spb/phd_thesis Public

1\section{Results}2\label{sec:results}34We organize our results as follows. We first describe the semantic variables (Section~\ref{sec:desc}), then report baseline responses to the composite MPS (Section~\ref{sec:baseline}), the tone-novelty decomposition (Section~\ref{sec:decomposition}), and the temporal dynamics of these effects (Section~\ref{sec:halflife}). Throughout, each hypothesis is evaluated against the coefficient restriction assigned to it in Table~\ref{tab:hyp_map}. The main finding is that tone and novelty load on different dependent variables: tone predicts directional returns, while novelty predicts volatility changes. The VIX model has the highest $R^2$ ($0.78$); equity and commodity models follow. Treasury results are weaker.56$R^2$ values for the return models are low (0.01--0.15), as is typical when predicting minute-level returns where microstructure noise dominates \citep{barndorff2002}. Low $R^2$ does not bias the coefficient estimates, but it means that FOMC communication accounts for a small share of total intra-day return variation. The VIX model is the exception: semantic variables explain up to 78\% of announcement-window variation in VIX futures, consistent with the hypothesis that these communications operate primarily on uncertainty rather than on the level of returns.78\subsection{Descriptive statistics}9\label{sec:desc}1011Table~\ref{tab:desc_1min_ret} reports descriptive statistics for 1-minute log returns on FOMC days. Table~\ref{tab:desc_rolling} reports summary statistics for the rolling realized measures. Figure~\ref{fig:D3} plots the average intraday volatility pattern on FOMC days, which spikes sharply at the 14:00~ET release.1213Novelty has a mean of 0.065. The scale runs from 0 (a statement identical to the previous one) to 2 (maximally opposite), so a mean of 0.065 corresponds to an average cosine similarity of 0.935 between consecutive statements---most meetings produce only small changes to the prior template. The median is lower (0.025), so the distribution is right-skewed: most meetings produce minor textual changes, but a few produce large departures. The maximum (0.494) occurs during the 2008 crisis, when the Fed introduced zero-lower-bound language (Figure~\ref{fig:D7}). Skewness is 2.45 and kurtosis is 8.16.1415The raw tone measure (hawkish-positive) has a mean of 0.309 on a theoretical $[-1, +1]$ scale, where $-1$ is the dovish centroid, $0$ is equidistant, and $+1$ is the hawkish centroid. The positive mean indicates that the average FOMC statement over 2008--2025 lies closer to the hawkish than to the dovish centroid. Because cosine similarities to both centroids are high, realized values occupy a narrow band within the theoretical scale; we therefore z-score tone in all regressions. Skewness is $-0.78$ and kurtosis is 6.96, driven by the most dovish statements in the sample, which mark its lower extremes (2008: $-0.081$; 2020: $-0.062$).1617The MPS measure has mean 0.004 and kurtosis 12.18---the fat tails reflect occasional large surprises during economic stress. Jarque-Bera tests reject normality for all three measures ($p < 0.01$), and ARCH-LM tests indicate time-varying variance ($p < 0.05$), which motivates our use of robust standard errors and multiple inference methods throughout.1819\subsection{Baseline Asset Price Responses to Monetary Policy Surprises}2021\label{sec:baseline}22We begin with the composite MPS, testing H3. The dependent variable is the 1-minute log return for each contract; the regressor is the z-scored MPS. A positive coefficient means that hawkish communication surprises are associated with higher returns.2324\subsubsection{Immediate Market Reactions}2526The equity market response to hawkish surprises is consistent with H3a (negative equity effect): the ES contract exhibits a $-1.2$ basis point response ($p < 0.05$). To put this magnitude in perspective, a one-standard-deviation hawkish surprise generates an immediate equity decline roughly equivalent to the average hourly return on a non-announcement day, concentrated in a single minute.2728Among commodities, crude oil (CL) falls by 1.0 bps ($p < 0.05$), consistent with tighter policy reducing growth expectations and energy demand. Gold (GC) falls by 0.6 bps, as an inflation hedge becomes less attractive when policy tightens. The Dollar Index (DX) rises by 0.8 bps, consistent with higher expected rate differentials increasing dollar demand.2930The VIX response is $+11.2$ bps ($p < 0.05$, H3b): a one-standard-deviation hawkish surprise is associated with an 11.2 bps increase in VIX futures, about 0.5\% of the average VIX level. This is the largest immediate response in our sample. Treasury securities (ZN, ZF) show small, insignificant responses, possibly because our textual MPS is largely orthogonal to the rate expectations already embedded in Treasury futures.3132\subsubsection{Dynamic Response Evolution}3334The 45-minute post-announcement window shows that different asset classes adjust at different speeds:3536\textit{Equities (ES).