1% ============================================================================2\section{Results}3\label{sec:results}4% ============================================================================56\subsection{Daily factors and the mimicking portfolios}7\label{sec:results-daily}89Table~\ref{tab:dailyfactors} summarizes the daily factors. Over 2008--2026 the level averages 3.5 percent with a daily-change10standard deviation of 6 basis points, the slope $-2.0$ percent (7 basis points) and the curvature $-2.9$ percent (17 basis11points). Daily changes in level and slope have a correlation of \corrDailyLs{}: when the long end moves and the short end is12pinned, as it was for most of the sample, the level and the slope move by nearly equal and opposite amounts. The level and13slope changes correlate at 0.96 and 0.79 with the same factors computed from the GSW zero curve; the curvature at 0.70. The two14curves differ at the short end, where the CMT includes bills and the GSW curve starts at one year.1516Appendix Table~\ref{tab:weights} reports the mimicking weights. The level portfolio is short the 10-year, bond and ultra-bond17contracts and long the 2- and 5-year notes: a rally at the long end lowers the level, and the long position in the short18contracts strips out the component of long-end moves that is common with the short end. The slope portfolio is short the 2-year19note and long every longer contract: since $S=y(0)-L$, a rally concentrated at the short end---a fall in the short rate20relative to the level---lowers the slope factor, which is negative on average, and the short 2-year position delivers that sign. The curvature portfolio is short the 2- and 5-year notes and21long the bond contracts: a rally in the two- to five-year sector relative to the long end lowers the curvature, whose loading22peaks at 30 months. The weights are therefore not the inverse durations that a contract-by-contract mapping would give; they23are the long--short positions that isolate each factor from the others, and the 2-year note, whose returns are the least24correlated with the long contracts (daily correlation \corrDailyZfZn{} between the 5- and 10-year notes against25\corrDailyUsUb{} between the two bond contracts), carries the largest weights in absolute value. The contract set grows from26four (2011--2012) to five (ultra bond, from \firstQuarterFiveRoots{}) and six (ultra 10-year, from \firstQuarterSixRoots{}) as27each contract accumulates three years of history.2829\input{tables/tab_fidelity}30\input{tables/tab_fidelity_alt}3132\begin{figure}[tp]33\centering34\includegraphics[width=\textwidth]{figures/fig_fidelity.pdf}35\caption{\textbf{Out-of-sample fidelity by year.} $R^2$ of the daily factor change on the cumulated intraday change, by calendar36year, for the primary CMT target (eleven maturities) and the GSW zero-curve target (1--30 years), with 90-percent intervals from37resampling days within the year. Horizontal lines mark the pre-registered H1 thresholds (0.90 for level and slope, 0.60 for38curvature). Weights are re-estimated quarterly on the previous three years and are out of sample for the year shown.}39\label{fig:fidelity}40\end{figure}4142\subsection{H1: Out-of-sample fidelity}43\label{sec:results-fidelity}4445Table~\ref{tab:fidelity} and Figure~\ref{fig:fidelity} give the first result. The out-of-sample daily regression explains the46daily change in the level factor with an $R^2$ of \fidLevelFull{}, the slope factor with \fidSlopeFull{} and the curvature factor47with \fidCurvFull{} over 2011--2026. The cumulated minute series---the object the rest of the paper uses, summed over all48\nYieldDaysFactors{} yield days on which it exists---gives \fidCumLevelAll{}, \fidCumSlopeAll{} and \fidCumCurvAll{}, with49regression slopes of actual on cumulated changes of \fidCumLevelAllSlope{}, \fidCumSlopeAllSlope{} and \fidCumCurvAllSlope{}, so50the series is unbiased in scale as well as correlated and loses almost nothing to the minutes dropped for inactivity51(\shareDaysGeSixHundredPct{} of days have at least 600 minutes of complete cross-section; the median is52\medianMinutesFactors{}). The level factor passes the pre-registered threshold of 0.90 in every sub-period (\fidTLevelZlb{},53\fidTLevelMid{}, \fidTLevelPandemic{}, \fidTLevelRecent{}). The slope factor passes it only during the zero lower bound54(\fidTSlopeZlb{}) and falls to \fidTSlopeMid{} in 2016--2019 and \fidTSlopeRecent{} in 