01Intended audience

Heads of research, data engineers and technical owners preparing rates data for a systematic process. The study is also the worked example behind stage 01 of the Research-to-Production sequence: a data-source ledger produced before any hypothesis is tested.

02Methodology

Two spot-rate series were retrieved from the European Central Bank's Data Portal through its public SDMX interface and joined on the observation date. The slope is defined as the ten-year spot rate minus the two-year spot rate, in percentage points. The daily series is reduced to month-end observations for the figure; the daily file is published unchanged as the download.

The procedure is deliberately minimal. The purpose of a data study is not analysis but documentation: to fix what the series is, where it comes from, how it is constructed, what changes it and when it was last observed, so that any later hypothesis can be judged against a known input.

03Data sources

04Assumptions

• The fitted spot curve is an adequate summary of the AAA government market at the two tenors. Fitted curves smooth through individual bonds; they are not tradable instruments.
• The two-year point is used as the short end because it is the shortest tenor at which the fitted curve is stable across the whole sample; the money-market end is out of scope for this study.
• Month-end sampling is a presentation choice. Every statement in Findings is a statement about the month-end series unless it says otherwise.

05Findings

These are descriptive facts about the input series, computed at build time from the downloaded data. They are not a view on rates.

• The slope ranged from -0.61 percentage points (2023-06-30) to +2.65 (2009-05-29) across 265 month-ends.
• The series crosses zero. Any hypothesis that treats the slope as a regime variable must specify how sign changes and near-zero readings are handled before estimation, which is what RN-001 does.
• The latest observation (2026-09-28) is +0.40 percentage points with the two-year at 3.23 % and the ten-year at 3.63 %.
• The daily file is complete on the common business-day calendar of the two series; no interpolation was applied.

06Limitations

• Composition changes. The AAA sample is defined by ratings. When a member state's rating changes, the bonds in the sample change, and the fitted curve moves for a reason unrelated to market pricing of the remaining issuers. Any regime analysis must carry a composition-change flag alongside the series.
• Model artefacts. Svensson fitting imposes a functional form. Differences between fitted and observed yields are largest at the ends of the curve and during dislocations. The two-year point is exposed to this.
• Not an investable series. Spot rates are derived quantities. A system that trades the slope must be specified against instruments (futures, swaps, cash bonds) and their costs, not against this series.
• Vintage. The download reflects the ECB database as of 2026-09-30. Corrections by the provider would change past values; the pinned hash in the reproducibility manifest is the only guarantee of an identical input.

07Implementation considerations

• Ingest through the SDMX endpoint with an explicit user agent and retry policy; store the raw CSV, the parsed table and the join, each with a content hash and the retrieval timestamp.
• Treat the ECB's OBS_STATUS and BREAKS fields as first-class columns; a break flag should stop the pipeline for review rather than pass silently.
• Fix the cut-off rule in writing: which observation date is the last admissible input for a decision taken at a given time on a given day.
• Schema tests: two numeric columns, monotonic business-day index, no duplicate dates, both tenors present on every date, values inside a declared plausibility band.
• Version the derived slope separately from the source series; the derivation is code and belongs in the manifest with the code hash.

08Related research

• RN-001
  Term-premium regimes in euro-area rates: a testable specification
  Macro · 2026-09-30
• SN-001
  A reproducibility manifest for research-to-production handover
  Systems · 2026-09-30

09Disclosure

Cite as: Solano, F. (2026). Euro-area AAA curve slope, 2004 to 2026: source ledger and data-readiness assessment. SINTESIS Data Study DS-001, v1.0, Berlin, 2026-09-30. https://sintesismacro.com/en/research/ds-001-euro-area-aaa-curve-slope/

01Intended audience

Heads of research, portfolio managers with internal quantitative teams and model-validation functions. No prior exposure to the literature is assumed; the arithmetic is shown.

02The problem, stated

Strategy research is a search. A team tries lookbacks, thresholds, universes, rebalancing rules and cost assumptions, and reports the configuration that looked best. Even if none of the configurations has any real edge, the best of N noisy backtests will show a positive Sharpe ratio, and the more configurations tried, the higher it will be. A backtest presented without its trial count is therefore not evidence of anything; it is the maximum of an unknown number of draws.

