	225	+
	226	+Our primary empirical specification estimates dynamic impulse response functions:
	227	+\begin{equation}
	228	+r_{i,m}^{(j)} = \alpha_i + \delta_j + \sum_{k=0}^{+45} \beta_k \cdot \mathbb{1}_{[m=k]} \cdot \text{MPS}_j + \varepsilon_{i,m,j}
	229	+\label{eq:dynamic}
	230	+\end{equation}
	231	+where $r_{i,m}^{(j)}$ denotes the log return of asset $i$ at minute $m$ relative to monetary policy announcement $j$, $\alpha_i$ represents asset fixed effects, $\delta_j$ captures event fixed effects, and $\beta_k$ measures the marginal impact of monetary policy surprises occurring exactly $k$ minutes relative to the announcement.
	232	+
	233	+\subsubsection{Semantic Decomposition Specification}
	234	+
	235	+To examine the differential effects of policy tone versus informational novelty, we estimate:
	236	+\begin{equation}
	237	+r_{i,m}^{(j)} = \alpha_i + \delta_j + \sum_{k=0}^{+45} \left[\beta_k^{(T)} \cdot \mathbb{1}_{[m=k]} \cdot \text{Tone}_j + \beta_k^{(N)} \cdot \mathbb{1}_{[m=k]} \cdot \text{Novelty}_j\right] + \varepsilon_{i,m,j}
	238	+\label{eq:decomp}
	239	+\end{equation}
	240	+
	241	+The tone coefficients $\{\beta_k^{(T)}\}$ measure the dynamic response to hawkish versus dovish content, while the novelty coefficients $\{\beta_k^{(N)}\}$ capture the response to informational content, independent of directional bias.
	242	+
	243	+\subsubsection{Rolling Realized Measures}
	244	+
	245	+In addition to return effects, we examine how policy communications affect market volatility using rolling realized measures computed from 1-minute log returns.
	246	+
	247	+\paragraph{Realized Variance.} We construct NA-tolerant rolling realized variance in $K$-minute windows:
	248	+\begin{equation}
	249	+\mathrm{RV}_K(t) = \frac{K}{n_{\text{valid}}} \sum_{s = t-K+1}^{t} r_s^2 \cdot \mathbb{1}[r_s \text{ valid}],
	250	+\end{equation}
	251	+where $n_{\text{valid}}$ is the number of non-missing observations in the window. We require at least 80\% valid observations.
	252	+
	253	+\paragraph{Realized Beta.} We compute rolling beta relative to the ES (S\&P 500) benchmark:
	254	+\begin{equation}
	255	+\hat{\beta}_K(t) = \frac{\sum_{s=t-K+1}^{t} r_{i,s} \cdot r_{m,s}}{\sum_{s=t-K+1}^{t} r_{m,s}^2},
	256	+\end{equation}
	257	+where $r_{m,s}$ denotes the ES benchmark return. We use $K = 5$ for panel minute-level regressions and $K = 30$ for event-level analysis.
	258	+
	259	+\subsubsection{Panel Minute-Level Regressions}
	260	+
	261	+For each ticker, we estimate:
	262	+\begin{equation}
	263	+\log(\mathrm{RV}_{i,t}) = \alpha + \beta \cdot (\text{Post}_t \times \text{Semantic}_i) + \varepsilon_{i,t},
	264	+\label{eq:panel}
	265	+\end{equation}
	266	+where $\text{Post}_t = \mathbb{1}[t > 0]$ indicates post-announcement minutes, and $\text{Semantic}_i$ is either \emph{Stance} or \emph{Novelty} (z-scored). Standard errors are clustered by event date.
