spb/wp47_uqo

1% ============================================================================2\section{Introduction}3\label{sec:introduction}4% ============================================================================56The three-factor curve of \citet{nelson1987parsimonious}, in the dynamic form given to it by \citet{diebold2006forecasting},7is the workhorse description of the Treasury yield curve. Level, slope and curvature summarize a dozen yields with three8numbers, forecast well, and carry the economic interpretation that central banks and market participants actually use.9They are also, almost without exception, observed once a day. The reason is practical rather than conceptual: the inputs are10end-of-day constant-maturity or zero-coupon yields, and nothing finer is published. Yet the questions one would most like to11ask about these factors are intraday questions. Which factor moves when the Federal Open Market Committee (FOMC) speaks?12How much of a day's yield-curve risk is realized in the thirty minutes after a price or employment release? Is the initial13move reversed or extended over the following days? Does the curvature of the curve, the factor most often dismissed as noise,14respond to news at all? Is the comovement of level and slope a feature of the curve or an artefact of the sampling? Daily data15cannot answer these questions, and the intraday Treasury quote data that could answer them directly are proprietary,16discontinuous across venues, and short.1718This paper offers a way around the constraint that uses only data that are continuously observed. Six Treasury futures19contracts---the 2-year, 5-year and 10-year notes, the ultra 10-year, the classic bond and the ultra bond---trade on the CME for2023 hours a day and have done so, in the case of the first three and the bond, since well before 2008. Their one-minute21prices are a complete, time-stamped record of the Treasury market's reaction to every scheduled release in the sample,22including the 08:30 releases that fall outside equity hours. We estimate, from daily data alone, the linear combination of23futures returns that best tracks the daily change in each Nelson--Siegel factor, in the spirit of the mimicking portfolios of24\citet{huberman1987mimicking} and the tracking portfolios of \citet{lamont2001economic}, and we apply these weights to25one-minute returns of the most-traded contract of each session. The result is a minute-by-minute series of changes in level,26slope and curvature on \nYieldDaysFactors{} trading days and \nMinutesFactorsM{} million minutes, from 2011 to 2026, with27weights that are re-estimated every quarter on a trailing three-year window and are therefore strictly out of sample for the28quarter to which they are applied. Figure~\ref{fig:cartography} maps the data, the pipeline and the validation loops.2930The construction is only useful if it is validated, and the first contribution of the paper is the validation. Summing the31intraday factor changes over a ``yield day'' that ends at 15:30~ET, when the Treasury's constant-maturity yields are read,32gives a daily change that can be compared with the daily change in the factor estimated from those yields. The comparison is33out of sample because the weights were estimated on earlier data, and it is a test of the series actually used, because the34cumulated minutes are the series. Over all \nYieldDaysFactors{} days the cumulated intraday series explains the daily change35in the level factor with an $R^2$ of \fidCumLevelAll{}, the slope factor with \fidCumSlopeAll{} and the curvature factor with36\fidCumCurvAll{}; the implied 2-, 5-, 10- and 30-year yields are reproduced with $R^2$ between \fidYTwoY{} and \fidYTenY{}.37We also show what the futures cannot see. The implied 3-month yield has an $R^2$ of \fidYThreeM{} and the Nelson--Siegel38short rate, the sum of level and slope, has none: no futures contract in the set has a maturity below two years, and the39short end of the fitted curve is an extrapolation that the futures do not discipline. Regressing the daily factor changes on40changes in the cash 2-, 5-, 10- and 30-year yields---the maturities the futures stand in for, without any basis or roll---raises41the $R^2$ to \ceilLevel{}, \ceilSlope{} and \ceilCurv{}, so the futures reach most of what the corresponding cash yields can42reach; the remainder is the bill segment that neither the futures nor the four cash yields span. Adding the front three-month43SOFR future as a seventh instrument in 2022--2026 raises the slope fidelity only marginally (\fidSlopeLateNoSofr{} to44\fidSlopeLateSofr{}). We also build the factors a second way, from five Treasury exchange-traded funds whose returns are45converted to yield changes through their durations and fitted to the Nelson--Siegel loadings minute by minute, with no daily46regression at all. The two constructions agree in direction and timing for the level factor and on FOMC windows for all three factors, though47not in scale for slope and curvature.4849The second contribution is a set of facts about when yield-curve factor risk is realized and whether it lasts. A50thirty-minute window around a scheduled FOMC statement accounts, on