What This Tests

This appendix is the first empirical check of the frozen BT-SFS v0.4 score. It does not re-estimate the score weights. It asks whether the score behaves in the direction we would expect against two observable outcomes: listed future sovereign stress events and current near-5-duration USD spread levels. Here, 5D means the selected USD bond has modified duration close to five years.

The goal is exploratory validation, not optimization. The evidence below supports construct and concurrent validity: weak scores line up with stress outcomes and wider spreads in the data we can observe today. It does not establish predictive validity.

The historical series is a current-vintage backcast. It uses currently available IMF/World Bank history, not the exact data investors had in each historical year. Predictive validation would require point-in-time macro vintages and a larger historical 5D USD spread panel.

This analysis was not pre-registered. To reduce cherry-picking, the primary event statistic is the weakest-score-quartile event-rate lift, and the primary spread statistic is the full-sample Spearman rank correlation. AUC, classifier tables, raw-spread regressions, and sample filters are diagnostic.

Data Used

Event-Risk Test

Rows are included only before the first listed default or restructuring event for each country. Lower BT-SFS means higher predicted risk. This rule prevents the same default/restructuring registry event from mechanically entering the score through the default penalty and then becoming the label.

The event-risk panel excludes rows at or after each country first registry event; no event-panel rows carry a non-zero default penalty from the same registry. Rows with non-zero default penalty in the event panel: 0; positive rows with non-zero default penalty: 0.

Because a single future restructuring can label several prior country-years as positive, positive row counts should not be read as independent defaults. The three-year weakest-quartile lift is 18.1x, with a naive row-level 95% interval of 5.5-59.8. The country-cluster bootstrap interval is useful, but with only 8 distinct event countries, it remains fragile. The one-year horizon is shown only as a robustness view.

Early Robustness Checks

These checks preview the v0.2 robustness phase on the frozen three-year panel. They rule out single-country dependence, chance under full country clustering, and a composite that underperforms its own pillars. They do not address current-vintage revision leakage.

Metric-level and agency-rating benchmarks need a historical metric panel and ratings history; they stay in the v0.2 phase.

Tier-Exclusion Sensitivity (Spread Fit)

Rating tiers are descriptive agency composites (median of Moody's/S&P/Fitch as of 2026-07-03, mapped to the S&P scale) used only to slice this diagnostic — ratings are never model inputs. Each row re-runs the primary log-spread fit ln(spread) = a + b·BT-SFS on a subsample of the frozen cross-section.

Three structural readings. First, the fit's explanatory power is concentrated between tiers, not within them: within single-B the fit explains essentially nothing (R² 0), so the score ranks credits across the quality spectrum and is not a within-tier relative-value signal. Second, the distressed tail sits off the single global curve: excluding the CCC-and-below cohort — recent default and restructuring credits — lifts the global R² from 0.576 to 0.688, while within that cohort the slope is roughly 2.9× the global one; one log-linear slope understates curvature at the distressed end. Third, the strong-fundamentals tail anchors the fit — excluding the A tier lowers R² to 0.472 — which argues for adding high-grade anchor countries in a future release.

Because the score separates rating tiers well, a fair question is whether it merely reconstructs agency ratings. It cannot by construction — no agency or market inputs enter the score — and this diagnostic shows where the two diverge: the score keeps discriminating inside the distressed cohort, where a tier label is flat.

Temporal-Split Sanity Check

This is the closest current approximation to the economist's suggestion, but it is not a true out-of-sample test because the macro history is current-vintage. Instead of re-estimating all BT-SFS weights, we estimate one simple cutoff on earlier rows and apply it to later rows.

Training years: 2016-2020
Test years:     2021-2022
Target:         default/restructuring within the next 3 years
Rule:           predict event if BT-SFS <= estimated cutoff

The temporal split inherits the same pre-event filter as the main event-risk panel. Countries with multiple registry events are cut off at the first event, so post-stress rows do not enter the panel under a later event label.

The cutoff chosen on the training sample is 43.86. This is a screening-burden view, not a production classifier.

This is a useful sanity check, but it is not enough to re-weight the model or claim forecast skill. The event sample is small, positive rows are clustered, and the false-discovery share remains high because event base rates are low.

Current Spread Cross-Section

The full finite-spread sample is shown first for rank correlation, so provisional outliers remain visible. The publishable sample is the quality-controlled fit because those rows have complete public BT-SFS scores. Provisional rows are separated because the public score definition treats them as not fully comparable, not because removing them improves the fit.

Publishable means the country has the required public macro inputs under BT-SFS v0.4 coverage rules. Provisional means at least one required public metric is missing or flagged. The gap between full-sample Spearman and Pearson is expected: rank ordering is robust, while Pearson and raw-spread fits are more sensitive to outliers such as Senegal.

Weakest-score quartile average spread: 333.5 bps. Strongest-score quartile average spread: 66.3 bps.

Provisional Rows

These rows are excluded from the primary spread fit because they are not fully comparable with publishable rows.

• Côte d'Ivoire: BT-SFS 51.53, spread 213 bps, flags macro_coverage_88.9%; 1_missing_metrics
• Benin: BT-SFS 49.84, spread 293 bps, flags sparse_curve; macro_coverage_88.9%; 1_missing_metrics
• Senegal: BT-SFS 41.36, spread 1605 bps, flags macro_coverage_88.9%; 1_missing_metrics

These rows are informative diagnostics. They highlight cases where missing public inputs, curve quality, liquidity, or market-specific stress can create large differences between the fundamentals score and observed spreads. Senegal is a real divergence between the current provisional score and market pricing, and the West African reserve-data gap is exactly why the provisional label exists.

Conclusion

The first validation supports BT-SFS as a transparent fundamentals score with construct and concurrent validity. Lower scores are associated with later listed stress events in the current-vintage panel, and stronger scores generally line up with lower current USD spreads.

It does not establish predictive validity and does not justify statistically re-estimating the weights. For that, BT needs a historical near-5-duration USD spread panel and point-in-time source vintages.

Next Validation Phases

BT-SFS v0.1 should be read as a first validation layer, not the end state. The next phases are sequenced so each step answers a specific criticism before moving toward model selection.

Validation Governance Checks

The validation keeps market prices outside score construction and separates public-score coverage from provisional diagnostics.

• Frozen BT-SFS v0.4 score weights.
• No spread, CDS, or agency-rating inputs in the score.
• Pre-event filter and default-penalty leakage check.
• Country-cluster bootstrap, quartile-lift counts, and screening-burden table.
• Full-sample Spearman, log-spread diagnostics, and provisional-row separation.