	267	+
	268	+\subsubsection{Event-Level Regressions}
	269	+
	270	+For each event, we compute pre/post changes:
	271	+\begin{equation}
	272	+\Delta \log(\mathrm{RV})_i = \overline{\log(\mathrm{RV})}_{\text{post}} - \overline{\log(\mathrm{RV})}_{\text{pre}},
	273	+\end{equation}
	274	+and regress on semantic measures:
	275	+\begin{equation}
	276	+\Delta Y_i = \alpha + \beta_1 \text{Stance}_i + \beta_2 \text{Novelty}_i + \beta_3 (\text{Stance}_i \times \text{Novelty}_i) + \varepsilon_i,
	277	+\label{eq:event}
	278	+\end{equation}
	279	+with Newey--West HAC standard errors. We estimate this specification for five dependent variables: $\Delta\mathrm{RV}$, $\Delta\log(\mathrm{RV})$, RV ratio, $\log$(RV ratio), and $\Delta\beta$.
	280	+
	281	+\subsubsection{Local Projection Impulse Response Functions}
	282	+
	283	+Following \citet{jorda2005}, for each horizon $h \in \{1, 2, 3, 5, 10, 15, 20, 30, 45, 60, 90, 120\}$ minutes post-announcement:
	284	+\begin{equation}
	285	+\text{CumRet}_i(0 \to h) = \alpha + \beta_1^{(h)} \text{Stance}_i + \beta_2^{(h)} \text{Novelty}_i + \beta_3^{(h)} (\text{Stance}_i \times \text{Novelty}_i) + \varepsilon_i^{(h)}.
	286	+\label{eq:irf}
	287	+\end{equation}
	288	+Abnormal cumulative returns are computed as $\text{CAR}_i(h) = \text{CumRet}_i(h) - \text{CumRet}_i^{\text{ES}}(h)$. This local projection approach is robust to misspecification of the data-generating process and allows horizon-specific inference without imposing a parametric impulse response shape. Because the post-meeting press conference typically begins 30 minutes after the statement release, we interpret responses at horizons beyond $h = 30$ as the joint effect of the statement and early press-conference communication.
	289	+
	290	+\subsubsection{Pre-Announcement Placebo Test}
	291	+
	292	+We estimate the same specification~\eqref{eq:irf} for $h$ minutes \emph{before} the announcement:
	293	+\begin{equation}
	294	+\text{CumRet}_i(-h \to 0) = \alpha + \beta_1^{(-h)} \text{Stance}_i + \beta_2^{(-h)} \text{Novelty}_i + \beta_3^{(-h)} (\text{Stance}_i \times \text{Novelty}_i) + \varepsilon_i^{(-h)}.
	295	+\label{eq:placebo}
	296	+\end{equation}
	297	+Under the null that announcement content is not anticipated, all $\beta^{(-h)}$ should be zero. This placebo test provides a direct validation of our event study design.
	298	+
	299	+\subsubsection{Statistical Inference and Robustness}
	300	+
	301	+We subject all event-level results to five alternative inference methods:
	302	+
	303	+\begin{enumerate}
	304	+\item \textbf{Newey--West HAC standard errors}: Robust to heteroskedasticity and autocorrelation.
	305	+\item \textbf{Wild bootstrap} ($B = 1{,}999$, Rademacher weights): Robust to heteroskedasticity with improved finite-sample properties.
	306	+\item \textbf{Clustered standard errors} (HC1, by event date): Accounts for cross-sectional dependence within events.
	307	+\item \textbf{Quantile regression} ($\tau = 0.5$): Robust to outliers and heavy tails in the dependent variable.
	308	+\item \textbf{Permutation test} ($B = 4{,}999$): Gold standard---shuffles semantic labels across events preserving panel structure, providing exact $p$-values under the null.
	309	+\end{enumerate}
	310	+
	311	+All $p$-values in panel and IRF regressions are adjusted for multiple testing using the Benjamini--Hochberg (BH) procedure within each family of tests (per dependent variable and model type) \citep{benjamini1995controlling}. We use only standard significance levels: 1\%, 5\%, and 10\%.
	312	+
	313	+\textbf{Sub-Period Stability.} We examine coefficient stability across six Fed policy regimes: crisis and recovery (2008--2012), post-crisis normalization (2013--2015), pre-pandemic tightening (2016--2019), pandemic response (2020--2021), and inflation tightening (2022--2025).