The remedy has three parts, and SINTESIS applies all three in every engagement: record the trials, hold out time in a way that respects the direction of information, and adjust the headline statistic for the search that produced it.

03Methodology: counting trials

Under the null hypothesis that a strategy has no edge, its estimated annualised Sharpe ratio over a sample is approximately normally distributed around zero with a standard deviation that depends on the sample length and the higher moments of returns. If N independent configurations are tried, the expected value of the maximum estimated Sharpe ratio is approximately

E[max SR] ≈ σ_SR · [ (1 − γ) · Z⁻¹(1 − 1/N) + γ · Z⁻¹(1 − 1/(N·e)) ] (1)

where Z⁻¹ is the inverse standard normal distribution function, γ ≈ 0.5772 is the Euler–Mascheroni constant and σ_SR is the standard deviation of the Sharpe estimates across trials. The formula follows Bailey and López de Prado (2014). It says that the best of ten trials is expected to sit about 1.6 standard deviations above zero and the best of a thousand about 3.3, with no edge anywhere.

The deflated Sharpe ratio turns this into a test. It takes the expected maximum from (1) as the benchmark SR₀ and asks how likely it is that the observed Sharpe ratio exceeds it, allowing for the sample length T and the skewness γ₃ and kurtosis γ₄ of returns:

DSR = Z[ (SR − SR₀) · √(T − 1) / √(1 − γ₃·SR + ((γ₄ − 1)/4)·SR²) ] (2)

A configuration is admitted to the evidence stage only if its DSR exceeds a pre-registered level. The N in (1) is taken from the trial register, which is written before the search starts and appended during it. Configurations that were tried and abandoned count.

A complementary measure, the probability of backtest overfitting (PBO), asks a different question: across many splits of the sample into halves, how often does the configuration that is best in one half rank below the median in the other. Combinatorially symmetric cross-validation (Bailey, Borwein, López de Prado and Zhu) produces this probability directly. SINTESIS reports PBO alongside DSR in the robustness matrix; both must pass.

04Walk-forward and purged validation

Splitting the sample is necessary but not sufficient. Financial observations overlap in time: a label computed over a three-month horizon at date t shares information with labels at t + 1 and t + 2. Random cross-validation leaks that information from the training to the test fold and flatters the result. Two rules follow.

• Walk-forward. Estimation windows always precede evaluation windows. SINTESIS uses anchored or rolling windows depending on the hypothesis about stationarity, and states which.
• Purging and embargo. Observations whose labels overlap the evaluation window are removed from the estimation window (purging), and a gap equal to the label horizon is left after each evaluation window before estimation resumes (embargo).

05Findings: what the arithmetic says

• A single in-sample Sharpe ratio, however high, carries no information about edge without the trial count that produced it. The table in section 03 gives the size of the effect.
• Reducing N is worth more than any statistical correction. Fewer, theory-driven configurations, registered in advance, produce evidence; unrestricted search produces maxima.
• Two failures are informative. A high DSR with a high PBO indicates a result that depends on the specific sample split; a low DSR with a low PBO indicates a stable but weak effect. The robustness matrix records both.
• Recent work on the in-sample versus out-of-sample gap for linear predictive models (arXiv:2501.03938) and on post-selection Sharpe estimation (arXiv:2606.01650) confirms the direction and roughly the magnitude of the effect for the model classes most often used in practice.

06Limitations

• Equation (1) assumes independent trials. Configurations that differ by a small parameter change are highly correlated; the effective number of trials is lower than the register count, and estimating it requires a clustering step that itself involves choices. SINTESIS reports both the raw N and the effective N with the method used.
• The DSR is a test of a single final candidate. If the candidate is chosen because it maximises DSR, the test is compromised. The pre-registered candidate rule must be fixed before evaluation.
• None of these tools measure implementation risk: capacity, latency, market impact and operational failure sit outside the statistics and inside the model-risk register.

07Implementation considerations

• The trial register is a table in version control, appended by the research tooling, not a document written afterwards. Each row: timestamp, configuration hash, sample, metric, author.
• Walk-forward folds, purge lengths and embargo lengths are configuration, hashed into the reproducibility manifest (SN-001).
• DSR and PBO are computed by the same code path in research and in the acceptance tests of the production system, so that a later re-estimation cannot silently use a different definition.