2022--2026. The curvature factor exceeds55its threshold of 0.60 in every sub-period except 2020--2021 (\fidTCurvPandemic{}). H1 is therefore supported for the level,56supported for the slope only when the short rate was pinned, and supported for the curvature with one exception.5758What the futures do and do not see is sharper in yield space. The implied changes in the 2-, 5-, 10- and 30-year yields,59$\Delta\hat y(\tau)=\Delta\hat L+\Delta\hat S f_2(\tau)+\Delta\hat C f_3(\tau)$, reproduce the corresponding CMT changes with60$R^2$ of \fidYTwoY{}, \fidYFiveY{}, \fidYTenY{} and \fidYThirtyY{}; the one-year yield with \fidYOneY{}; the three-month yield61with \fidYThreeM{}; and the Nelson--Siegel short rate $\Delta\hat L+\Delta\hat S$ has an $R^2$ of \fidYShortRateVsOneM{} against62the one-month bill. The intraday factors are a 2--30-year object. The slope and curvature factors inherit from the fitted63curve a short-end component that the futures cannot discipline, which is why their fidelity is below the level's and falls when64bills move with policy expectations, as they did from 2016 on and again in 2022--2026. We therefore do not report results for65the implied short rate, and we read ``slope'' and ``curvature'' below as the 2--30-year shape of the curve.6667Table~\ref{tab:fidelityalt} shows where the shortfall comes from. The \emph{cash-yield ceiling}---the same rolling regressions68with the daily changes in the cash 2-, 5-, 10- and 30-year CMT yields in place of the futures returns, the maturities the futures69stand in for with no basis, no roll and no cheapest-to-deliver---gives $R^2$ of \ceilLevel{}, \ceilSlope{} and \ceilCurv{}. The70futures therefore reach about 96 percent of what the four cash yields reach for the level and slope and 89 percent for the71curvature; the rest of the shortfall relative to one is what neither the futures nor the four cash yields see, which, given the implied-yield72fidelities above, is the segment below two years.73With the GSW zero curve, which starts at one year, as target the fidelities are \gswLevelFull{}, \gswSlopeFull{} and74\gswCurvFull{}. Adding the front three-month SOFR future as a seventh instrument in 2022--2026, the only period in which it trades75densely at the minute frequency, raises the slope $R^2$ from \fidSlopeLateNoSofr{} to \fidSlopeLateSofr{} and leaves the level76(\fidLevelLateSofr{}) and curvature (\fidCurvLateSofr{}) essentially unchanged: a three-month instrument helps little because the77unspanned component is the one- to twelve-month segment taken together, not the first three months alone.7879\subsection{Minute-level validation}80\label{sec:results-etf}8182Two checks bear on the minute-level series directly. The first is a spanning test (Appendix Table~\ref{tab:spanning}): for832019--2026, when all six contracts trade, we extract three principal components from the minute returns of five contracts and84ask how well they explain the sixth. During US hours three components explain \pcThreeOneMin{} of the one-minute return variance85of the six contracts and \pcThreeThirtyMin{} at thirty minutes; the held-out 10-year note is explained with $R^2$ of86\spanZnOneMin{} at one minute and \spanZnThirtyMin{} at thirty, the 2-year note with \spanZtOneMin{} and \spanZtThirtyMin{}. A87three-factor structure is present in the minute returns, with the usual attenuation from microstructure noise at the highest88frequency and at the short end, where the tick is large relative to the move.8990\begin{figure}[tp]91\centering92\includegraphics[width=\textwidth]{figures/fig_etf_crossval.pdf}93\caption{\textbf{Independent cross-check with Treasury ETFs.} Thirty-minute FOMC-window changes (basis points) in level, slope and94curvature from the futures mimicking portfolios (vertical axis) against the same changes from a duration-based construction on95five Treasury ETFs (horizontal axis) that uses no futures and no daily regression, 2011--2026 scheduled statements with ETF96coverage. The 45-degree line and the OLS fit are shown; correlations, slopes and the number of windows are in the panels. The97ETF construction uses fixed approximate durations, which scales its slope and curvature changes differently.