	314	+
	315	+\textbf{Alternative Semantic Measures.} The dual-model ensemble itself provides a built-in robustness check: by comparing results from MiniLM-only, BERT-only, and ensemble measures, we verify that findings are not driven by model-specific artifacts.
	316	+
	317	+\subsection{Hypotheses and Testable Predictions}
	318	+\label{sec:hypotheses}
	319	+
	320	+We now state our hypotheses and, for each one, the coefficient restriction that operationalizes it in the specifications of Section~\ref{sec:econometric}. Recall the sign conventions: the z-scored stance regressor in equations~\eqref{eq:decomp}--\eqref{eq:irf} is dovish-positive, while the composite MPS in equation~\eqref{eq:dynamic} is hawkish-positive. Table~\ref{tab:hyp_map} summarizes the mapping from hypotheses to coefficients, equations, and the tables in which each test is reported.
	321	+
	322	+\textbf{Hypothesis 1 (Tone Effects on Returns).}
	323	+\begin{itemize}
	324	+\item \textbf{H1a.} Dovish tone increases returns on risk assets (equities, commodities). \textit{Test:} $\beta_k^{(T)} > 0$ in the semantic decomposition~\eqref{eq:decomp} and $\beta_1^{(h)} > 0$ in the local projection~\eqref{eq:irf} for ES and CL.
	325	+\item \textbf{H1b.} Dovish tone decreases returns on safe-haven assets, as accommodative policy triggers portfolio rebalancing away from safe havens toward risk assets. \textit{Test:} $\beta_1^{(h)} < 0$ in~\eqref{eq:irf} for GC, ZN, and ZF.
	326	+\item \textbf{H1c.} Tone effects strengthen with the horizon as markets progressively process policy implications. \textit{Test:} $|\beta_1^{(h)}|$ increasing in $h$ in~\eqref{eq:irf} for ES.
	327	+\end{itemize}
	328	+
	329	+\textbf{Hypothesis 2 (Novelty Effects on Volatility).}
	330	+\begin{itemize}
	331	+\item \textbf{H2a.} High novelty increases market volatility through information processing complexity. \textit{Test:} $\beta_2 > 0$ in the event-level regression~\eqref{eq:event} with $\Delta\mathrm{RV}$ as the dependent variable, and $\beta > 0$ in the panel regression~\eqref{eq:panel} with $\text{Semantic} = \text{Novelty}$, most directly for VX.
	332	+\item \textbf{H2b.} Novelty effects dissipate rapidly as markets resolve uncertainty. \textit{Test:} $|\beta_2^{(h)}|$ decreasing in $h$ in~\eqref{eq:irf} for VX.
	333	+\item \textbf{H2c.} Novelty has minimal effects on directional returns. \textit{Test:} $\beta_2^{(h)} \approx 0$ (statistically indistinguishable from zero) in~\eqref{eq:irf} for the return contracts (ES, CL, GC, DX).
	334	+\end{itemize}
	335	+
	336	+\textbf{Hypothesis 3 (Policy Surprise Effects).}
	337	+\begin{itemize}
	338	+\item \textbf{H3a.} Hawkish policy surprises reduce equity returns. \textit{Test:} $\beta_0 < 0$ in the dynamic response function~\eqref{eq:dynamic} for ES.
	339	+\item \textbf{H3b.} Policy surprises increase implied volatility. \textit{Test:} $\beta_0 > 0$ in~\eqref{eq:dynamic} for VX.
	340	+\item \textbf{H3c.} Surprise effects on volatility are most pronounced immediately after the announcement. \textit{Test:} $|\beta_k|$ in~\eqref{eq:dynamic} largest at $k = 0$ and decaying in $k$ for VX.
	341	+\end{itemize}
	342	+
	343	+\textbf{Hypothesis 4 (Cross-Asset Patterns).}
	344	+\begin{itemize}
	345	+\item \textbf{H4a.} Risk assets respond to tone in the same direction (risk-on/risk-off). \textit{Test:} $\text{sign}\bigl(\beta_1^{(h)}\bigr)$ equal across ES and CL in~\eqref{eq:irf}, opposite for GC, ZN, ZF.