08Related research and sources

• RN-001
  Term-premium regimes in euro-area rates: a testable specification
  Macro · 2026-09-30
• SN-001
  A reproducibility manifest for research-to-production handover
  Systems · 2026-09-30

Sources

• Bailey, D. H. and López de Prado, M. (2014). The deflated Sharpe ratio: correcting for selection bias, backtest overfitting and non-normality. Journal of Portfolio Management, 40(5), 94–107.
• Bailey, D. H., Borwein, J. M., López de Prado, M. and Zhu, Q. J. (2014). Pseudo-mathematics and financial charlatanism: the effects of backtest overfitting on out-of-sample performance. Notices of the American Mathematical Society, 61(5), 458–471.
• Bailey, D. H., Borwein, J. M., López de Prado, M. and Zhu, Q. J. (2017). The probability of backtest overfitting. Journal of Computational Finance, 20(4), 39–69.
• Harvey, C. R., Liu, Y. and Zhu, H. (2016). … and the cross-section of expected returns. Review of Financial Studies, 29(1), 5–68.
• White, H. (2000). A reality check for data snooping. Econometrica, 68(5), 1097–1126.
• López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley. Chapters 7 and 11 on purged cross-validation and backtest statistics.
• In-sample and out-of-sample Sharpe ratios for linear predictive models (2025). arXiv:2501.03938.
• Post-selection estimation of Sharpe ratios (2026). arXiv:2606.01650.
• Spurious predictability in financial machine learning (2026). arXiv:2604.15531.

09Disclosure

Cite as: Solano, F. (2026). Selection under multiplicity: walk-forward validation and the deflated Sharpe ratio. SINTESIS Method Note MN-001, v1.0, Berlin, 2026-09-30. https://sintesismacro.com/en/research/mn-001-selection-under-multiplicity/

01Intended audience

Chief investment officers and heads of quantitative research who want to see how a discretionary macro thesis is converted into a testable programme. It is also the reference example for the Macro-to-Systematic specialisation: a narrative thesis reduced to variables, measurable statements and a plan that can fail.

02Objective and variable map

Objective. Determine whether the euro-area term premium, or a documented proxy for it, exhibits persistent regimes that are (a) identifiable in real time from information available at the decision date and (b) associated with measurably different distributions of subsequent changes in the AAA curve slope.

Narrative thesis being translated. Long-horizon compensation for holding duration is not constant. It is compressed when central-bank balance sheets absorb duration and inflation uncertainty is low, and it rebuilds when supply returns to private hands and inflation uncertainty rises. If that is true, the state of a small number of observable variables should carry information about the regime.

03Hypotheses

Each hypothesis states what would falsify it. A hypothesis without a falsification condition is not admitted.

• H1 · Persistence. Regimes identified from V1 alone persist beyond the monthly horizon. Falsified if the estimated transition matrix of a two- or three-state model is statistically indistinguishable from independent draws at the 5 % level on the pre-2020 sample and on the full sample.
• H2 · Real-time identifiability. The regime at month t can be classified using only data available on the last business day of month t with an out-of-sample accuracy exceeding the unconditional base rate by a pre-registered margin. Falsified if the margin is not met on the walk-forward folds defined in section 05.
• H3 · Conditional distribution. The distribution of the subsequent three-month change in slope differs across regimes in location or scale. Falsified if a distribution test cannot reject equality at the 5 % level after adjustment for the number of regime definitions tried.

Note what is absent: no hypothesis states that a trading rule conditioned on the regime is profitable. Profitability is a separate question that follows, with instrument-level costs, only if H1 to H3 survive.

04Data specification

The blocked row is the decision point of this specification. Estimation does not start until the licence status of every input is resolved, or the input is dropped from the map in a dated revision.