}98\label{fig:etf}99\end{figure}100101The second check uses a different instrument set and a different construction (Appendix Table~\ref{tab:etf},102Figure~\ref{fig:etf}). The one-minute returns of five Treasury ETFs---SHY, IEI, IEF, TLH and TLT, which hold 1--3, 3--7, 7--10,10310--20 and 20+ year Treasuries---are converted to yield changes at the funds' approximate maturity points through their durations104and fitted to the Nelson--Siegel loadings minute by minute, with no daily regression and no futures. Over the 09:35--15:55~ET105window the two constructions have a correlation of \etfCorrLevelOne{} at one minute and \etfCorrLevelThirty{} at thirty for the106level, \etfCorrSlopeThirty{} and \etfCorrCurvThirty{} at thirty minutes for the slope and curvature, and \etfDailyLevel{} for the107level cumulated over regular hours. On the \etfFomcN{} FOMC windows the correlations are \etfFomcLevel{}, \etfFomcSlope{} and108\etfFomcCurv{}. The ETF series are noisier and their fixed durations are approximate, so the regression slopes of futures-based on109ETF-based changes are below one for all three factors and well below one for slope and curvature; the ETF construction is a check110of direction and timing, not of scale. The agreement on the level and on announcement windows, where the signal is large, is the111relevant evidence: two constructions that share no data and no estimation step see the same factor moves.112113\subsection{H2: Announcements}114\label{sec:results-events}115116\begin{figure}[tp]117\centering118\includegraphics[width=\textwidth]{figures/fig_sample_days.pdf}119\caption{\textbf{Four announcement days at one-minute resolution.} Cumulative changes (basis points) in the level, slope and120curvature factors and in the implied 2- and 10-year yields over the yield day (15:30~ET of the previous business day to12115:30~ET) for the FOMC statements of 19 June 2013 and 15 June 2022, the CPI release of 10 November 2022 and the Employment122report of 2 August 2024. The vertical line marks the scheduled release time. Factors are the out-of-sample mimicking-portfolio123changes of equation~\eqref{eq:intraday}; the curvature is on the factor scale, whose loading on any yield is at most 0.30.}124\label{fig:sample}125\end{figure}126127Figure~\ref{fig:sample} shows four days. On 19 June 2013, the taper-tantrum FOMC, the level rises and the slope falls through128the statement and the press conference, with the implied 2-year and 10-year yields ending the yield day 9 and 13 basis points129higher, and the curvature factor also rises. On 15 June 2022, the 75-basis-point hike, the 2-year yield falls 24 basis points130over the day, about half of it after the 14:00 statement and through the press conference, as the market reads the path as less hawkish than priced; in131factor terms this is almost entirely a fall in the curvature (75 basis points on the factor scale), the level and slope barely132moving. On 10 November 2022 the soft CPI print moves the implied 2-year yield by 17 basis points in the first minute after 08:30, 20 within five minutes133and 23 over the day, again mostly through the curvature and through offsetting level and slope changes. On 2 August 2024 the134weak Employment report lowers the 2-year yield by 25 basis points and the 10-year by 19; the level falls 12 basis points, the135slope rises by the same amount and the curvature falls 64, so the move is a bull steepening concentrated in the two- to136five-year sector, not a parallel shift. Three of the four days are curvature events in Nelson--Siegel terms, which is the first137indication that the curvature factor is where announcement risk lives once the short rate is no longer pinned.138139\begin{figure}[p]140\centering141\includegraphics[width=\textwidth,height=0.74\textheight,keepaspectratio]{figures/fig_event_heatmap.pdf}142\caption{\textbf{Every announcement, one row each.} Cumulative change in the implied 2-year yield (basis points) from five minutes143before the release, minute by minute from $-30$ to $+120$ minutes, for every scheduled FOMC statement (A), CPI release (B) and144Employment report (C) of 2011--2026 with complete coverage, oldest at the bottom; the colour scale is clipped at $\pm15$ basis145points (blue: fall, vermillion: rise) and the horizontal lines mark the regime boundaries of 16 December 2015, 1 January 2020 and1461 January 2022. The dashed vertical line is the start of cumulation and the solid one the release; on FOMC days the line at $+30$147minutes is the start of the press conference. In grayscale the figure shows magnitude but not sign.