average, for \fomcRvShareLevelPct{} of the yield day's51realized level variance, \fomcRvShareSlopePct{} of the slope variance and \fomcRvShareCurvPct{} of the curvature variance,52against an unconditional share of \benchSharePct{} for a window of that length; the Employment Situation report is larger53still, at \empRvShareLevelPct{} of level variance, and the Consumer Price Index release sits in between. Measured against54placebo windows at the same clock time on matched non-announcement days, the standard deviation of the ten-year change in the55FOMC window is \fomcRatioTen{} times its placebo value. The composition of the response has changed: during the zero-lower-bound56years the CPI release barely moved the curve, while in 2022--2026 it moves the implied two-year yield by \cpiLateSdTwo{} basis57points and the curvature factor by \cpiLateSdCurv{} basis points in thirty minutes, more than the FOMC statement itself.58Local projections of the subsequent path on the window move show that FOMC moves persist and, if anything, extend over the59following two weeks (\lpFomcTwoYDTen{} basis points per basis point at ten days for the two-year yield), whereas CPI moves are60partly reversed on average (\lpCpiTwoYDTen{}, with an interval that includes one). A five-minute vector autoregression finds little cross-factor dynamics within the hour61(total connectedness of \varTotalFull{} percent), but the daily volatilities of the three factors are tightly connected62(\volTotal{} percent), with level and slope volatility transmitting to curvature volatility and not the reverse. These are63descriptive statements about variance and persistence, not identified causal effects; the high-frequency identification64literature \citep{kuttner2001monetary,gurkaynak2005actions,nakamura2018high,swanson2021measuring} uses the same windows for a65different purpose, and we relate our factors to it in the discussion.6667The third contribution concerns the volatility and comovement of the factors at high frequency. Factor volatility has a68pronounced intraday periodicity, with a spike at 08:30~ET, a maximum in the first hours of the US session and a trough in69Asian hours. The one-minute realized correlation between level and slope changes is \corrLsOneMin{}; independent tick-size70rounding noise in the six contracts alone would produce \noiseCorrLs{}, because the level and slope portfolios load on the same71contracts with opposite signs, and such noise accounts for about \noiseShareLevelOneMinPct{} of the one-minute variance of the72level factor. At five- and thirty-minute sampling the correlation remains strongly negative, as in the daily data, so the73comovement is real; but one-minute factor covariances cannot be read as information about the curve, and we use five-minute74sampling for covariation and forecasting. Heterogeneous autoregressive (HAR) models in the spirit of \citet{corsi2009simple}75fitted to the realized factor variances forecast those variances better than a GARCH(1,1) fitted to the daily factor changes76under the QLIKE loss at horizons of one, five and 22 days for all three factors, with \harHolmBelowFive{} of the nine77comparisons significant at five percent after a Holm adjustment; under mean squared error the ranking is the same but only78\harDmMseSigFive{} comparison is significant, so the pre-registered forecasting hypothesis is supported for one of its two79loss functions.8081The paper is a measurement paper and we try to state its limits as precisely as its results. The intraday factors are changes,82not levels; they are defined up to the mimicking weights, which absorb the futures--cash basis, the cheapest-to-deliver option83and duration drift; they do not see the bill segment or the Nelson--Siegel short rate; and at the one-minute frequency they84inherit the microstructure noise of the underlying contracts. Within those limits, the construction turns a daily object into an85intraday one with data that are available to any researcher with access to futures prices, and the validation shows how much86is lost in the process. The design, hypotheses and thresholds of the paper were written and frozen before any intraday result87was computed; a referee-style review of that design was obtained before the event-study results were inspected; three88referee-style reviews of a first complete draft led to a rebuild of the return panel from individual contracts and to several89corrected claims. Appendix~\ref{app:design} lists every change.9091The remainder of the paper is organized as follows. Section~\ref{sec:literature} places the construction in the literature.92Section~\ref{sec:data} describes the futures, yield and calendar data and the session conventions. Section~\ref{sec:methodology}93sets out the daily factor estimation, the mimicking portfolios, the realized measures, the dynamic specifications and the94hypotheses. Section~\ref{sec:results} reports the validation, the announcement anatomy and impulse responses, the intraday95periodicity, covariation and connectedness, and the forecasting results. Section~\ref{sec:robustness} examines alternative96targets, instruments, sampling schemes and timing. Section~\ref{sec:conclusion} concludes.97