05Acceptance criteria and validation plan

• Trial register. Every model specification, regime count and variable subset tried is logged before estimation. The final multiplicity adjustment uses the register count, not a recollection (see MN-001).
• Sample split. Specification search on data up to 2016-12-31. Walk-forward evaluation from 2017-01-31 with annual re-estimation and a three-month embargo between estimation and evaluation windows.
• Held-out regime. The 2011 to 2013 euro-area sovereign stress period is excluded from specification search and evaluated separately as a stress case.
• Pre-registered thresholds. H2 margin over base rate, H3 test statistic and adjustment method are fixed in the internal version of this document and hashed; the hash will be published with the results note.
• Stopping rule. If H1 fails, the programme stops and a short note records the negative result. If H2 or H3 fail, one dated revision of the variable map is permitted; a second failure stops the programme.

06Assumptions and limitations

• The term premium is not observable. Every proxy embeds a model of expected short rates, and results may depend on that model more than on the regimes. The slope fallback avoids the model but conflates expectations and premium.
• The sample contains one long easing cycle and one rapid tightening cycle. Regimes identified on such a sample may be regimes of monetary policy rather than of risk compensation.
• Composition changes in the AAA set (DS-001) can create spurious regime shifts. Estimation will include the composition flag as a control and report results with and without it.
• This is a study of distributions, not of a trading rule. Even a confirmed set of hypotheses does not imply a profitable or implementable strategy.

07Implementation considerations

Should the hypotheses survive, the path to a system runs through the standard sequence: an instrument-level specification (futures or swaps, not fitted spot rates), a cost model, the robustness matrix, a model-risk register listing the composition and vintage risks above, and a monitoring indicator for regime-classification confidence. The research code for this specification is being written under the reproducibility manifest defined in SN-001 from the first commit, so that the eventual results note regenerates from its manifest.

08Related research and sources

• DS-001
  Euro-area AAA curve slope, 2004 to 2026: source ledger and data-readiness assessment
  Data studies · 2026-09-30
• MN-001
  Selection under multiplicity: walk-forward validation and the deflated Sharpe ratio
  Methods · 2026-09-30

Sources consulted for the specification

• Adrian, T., Crump, R. K. and Moench, E. (2013). Pricing the term structure with linear regressions. Journal of Financial Economics, 110(1), 110–138.
• Kim, D. H. and Wright, J. H. (2005). An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates. Federal Reserve Board, Finance and Economics Discussion Series 2005-33.
• Ang, A. and Bekaert, G. (2002). Regime switches in interest rates. Journal of Business & Economic Statistics, 20(2), 163–182.
• Diebold, F. X. and Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364.
• Regime-switching affine term structures (2023). arXiv:2302.07721.
• Machine learning and the yield curve: tree-based macroeconomic regime switching (2024). arXiv:2408.12863.
• European Central Bank. Euro area yield curves, technical notes. Data Portal dataset YC.

09Disclosure

Cite as: Solano, F. (2026). Term-premium regimes in euro-area rates: a testable specification. SINTESIS Research Note RN-001, v0.3 (specification), Berlin, 2026-09-30. https://sintesismacro.com/en/research/rn-001-term-premium-regimes-specification/

01Intended audience

Chief technology officers, heads of engineering and the technical owners who will operate a delivered system. The manifest is the central artifact of stage 04 (System) and the precondition of stage 05 (Handover).

02Why a manifest

A backtest that cannot be regenerated is an anecdote. A production system whose behaviour cannot be traced to a specific version of code, data and environment cannot be operated responsibly by anyone, least of all by a team that did not build it. The manifest closes both gaps with a single document: for every result the system has produced or will produce, it names the exact inputs that produce it and the procedure that checks the claim.

The manifest is not documentation in the narrative sense. It is machine-readable, hashed and verified by running it. Documentation explains; the manifest proves.