	346	+\item \textbf{H4b.} Volatility responses to novelty are asset-specific. \textit{Test:} $\beta_2$ and $\beta_3$ in~\eqref{eq:event} differ in magnitude and significance across the seven contracts.
	347	+\end{itemize}
	348	+
	349	+Finally, the validity of the design itself is testable: under no anticipation of statement content, all pre-announcement coefficients in the placebo specification~\eqref{eq:placebo} should be zero, $\beta_1^{(-h)} = \beta_2^{(-h)} = \beta_3^{(-h)} = 0$ for all $h$.
	350	+
	351	+\begin{table}[H]
	352	+\centering
	353	+\footnotesize
	354	+\caption{Mapping of Hypotheses to Coefficients, Equations, and Evidence}
	355	+\label{tab:hyp_map}
	356	+\begin{tabular}{lp{4.5cm}p{4.3cm}p{3.3cm}}
	357	+\toprule
	358	+Hyp. & Prediction & Coefficient restriction (equation) & Evidence \\
	359	+\midrule
	360	+H1a & Dovish tone $\Rightarrow$ risk-asset returns $\uparrow$ & $\beta_1^{(h)} > 0$ in \eqref{eq:irf}, ES/CL & Table~\ref{tab:irf_stance_ret_h} \\
	361	+H1b & Dovish tone $\Rightarrow$ safe-haven returns $\downarrow$ & $\beta_1^{(h)} < 0$ in \eqref{eq:irf}, GC/ZN/ZF & Table~\ref{tab:irf_stance_ret_h} \\
	362	+H1c & Tone effects build with horizon & $|\beta_1^{(h)}|$ increasing in $h$, ES & Table~\ref{tab:irf_stance_ret_h}; Fig.~\ref{fig:R8} \\
	363	+H2a & Novelty $\Rightarrow$ volatility $\uparrow$ & $\beta_2 > 0$ in \eqref{eq:event}, $\Delta$RV & Tables~\ref{tab:panel_logrv_novelty}, \ref{tab:rolling_delta_rv_30min} \\
	364	+H2b & Novelty effects decay quickly & $|\beta_2^{(h)}|$ decreasing in $h$, VX & Table~\ref{tab:irf_novelty_ret_h} \\
	365	+H2c & Novelty does not move returns & $\beta_2^{(h)} \approx 0$ in \eqref{eq:irf} & Table~\ref{tab:irf_novelty_ret_h}; Fig.~\ref{fig:R9} \\
	366	+H3a & Hawkish surprise $\Rightarrow$ equity returns $\downarrow$ & $\beta_0 < 0$ in \eqref{eq:dynamic}, ES & Section~\ref{sec:baseline} \\
	367	+H3b & Surprise $\Rightarrow$ implied volatility $\uparrow$ & $\beta_0 > 0$ in \eqref{eq:dynamic}, VX & Section~\ref{sec:baseline} \\
	368	+H3c & Surprise effects peak on impact & $|\beta_k|$ max at $k=0$ in \eqref{eq:dynamic}, VX & Section~\ref{sec:baseline} \\
	369	+H4a & Homogeneous return response, risk assets & $\text{sign}(\beta_1^{(h)})$ equal, ES/CL in \eqref{eq:irf} & Table~\ref{tab:irf_stance_ret_h} \\
	370	+H4b & Heterogeneous volatility responses & $\beta_2, \beta_3$ vary across contracts in \eqref{eq:event} & Tables~\ref{tab:rolling_delta_rv_30min}, \ref{tab:robustness_A} \\
	371	+Placebo & No pre-announcement effects & $\beta^{(-h)} = 0$ in \eqref{eq:placebo}, all contracts & Fig.~\ref{fig:placebo_stance}, \ref{fig:placebo_novelty} \\
	372	+\bottomrule
	373	+\end{tabular}
	374	+\end{table}
	375	+

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