}148\label{fig:heatmap}149\end{figure}150151Figure~\ref{fig:heatmap} shows every event. The 08:30 releases are vertical steps: the colour appears at the release minute and152stays constant to the right, and the step is larger and more frequent after 2021. The FOMC rows show a step at the statement and a153second, often larger, shading change from the press conference onward, and the 2015--2019 and 2022--2026 rows are more coloured154than the zero-lower-bound rows, when the 2-year yield had little room to move.155156\input{tables/tab_events_a}157\input{tables/tab_events_b}158159Tables~\ref{tab:eventsa} and~\ref{tab:eventsb} aggregate over \nFomcEventsUsed{} scheduled FOMC statements, \nCpiEventsUsed{} CPI160releases and \nEmpEventsUsed{} Employment releases from 2011 to 2026. The thirty-minute FOMC window carries, on average,161\fomcRvShareLevelPct{} of the yield day's realized level variance, \fomcRvShareSlopePct{} of the slope variance and162\fomcRvShareCurvPct{} of the curvature variance, against \benchSharePct{} for an arbitrary window of that length. The Employment163report carries \empRvShareLevelPct{}, \empRvShareSlopePct{} and \empRvShareCurvPct{}, the CPI release \cpiRvShareLevelPct{},164\cpiRvShareSlopePct{} and \cpiRvShareCurvPct{}. The shares are \rvShareRatioMin{} to \rvShareRatioMax{} times the benchmark;165H2 predicted at least ten times, which holds for the three Employment shares and for the FOMC curvature share but not for the166FOMC level and slope shares nor for the three CPI shares. The ordering within the FOMC window (curvature above slope above level) is not the predicted one167(slope above level above curvature), and the Employment report, not the FOMC statement, is the single most concentrated event.168Against placebo windows at the same clock time on matched days, the standard deviation of the ten-year change in the FOMC window is169\fomcRatioTen{} times its placebo value (Table~\ref{tab:eventsa}); the ratios for the two 08:30 releases are of the same order.170171The composition of the response has changed with the policy regime. In 2011--2015 the FOMC window moved the 2-year yield by1723.9 basis points on average and the CPI release moved nothing: window standard deviations of \cpiZlbSdLevel{} and173\cpiZlbSdSlope{} basis points for level and slope, a ten-year ratio to placebo of \cpiZlbRatioTen{}, and a level variance share174of \cpiZlbRvShareLevelPct{}. In 2022--2026 the CPI release moves the implied two-year yield by \cpiLateSdTwo{} basis points and175the curvature by \cpiLateSdCurv{} basis points in thirty minutes---a ten-year ratio of \cpiLateRatioTen{} and a curvature176variance share of \cpiLateRvShareCurvPct{}---while the FOMC statement moves the two-year yield by \fomcLateSdTwo{} basis points.177When policy is data-dependent and the data arrive at 08:30, the yield-curve risk of monetary policy is realized on CPI and178payroll days rather than on FOMC days, and it is realized in the two- to five-year sector, which is where the curvature factor179lives. H2's prediction of a larger slope share after 2021 than during the zero lower bound is supported for the CPI release and180not for the FOMC statement, whose level and slope shares fall from \fomcZlbRvShareLevelPct{} to \fomcLateRvShareLevelPct{}181while its curvature share stays at \fomcLateRvShareCurvPct{} against \fomcZlbRvShareCurvPct{} during the zero lower bound.182183\begin{figure}[tp]184\centering185\includegraphics[width=\textwidth]{figures/fig_event_paths.pdf}186\caption{\textbf{Cumulative response paths around scheduled releases.} Root mean square across events of the cumulated factor187change (basis points) from 60 minutes before to 120 minutes after the release time, for FOMC statements, CPI releases and188Employment reports, 2011--2026, with 90-percent bands from resampling events. Series: level, slope, curvature, short rate189($\Delta L+\Delta S$) and implied 10-year yield; the short rate is shown for completeness although Section~\ref{sec:results-fidelity}190shows that the futures do not identify it. Events require complete coverage over the whole window, so $n$ is slightly below the191counts of Table~\ref{tab:eventsa}.