03The manifest, field by field

manifest_version: 1
system:  { name: client-rates-regime, version: 1.4.0, engagement: R2P-EXAMPLE }
code:    { repo: git@client:quant/rates-regime, commit: 7f3a9c2e…, tag: v1.4.0, signed: true }
dependencies: { lockfile: poetry.lock, sha256: 41be7c…  }
environment:  { image: registry.client/rates-regime@sha256:c0d1e2…, os: debian-12, arch: x86_64, runtime: python-3.12.6 }
data:
  - { id: DS-001, path: data/ecb-yc-aaa-2y-10y-daily.csv, sha256: 9f3c11…, cutoff: 2026-09-28, licence: public-attribution }
  - { id: CLIENT-FUT-01, path: data/futures-ticks/, sha256: e5a9b0…, cutoff: 2026-09-26, licence: client }
configuration: { walk_forward.yaml: 2d4f…, costs.yaml: 8a1c…, universe.yaml: 77e0… }
seeds: [11, 23, 47]
tolerance: { evidence_tables: 1e-9, signal_history: exact }
tests: { run_id: ci-2026-09-29-1142, unit: pass, integration: pass, replay: pass, acceptance_map: docs/acceptance-map.md }
outputs: { robustness_matrix.csv: 3b6d…, evidence.parquet: a01f…, signals.parquet: 55c2… }
owner: { name: "[client technical owner]", handover_record: H-04, date: 2026-10-… }

Sanitized example. Hashes are truncated placeholders; names and dates are illustrative. No client data is shown.

04Regeneration protocol

1. The client's technical owner checks out the tagged commit on the client's own environment, not on a SINTESIS machine.
2. Dependencies are installed from the lockfile; the resolved tree is hashed and compared.
3. Every data snapshot is rehashed. A mismatch stops the protocol; there is no override flag.
4. The full pipeline runs twice with the declared seeds. The two runs are compared within the declared tolerances.
5. Outputs are compared with the manifest hashes, again within tolerance.
6. The test suite runs and its summary is compared with the recorded run.
7. The owner signs the acceptance record. Only then does the engagement move to handover.

The protocol is itself a script in the repository, so that step one to seven can be repeated after any client-side change. A client who modifies the system later has a way to know exactly what changed.

05Findings from practice

• Most regeneration failures are environmental, not algorithmic: unpinned system libraries, locale-dependent parsing and time-zone handling of cut-offs. The environment and configuration fields exist because of them.
• Declared tolerances are a design decision, not an admission. Parallel floating-point reduction is legitimately non-deterministic; pretending otherwise leads to either false failures or disabled checks.
• The data hash is the field clients most often want to relax, and the one that must never be relaxed. A system that runs on unverified data has no evidence behind it.

06Limitations

• The manifest proves that a result regenerates. It does not prove that the result is right, that the hypothesis is sound or that the system will perform. Those questions belong to the evidence stage and the model-risk register.
• Regeneration on the client environment requires that environment to exist and to be accessible during the engagement. Engagements without a target environment cannot complete stage 04.
• Live market connectivity, venue behaviour and brokerage integrations are outside the manifest's scope and outside the SINTESIS engagement unless separately contracted; they are the client's domain.

07Implementation considerations

• Write the manifest generator before the first experiment. Retrofitting it is possible but every result produced before it exists must be regenerated to enter the evidence.
• Store snapshots immutably with content-addressed names; never overwrite a snapshot in place.
• Treat the acceptance map (criterion → tests) as part of the manifest, so that a change to a criterion is visible as a change to a hash.
• Third-party or open-source components used in the system are listed with licence and, where relevant, commercial affiliation. SINTESIS may recommend third-party, open-source or affiliated software based on technical requirements. Relevant commercial affiliations are disclosed before selection.

08Related research and sources

• DS-001
  Euro-area AAA curve slope, 2004 to 2026: source ledger and data-readiness assessment
  Data studies · 2026-09-30
• MN-001
  Selection under multiplicity: walk-forward validation and the deflated Sharpe ratio
  Methods · 2026-09-30

Sources

• Sculley, D. et al. (2015). Hidden technical debt in machine learning systems. Advances in Neural Information Processing Systems 28.
• Gebru, T. et al. (2021). Datasheets for datasets. Communications of the ACM, 64(12), 86–92. arXiv:1803.09010.
• Mitchell, M. et al. (2019). Model cards for model reporting. Proceedings of the Conference on Fairness, Accountability, and Transparency. arXiv:1810.03993.

09Disclosure

Cite as: Solano, F. (2026). A reproducibility manifest for research-to-production handover. SINTESIS Systems Note SN-001, v1.0, Berlin, 2026-09-30. https://sintesismacro.com/en/research/sn-001-reproducibility-manifest/