spb/wp47_uqo

1# WP47 — Design and pre-registered analysis plan23**Title (working):** The Yield Curve at One-Minute Resolution: Nelson–Siegel Factor-Mimicking Portfolios from Treasury Futures4**Author:** Guillaume Manseau (Université Laval) · **Date frozen:** 2026-11-09 (git tag `design-frozen`, set before any result of §4–§6 is inspected)56## 1. Question and contribution78The Nelson–Siegel (NS) curve and its dynamic version (Diebold–Li 2006) summarise the Treasury yield curve by three factors —9level, slope and curvature — observed at the daily or monthly frequency because the inputs are end-of-day yields.10Nothing in the model requires that frequency. This paper asks what the three NS factors look like **minute by minute**,11over the full 23-hour CME session, from 2008 to 2026.1213Contribution. (i) A construction: factor-mimicking portfolios of Treasury futures that reproduce daily NS factor changes14and can be applied to one-minute futures returns, yielding intraday level, slope and curvature changes for ~4 700 sessions15and ~6 million minutes. The construction is validated **out of sample** against daily factors that are never used to form16the weights. (ii) New facts: the intraday anatomy of the three factors around FOMC statements, CPI and Employment releases17(which factor moves, how much of the daily factor variance is realised in a 30-minute window, how the mix has changed from the18zero-lower-bound era to the 2022–2026 tightening/easing cycle); the intraday periodicity of factor volatility; the realized19covariance structure of the factors (the sign and stability of level–slope correlation at high frequency, Epps-type20attenuation). (iii) A forecasting application: HAR models on realized factor variances versus daily-data benchmarks.2122Closest literature: Andersen, Bollerslev, Diebold & Vega (2007) on announcement effects in bond futures (single contracts, not23factors); Gürkaynak, Sack & Swanson (2005) and Swanson (2021) on target/path/LSAP factors from FOMC-window asset moves (factor24structure of the *surprise*, not of the *curve*); Fleming & Remolona (1999) on price formation around announcements;25Hansen (2023, JFEC) on a joint model of yields and realized yield-curve covariation from high-frequency data (daily realized26measures, not NS factors nor a futures-based intraday construction); Cieslak & Povala (2016) on information in the Treasury27market; Diebold & Rudebusch (2013) book. We did not find a paper that constructs minute-frequency NS factors from futures and28validates them against daily factors (searches of 2026-11-09 documented in `docs/literature_search.md`).2930## 2. Data3132| Input | Source | Use |33|---|---|---|34| 1-minute OHLCV, continuous front-contract series (raw splice), roots ZT (2y), ZF (5y), ZN (10y), TN (ultra-10), US (30y bond), UB (ultra bond) | FinData OS (FirstRate Data), dataset `market_bars.futures.1m.continuous_raw` v132, 2008-01-02 → 2026-11-06 (TN from 2016-01, UB from 2010-01) | intraday returns |35| Daily continuous ratio-adjusted series | FinData OS `market_bars.futures.1d.continuous_ratio` v133 | roll checks |36| Constant-maturity Treasury yields, 1m/3m/6m/1/2/3/5/7/10/20/30y | FRED `DGS*` (H.15), downloaded 2026-11-09 | daily NS factors (primary) |37| Gürkaynak–Sack–Wright zero-coupon curve & Svensson parameters | Fed `feds200628.csv`, downloaded 2026-11-09 | daily NS factors (robustness) |38| FOMC meeting & statement dates 2008–2026 | Fed historical/calendar pages, parsed | events |39| CPI and Employment Situation release dates | ALFRED release pages rid 10 / 50 | events (08:30 ET) |40| Effective federal funds rate | FRED `DFF` | regime definition |4142Session convention. A "yield day" t runs from 15:30 ET on business day t−1 to 15:30 ET on day t (H.15 CMT yields are43read at approximately 15:30 ET). Intraday returns are one-minute log price changes computed within the CME session only44(no return across the 17:00–18:00 ET maintenance break; no return across a roll splice; first bar after a gap > 5 minutes starts45a new segment). Minutes without a bar carry a zero return for the grid but are flagged; a minute enters the cross-section only46if all six (or five, pre-2016) roots trade.4748Known limitations to state: futures returns reflect the cheapest-to-deliver, carry and the futures–cash basis; the49construction identifies *changes* in factors, not levels; the 1-minute bars are open-to-open prices built from trades.5051## 3. Construction5253**3.1 Daily factors.