}192\label{fig:paths}193\end{figure}194195Figure~\ref{fig:paths} shows the root-mean-square cumulative response from 60 minutes before to 120 minutes after each release.196The 08:30 releases are step functions: the response is complete within five minutes and flat thereafter. The FOMC response is not:197the ten-year yield's window standard deviation rises from \fomcWFifteenSdTen{} basis points at $[-5,+15]$ to198\fomcWTwentyfiveSdTen{} at $[-5,+25]$ and \fomcWNinetySdTen{} at $[-5,+90]$, and in 2022--2026 the curvature's from199\fomcLateWTwentyfiveSdCurv{} to \fomcLateWNinetySdCurv{} basis points, so the press conference adds as much curve risk as the200statement. The pre-announcement drift in the level factor over the 24 hours before FOMC statements is \preFomcLevel{} basis points201(bootstrap interval \preFomcLevelLo{} to \preFomcLevelHi{}), not distinguishable from zero; the bond-market counterpart of the202equity pre-FOMC drift of \citet{lucca2015pre} is not visible in the factors.203204\subsection{Impulse responses: does the announcement move last?}205\label{sec:results-irf}206207\input{tables/tab_lp}208209\begin{figure}[tp]210\centering211\includegraphics[width=\textwidth]{figures/fig_lp.pdf}212\caption{\textbf{Local-projection responses to announcement-window shocks.} Coefficient $\beta_h$ of equation~\eqref{eq:lp}: the213cumulated change from five minutes before the release to horizon $h$ (25 minutes to 10 yield days) in the implied 2-year yield,214the implied 10-year yield, the level and the slope, per basis point of the 2-year change in the $[-5,+25)$ window, across scheduled215FOMC statements (A), CPI releases (B) and Employment reports (C), 2011--2026, with 95-percent intervals from resampling events.216The dotted line at one is full persistence of the initial 2-year move; the vertical dashed line separates intraday from daily217horizons. The curvature coefficient, which is on a different scale, is in Table~\ref{tab:lp}.}218\label{fig:lp}219\end{figure}220221The event tables measure what happens in thirty minutes. Table~\ref{tab:lp} and Figure~\ref{fig:lp} ask whether it lasts, by222projecting the cumulated change at horizons from 25 minutes to ten yield days on the initial 2-year move in the window. Two223patterns stand out. First, FOMC moves persist and extend. The 2-year response per basis point of the window move is224\lpFomcTwoYDTen{} at ten days (bootstrap interval \lpFomcTwoYDTenLo{} to \lpFomcTwoYDTenHi{}), so a statement that moves the2252-year yield by one basis point in thirty minutes is associated with a move of more than one and a half basis points two weeks226later, and the 10-year yield, which moves \lpFomcTenYMTwentyFive{} basis points per basis point of 2-year in the window, has moved227\lpFomcTenYDTen{} by day ten. Second, CPI moves are partly reversed: the 2-year coefficient falls from one in the window to228\lpCpiTwoYDOne{} the next day and \lpCpiTwoYDTen{} at ten days (interval \lpCpiTwoYDTenLo{} to \lpCpiTwoYDTenHi{}), while229Employment moves neither extend nor reverse (\lpEmpTwoYDTen{} at ten days). The intraday horizons show no drift in any direction230for any release: price discovery is complete at 25 minutes and the subsequent dynamics are a matter of days, not minutes. The231daily-horizon intervals are wide, as they must be with 126 to 190 events and ten-day cumulated changes whose standard deviation232is several times that of the window move, and the FOMC extension excludes one only at day ten (the day-five interval is 0.85 to 1.59). We233read the pattern as consistent with FOMC statements carrying information about the path of policy that the market continues to234price in, and CPI surprises carrying information that is partly transitory, but the local projections identify associations, not235shocks.236237\input{tables/tab_connect}238239\begin{figure}[tp]240\centering241\includegraphics[width=0.95\textwidth]{figures/fig_girf.pdf}242\caption{\textbf{Cumulative generalized impulse responses, five-minute VAR.} Cumulated response (basis points) of the short rate,243the level and the curvature to a one-standard-deviation generalized shock to each variable \citep{pesaran1998generalized}, over244one hour, from a VAR on five-minute factor changes in US hours (08:00--16:00~ET) estimated on within-day observations, for2452011--2026 (A), 2011--2015 (B) and 2022--2026 (C); lag order by BIC. Bands are 95-percent intervals from resampling the residual246covariance. A response that settles below its impact value indicates partial reversal of the shock within the hour.