} The initial decline ($-1.2$ bps at $t = 0$) deepens to $-3.8$ bps by $t = 15$ and $-6.8$ bps by $t = 45$. The cumulative response is 5.7 times the instantaneous reaction, so the first-minute price change captures only a fraction of the total adjustment.3738\textit{VIX futures.} The initial spike ($+11.2$ bps at $t = 0$) loses roughly half its magnitude by $t = 20$ and returns near its pre-announcement level by $t = 45$.3940\textit{Treasuries (ZN, ZF).} Responses become marginally significant only at $t = 30$--$45$, consistent with slower transmission to term premiums.4142\textit{Commodities (CL, GC).} Crude oil effects continue to grow through $t = 45$, consistent with the slower adjustment typical of physical commodity markets.4344These patterns support H3c for volatility---the VIX response peaks on impact and decays---but equity and commodity responses continue to build, foreshadowing the gradual tone effects documented below. The speed of adjustment varies across assets, which motivates the asset-specific decomposition.4546\subsection{Semantic Decomposition: Tone vs.\ Novelty Effects}47\label{sec:decomposition}4849We now separate tone from novelty. The dependent variables are log returns (testing H1) and realized volatility changes (testing H2). The regressors are the z-scored tone and novelty measures, entered separately and jointly.5051\subsubsection{Tone Effects on Asset Returns (H1)}5253A one-standard-deviation dovish shift in tone is associated with ES gains that build steadily over the post-announcement window: 3.8 bps by $h = 30$, 6.8 bps by $h = 60$, and 12.0 bps by $h = 120$ (Table~\ref{tab:irf_stance_ret_h}, H1a)---several days of average equity returns compressed into two hours. This is consistent with lower discount rates, higher growth expectations, and greater risk appetite.5455Safe-haven assets move in the opposite direction: at $h = 15$, gold falls by 3.1 bps and 10-year Treasuries (ZN) by 1.1 bps following dovish tone (H1b), consistent with a ``risk-on'' rotation out of safe havens. The Dollar Index response is small and changes sign across horizons ($+1.4$ bps at $h = 15$, $-4.0$ bps at $h = 120$).5657Tone effects grow stronger, not weaker, over the post-announcement window: the ES coefficient rises monotonically from 0.2 bps at $h = 5$ to 3.8 bps at $h = 30$ and 12.0 bps at $h = 120$ (Table~\ref{tab:irf_stance_ret_h}, H1c). This gradual amplification---rather than the immediate level shift that a frictionless model would imply---is consistent with sequential portfolio adjustment by heterogeneous participants (algorithms, institutions, retail).5859\subsubsection{Novelty Effects on Volatility (H2)}6061Novelty loads on volatility, not on returns. The VIX response to a one-standard-deviation increase in novelty is $-5.57$ bps ($p < 0.05$), meaning that genuinely new language is associated with \textit{lower} implied volatility. This sign is opposite to our ex ante prediction (H2a) but has a straightforward interpretation: a statement that departs substantially from the prior meeting's language sends a clearer signal about the Fed's current assessment, helping investors narrow the range of possible outcomes. A repetitive statement, by contrast, leaves open the question of whether the unchanged wording reflects genuine stability or simply a failure to update the language.6263The VIX novelty coefficient is largest in the first 5 minutes and falls to near zero by $t = 30$ (H2b). Novelty coefficients on directional returns (ES, CL, GC, DX) are small and insignificant (H2c). The combination---novelty predicts volatility but not returns---separates our measure from standard ``surprise'' variables, which conflate direction and information content.6465\subsubsection{Panel Minute-Level Results}6667Tables~\ref{tab:panel_logrv_stance}--\ref{tab:panel_logrv_novelty} report panel regressions of $\log(\text{RV})$ on the interaction of post-announcement indicators with semantic measures. The coefficient on Post$\times$Stance is negative and significant at 1\% for 6 of 7 contracts: ES ($-5.31$), VX ($-3.28$), ZN ($-5.25$), ZF ($-4.16$), CL ($-5.87$), and GC ($-6.03$). Only DX is insignificant ($+0.15$). The negative sign means that dovish stance is associated with lower post-announcement realized volatility---accommodative statements calm markets---while hawkish statements are followed by larger volatility increases, consistent with contractionary signals generating more repricing. By contrast, the Post$\times$Novelty coefficients (Table~\ref{tab:panel_logrv_novelty}) are smaller and significant only for the Treasury contracts (ZN: $-1.81$, $p < 0.01$; ZF: $-1.22$, $p < 0.10$).6869\subsubsection{Event-Level Results}7071Tables~\ref{tab:rolling_delta_rv_30min}--\ref{tab:rolling_delta_beta_30min} report event-level regressions with the interaction specification $\Delta Y_i = \alpha + \beta_1 \text{Stance} + \beta_2 \text{Novelty} + \beta_3 (\text{Stance} \times \text{Novelty}) + \varepsilon_i$. The stance$\times$novelty interaction is negative and significant for