** For each day t, fit $y_t(\tau)=\beta_{1t}+\beta_{2t}\frac{1-e^{-\lambda\tau}}{\lambda\tau}54+\beta_{3t}\left(\frac{1-e^{-\lambda\tau}}{\lambda\tau}-e^{-\lambda\tau}\right)$ by OLS on the 11 CMT maturities with55$\lambda=0.7308$ per year (curvature loading maximised at 30 months, Diebold–Li), giving $\beta_t=(L_t,S_t,C_t)$ in percentage56points. Robustness: $\lambda$ estimated by NLS on the full sample; GSW zero yields at 1–30 years.5758**3.2 Mimicking portfolios.** Let $r_t\in\mathbb{R}^K$ be the vector of daily futures log returns (percent) over the yield day,59$K=5$ (2008–2015) or $6$ (2016–). For each factor $k$ estimate by OLS on a trailing window60$\Delta\beta_{kt}=a_k+w_k' r_t+e_{kt}$. Weights $w_k$ are re-estimated every calendar quarter using the previous 3 years61(≥ 500 days) and applied to the following quarter only (strictly out of sample). Pre-specified alternatives: expanding62window; full-sample weights (in-sample upper bound); structural inversion using cheapest-to-deliver durations.6364**3.3 Intraday factors.** For minute m of day t, $\Delta\hat\beta_{t,m}=\hat W_{q(t)}\, r_{t,m}$ (no intercept). Realized65factor variance $RV^{(k)}_t=\sum_m \Delta\hat\beta^2_{k,t,m}$, realized covariance analogously, at 1, 5 and 30 minutes.6667## 4. Hypotheses (frozen)6869- **H1 (fidelity).** Out of sample, $\sum_m\Delta\hat\beta_{k,t,m}$ explains daily $\Delta\beta_{kt}$ with $R^2\ge0.90$ for70  level and slope and $\ge0.60$ for curvature; the slope coefficient of daily on cumulated intraday is within $[0.9,1.1]$.71  Fidelity is lower before 2016 (five roots) and in 2008–2009.72- **H2 (announcement anatomy).** In the [−5, +25]-minute window around FOMC statements the share of the yield day's realized73  variance is largest for slope, then level, then curvature; CPI and Employment releases load mainly on level and slope with a74  larger slope share after 2021 than during 2009–2015 (ZLB), when short-rate expectations were pinned. Variance shares in75  announcement windows are at least 10× the unconditional share of a 30-minute window (30/1380 ≈ 2.2%).76- **H3 (periodicity).** Factor volatility has a pronounced intraday pattern: a 08:30 ET spike, a maximum between 08:30 and77  11:00 ET, a minimum during the Asian session; curvature volatility is more concentrated in US hours than level volatility.78- **H4 (covariation).** The 1-minute level–slope realized correlation is negative on average, less negative at 5 and79  30 minutes (Epps effect), and its sign/magnitude differs between the ZLB period and 2022–2026.80- **H5 (forecasting).** HAR models on log realized factor variances beat (lower QLIKE and MSE, Diebold–Mariano at 5%) a81  GARCH(1,1) fitted to daily factor changes and a rolling 22-day variance, at horizons of 1, 5 and 22 days, out of sample82  2016–2026 with weights re-estimated monthly.8384Secondary/descriptive (not hypotheses): factor drift in the hours before announcements (pre-FOMC drift, Lucca–Moench852015), cumulative response paths, decomposition by meeting type (press-conference vs not).8687## 5. Inference and evaluation8889Newey–West (bandwidth 1.3 T^{1/2}) for daily regressions; block bootstrap (daily blocks) for event-window variance shares;90Diebold–Mariano with HAC for forecast comparisons; all tests two-sided, 5%. Samples: full (2008–2026), sub-periods912008–2009 (crisis), 2010–2015 (ZLB), 2016–2019 (normalisation), 2020–2021 (pandemic ZLB), 2022–2026 (tightening/easing).9293## 6. Outputs9495Tables: data coverage; daily factor summary; mimicking weights and OOS fidelity (H1); announcement variance shares (H2);96intraday periodicity (H3, figure); realized correlations (H4); HAR forecast evaluation (H5). Figures: intraday factor97paths on selected FOMC days; average cumulative response; intraday volatility signature; time series of realized factor98volatility; rolling fidelity $R^2$.99100## 7. What would falsify the construction101102If H1 fails (R² < 0.6 for level or slope), the paper is re-scoped to a methods note on why futures do not span the NS factors103(basis/CTD/term-premium reasons) and the event-study results are not reported as factor results.104