}247\label{fig:girf}248\end{figure}249250Table~\ref{tab:connect} and Figure~\ref{fig:girf} describe the within-hour dynamics. The five-minute VAR finds little251cross-factor predictability: the Diebold--Yilmaz total connectedness is \varTotalFull{} percent over 2011--2026, \varTotalZlb{}252during the zero lower bound and \varTotalRecent{} in 2022--2026, and the contemporaneous residual correlations carry almost all253the comovement. The one-hour cumulative responses settle at \varRatioSrFull{} of the impact for a shock to the short rate,254\varRatioLevelFull{} for the level and \varRatioCurvFull{} for the curvature: within the hour, part of a five-minute short-rate255move is reversed, which is the signature of bid--ask bounce and stale quotes at the short end rather than of information, while256level moves are permanent. The daily volatilities are a different matter. The HAR-VAR on log realized variances gives a total257connectedness of \volTotal{} percent, with level and slope volatility each net transmitters (\volNetLevel{} and \volNetSlope{}258percentage points) and curvature volatility a net receiver (\volNetCurv{}). The rolling index (Figure~\ref{fig:connect}) moves259between \volRollMin{} and \volRollMax{} percent, peaking in \volRollMaxDate{} and troughing in \volRollMinDate{}: when260volatility is high and driven by common shocks, as in 2020--2021, it is also more connected across factors.261262\begin{figure}[tp]263\centering264\includegraphics[width=\textwidth]{figures/fig_connect.pdf}265\caption{\textbf{Volatility connectedness across factors, 2011--2026.} A: Diebold--Yilmaz total connectedness index (percent)266from a VAR(2) on the daily log realized variances (five-minute sampling) of level, slope and curvature, 10-day generalized267forecast-error variance decomposition, 250-day rolling windows stepped every five days. B: net directional connectedness268(to others minus from others, percentage points) of each factor's volatility. Shaded areas: 2011--2015 and 2020--2021269zero-lower-bound periods.}270\label{fig:connect}271\end{figure}272273\subsection{H3: Intraday periodicity}274\label{sec:results-periodicity}275276\begin{figure}[tp]277\centering278\includegraphics[width=\textwidth]{figures/fig_periodicity.pdf}279\caption{\textbf{Intraday periodicity of factor volatility.} Root mean square one-minute change (basis points per minute),28015-minute centred moving average, by minute of the day in Eastern time from 18:00 to 17:00, for level, slope and curvature, on281days with and without a scheduled FOMC, CPI or Employment release, 2011--2026. The smoothing damps the 08:30 spike relative to the282unsmoothed values quoted in the text; vertical lines mark 08:30 and 14:00~ET.}283\label{fig:periodicity}284\end{figure}285286Figure~\ref{fig:periodicity} plots the root-mean-square one-minute factor change by minute of the day, smoothed over fifteen287minutes, for announcement and non-announcement days. On non-announcement days the level factor's smoothed volatility peaks at288\perPeakLevel{}~ET and troughs at \perTroughLevel{}~ET; the 08:30 minute itself has a root-mean-square change of289\perSpikeLevel{} basis points against a median minute of \perMedianLevel{}, because releases other than the CPI and the290Employment report (producer prices, retail sales, GDP, claims) also arrive at 08:30; on our announcement days the 08:30 minute291reaches \perSpikeEvLevel{} basis points. Volatility between 08:30 and 11:00~ET is \perUsAsiaLevel{} times its level in Asian292hours (19:00--05:00~ET) for the level factor, \perUsAsiaSlope{} for the slope and \perUsAsiaCurv{} for the curvature. H3's293timing predictions are supported; its prediction that the curvature is more concentrated in US hours is not---the curvature294factor's day--night ratio is the smallest of the three. The curvature portfolio has the largest gross weights, so overnight,295when trading is thin, a larger share of its one-minute variance is tick noise, which raises its night-time floor.296297\subsection{H4: Covariation and the noise benchmark}298\label{sec:results-cov}299300\input{tables/tab_correlations}301302\begin{figure}[tp]303\centering304\includegraphics[width=\textwidth]{figures/fig_signature.pdf}305\caption{\textbf{Volatility and correlation signatures.} A: average daily realized variance (bp$^2$) of each factor by sampling306interval (1, 5, 30 minutes). B: realized correlations between factor changes by sampling interval; dotted lines are the daily307CMT correlations over 2011--2026 and the dashed line is the level--slope correlation implied by independent tick-size noise in the308six contracts.