VIX ($-7.96$, $t = -3.12$, $p < 0.01$), ZF ($-2.48$, $t = -2.22$), ZN ($-1.66$, $t = -1.99$), and CL ($-8.61$, $p < 0.10$); Figure~\ref{fig:R6a} summarizes the coefficient estimates as a heatmap. The interaction indicates that stance and novelty reinforce each other: the volatility decline associated with a dovish statement is larger when the statement also departs substantially from prior language, whereas a statement that repeats the previous meeting's wording has a smaller volatility effect regardless of its tone.7273$R^2$ values are much higher for volatility than for returns: $\Delta\text{RV}$ regressions achieve 0.286 (ES), 0.268 (CL), and 0.245 (ZF), versus below 0.05 for most return regressions. The semantic variables explain more of the variation in volatility (which depends on information content) than in returns (which depend on the direction of the surprise in a noisy environment).7475\subsubsection{Local Projection Impulse Response Functions}7677Tables~\ref{tab:irf_stance_ret_h}--\ref{tab:irf_stance_x_novelty_abn_h} and Figures~\ref{fig:R10_stance}--\ref{fig:R10_abn_interaction} report local projection estimates. The VIX response to stance is negative at every horizon, statistically strongest between 5 and 30 minutes ($-14.74$ bps at $h = 5$, $-22.03$ at $h = 30$), and attenuates thereafter ($-14.27$ at $h = 120$, with much wider standard errors); the profile is hump-shaped, peaking near 30 minutes. The stance$\times$novelty interaction on abnormal VIX returns (Figure~\ref{fig:R10_abn_interaction}) is significant from $h = 5$ through $h = 120$, with the $t$-statistic reaching $-5.06$.7879The ES coefficient on stance grows monotonically from near zero at $h = 5$ to 12.0 bps at $h = 120$ (standard errors also grow). A frictionless model would predict an immediate level shift; the gradual increase we observe is more consistent with sequential adjustment by heterogeneous investors.8081\subsubsection{Cross-Asset Patterns (H4)}8283Risk assets (ES, CL) both rise after dovish tone, with similar timing (H4a). Safe havens (GC, ZN, ZF) fall, consistent with risk-on/risk-off. But the volatility responses differ across assets (H4b): VIX responds most to the stance$\times$novelty interaction, Treasury volatility responds mainly to stance alone, and commodity volatility responds to both. The return homogeneity and volatility heterogeneity suggest that the two channels operate with different relative strength across asset classes.8485\subsubsection{Pre-Announcement Placebo Tests}8687Figures~\ref{fig:placebo_stance}--\ref{fig:placebo_novelty} report pre-announcement placebo tests: we estimate the same IRF specification for cumulative returns from $-h$ to 0. If statement content is not anticipated, all pre-announcement coefficients should be zero. None is significant at 10\% across any ticker, horizon, or semantic measure. This rules out information leakage and pre-existing trends.8889\subsubsection{Multi-Method Robustness}9091Tables~\ref{tab:robustness_A}--\ref{tab:robustness_B} report five alternative inference methods for every event-level coefficient. We call a result ``robust'' if at least 3 of 5 methods give $p < 0.10$. The most robust results are: stance on $\Delta\log\text{RV}$ for ES, CL, GC, ZF, and ZN (each $\#\text{Sig} = 3$); stance on $\Delta\text{RV}$ for ES, CL, and DX (each $\#\text{Sig} = 3$); and novelty on $\Delta\text{RV}$ for ES and CL ($\#\text{Sig} = 4$). Figure~\ref{fig:rob_heatmap} displays these counts. Sub-period analysis (Figure~\ref{fig:rob_subperiod}) shows consistent coefficient signs across six Fed regimes, though magnitudes vary.9293With 7 assets and multiple dependent variables, we test many coefficients; results with $\#\text{Sig} = 1$ should be treated with caution. We rely on the Benjamini--Hochberg correction and the robustness counts to limit false discovery.9495\subsection{Economic Interpretation: Temporal Dynamics and Half-Lives}96\label{sec:halflife}9798We summarize the speed of adjustment using half-lives: the time for an initial effect to fall to half its peak. For exponential decay, $t_{1/2} = \ln(2)/\lambda$.99100The VIX response ($+11.2$ bps on impact) falls to half its peak within 15--20 minutes; reading the decay as approximately exponential gives a half-life of about 17.5 minutes. Once the statement text is known, uncertainty about the Fed's message dissipates quickly.101102Equity returns show the opposite pattern. The ES response to dovish tone \textit{grows} steadily over the post-announcement window, roughly tripling between $h = 30$ (3.8 bps) and $h = 120$ (12.0 bps). Fundamental repricing---revising expected cash flows and discount rates---takes longer than uncertainty resolution, consistent with gradual diffusion across heterogeneous investors.103104The two patterns together---fast volatility decay and slow return amplification---are hard to reconcile with a single channel. The informational dimension (is the statement new?) resolves quickly; the directional dimension (is it hawkish or dovish?) takes longer to price in.105106