}309\label{fig:signature}310\end{figure}311312\begin{figure}[tp]313\centering314\includegraphics[width=\textwidth]{figures/fig_realized_vol.pdf}315\caption{\textbf{Realized factor volatility, 2011--2026.} Square root of the daily realized variance from five-minute sampling316(basis points per day) and its 22-day moving average, for level, slope and curvature. The vertical axes are truncated at the31799.7th percentile and the number of truncated days is noted in each panel. Shaded areas: 1 January 2011--16 December 2015 and31815 March 2020--31 December 2021 zero-lower-bound periods.}319\label{fig:realizedvol}320\end{figure}321322Table~\ref{tab:correlations} and Figure~\ref{fig:signature} report the realized correlations; Figure~\ref{fig:realizedvol} the323realized volatilities over time. The one-minute level--slope correlation is \corrLsOneMin{} over 2011--2026, \corrLsFiveMin{} at324five minutes and \corrLsThirtyMin{} at thirty, against \corrLsDaily{} in the daily CMT data. The pre-registered prediction---negative325at one minute and less negative at coarser sampling---is rejected in form: the correlation becomes \emph{more} negative as the326interval lengthens. The reason is the one the design review anticipated. The level and slope portfolios load on the same327contracts with opposite signs, so independent rounding noise in the contract prices induces a correlation between them of328\noiseCorrLs{} on average, computed from the weights and the contracts' tick sizes alone (Table~\ref{tab:correlations}). The329one-minute realized value is \corrLsGapNoise{} away from that benchmark, and the tick-noise variance is about330\noiseShareLevelOneMinPct{} of the level factor's one-minute realized variance (the one-minute realized variance of the level is331\rvOneOverThirtyLevel{} times its thirty-minute value and the curvature's \rvOneOverThirtyCurv{} times). Noise is therefore a332large part, not the whole, of the one-minute comovement; as sampling coarsens it averages out and the correlation converges333towards the strongly negative value that the daily data also show. The level--curvature correlation behaves differently:334\corrLcOneMin{} at one minute, \corrLcThirtyMin{} at thirty and \corrLcDaily{} in daily data, with a sign that differs across335regimes. H4's regime prediction is supported in the sense that the five- and thirty-minute correlations differ between3362011--2015 and 2022--2026, but the level--slope correlation is so close to $-1$ in both that the difference is not economically337interesting; the regime dependence is in the level--curvature and slope--curvature pairs. For every result that involves338variances or covariances we therefore use five-minute sampling.339340\subsection{H5: Forecasting realized factor variance}341\label{sec:results-forecast}342343\input{tables/tab_har}344345Table~\ref{tab:har} compares HAR forecasts of the realized factor variances with a GARCH(1,1) on the daily factor changes and a34622-day rolling variance, out of sample from January 2016 to November 2026. HAR has the lowest QLIKE and the lowest mean squared347error for every factor at every horizon. The QLIKE gains over GARCH are \harGainLevelHOne{}, \harGainSlopeHOne{} and348\harGainCurvHOne{} at one day for level, slope and curvature, and remain positive at 22 days (\harGainLevelHTwentyTwo{},349\harGainSlopeHTwentyTwo{}, \harGainCurvHTwentyTwo{}). The QLIKE Diebold--Mariano statistics range from \harDmMin{} to350\harDmMax{}; \harHolmBelowFive{} of the nine are significant at the five-percent level after the Holm adjustment and351\harHolmBelowTen{} at ten percent, the exceptions being the level at the longer horizons. Under mean squared error, which the352pre-registered H5 also named, HAR is also the best model in every cell, but only \harDmMseSigFive{} of the nine comparisons is353significant before the Holm adjustment and none after it, because the MSE loss is dominated by a few extreme days. H5 is therefore supported under QLIKE and not under MSE.354The gains over the rolling variance are larger under both losses. The result is the fixed-income-factor analogue of the355familiar finding that realized measures forecast volatility better than daily-return models, and its practical content is that356a risk manager who tracks exposures to level, slope and curvature can forecast the variance of those exposures from the futures357tape rather than from the previous month of daily yield changes.358