This appendix shows how the numbers in the article were built and what has and has not been tested. Data cutoff: October 2, 2026.
What is being forecast
- Target: the 10-year Treasury constant-maturity yield (Treasury daily yield curve; FRED series DGS10). It is not the yield on one particular bond bought today.
- Horizons: the end of Q4 2026, the end of Q1 2027 and the end of Q3 2027, about 90, 180 and 360 calendar days from October 4, 2026. Each estimate is checked against the last trading day of its quarter: December 31, 2026, March 31, 2027 and September 30, 2027.
- The numbers are end-of-period readings, not monthly or quarterly averages.
The historical test below uses 90, 180 and 365-day horizons from month-end starting points, taking the first trading day on or after the target date, within five days. The quarter-end horizons are a few days shorter; the difference does not change the ranges.
Four kinds of numbers appear in the article and are kept separate: observed data, market pricing, a tested history-based range, and my scenario ranges, which are judgment.
Test: do simple models beat assuming no change?
I made forecasts from the last trading day of each month, using only information available on that date, and compared them with what happened. Each model was refit every month on outcomes that were already complete. Test period: January 2007 to the latest date with a known outcome. Training data starts in 1992.
- No-change: the yield stays where it is.
- Own-history model: the change in the yield predicted from its starting level.
- Small model: starting level, the 10-year minus 2-year gap, the Moody's Baa corporate spread, six-month core CPI inflation and the trend in jobless claims.
- Small model plus oil: adds the three-month change in the Brent spot price.
Mean absolute error in basis points (root mean squared error in parentheses):
| Horizon | Forecasts | No-change | Own-history | Small model | Small model plus oil |
|---|---|---|---|---|---|
| 90 days | 234 | 34.0 (44.2) | 34.7 (45.1) | 36.0 (46.6) | 36.0 (47.0) |
| 180 days | 231 | 49.1 (62.5) | 50.3 (64.9) | 54.5 (69.6) | 55.0 (69.9) |
| 365 days | 225 | 70.1 (85.5) | 77.3 (92.9) | 83.4 (104.6) | 85.0 (105.5) |
No model beat the no-change benchmark over the full test period. Adding oil did not help. From 2016 to 2026 alone, the own-history model was slightly ahead of no-change at 365 days (73.4 against 76.6), which is too small and too period-dependent to rely on.
For reference, the models' readings from October 2 were 5.21% to 5.25% at 90 days, 5.13% to 5.16% at 180 days and 4.86% to 4.98% at a year. I do not use them in the article because they did not outperform.
Limits of this test:
- It uses today's revised data, not the data as first published. It is a historical test, not a full real-time simulation.
- Monthly forecasts over 180 and 365 days overlap heavily, so they are not independent observations.
- The Baa corporate spread stands in for the high-yield spread because FRED carries only three years of the high-yield series.
- A Dynamic Nelson-Siegel yield-curve model has not been tested.
History-based range (the grey band)
The band uses the middle 80% of past changes in the 10-year yield over each horizon, from month-end starting points since 1992, added to today's 5.28%.
| Horizon | 10th to 90th percentile change | Range from 5.28% | Share of outcomes inside, 2007 to 2026 test | Largest rise and fall since 1992 |
|---|---|---|---|---|
| 90 days | -0.57 to +0.60 points | 4.71% to 5.88% | 82% | +1.39, -1.72 |
| 180 days | -0.83 to +0.81 points | 4.45% to 6.09% | 78% | +1.65, -1.86 |
| 365 days | -1.24 to +1.04 points | 4.04% to 6.32% | 81% | +2.55, -2.24 |
In the test, each interval was built only from outcomes known at the time. This band is unconditional. It says nothing about which scenario happens, and it should not be attached to the scenario ranges as a probability.
It is a historical comparison, not an 80% probability forecast. A pooled record does not guarantee the same range for every starting yield or economic condition.
How the escalation ranges compare with the band:
| Horizon | Historical band | Escalation range | Relationship |
|---|---|---|---|
| End of Q4 2026 | 4.7% to 5.9% | 6.0% to 6.3% | Entirely above |
| End of Q1 2027 | 4.5% to 6.1% | 6.2% to 6.8% | Entirely above |
| End of Q3 2027, no recession | 4.0% to 6.3% | 6.1% to 6.5% | Partly overlaps |
| End of Q3 2027, recession | 4.0% to 6.3% | 5.0% to 5.4% | Entirely inside |
Scenario ranges are judgment
The cool-down, stalemate and escalation ranges are my estimates, conditional on the assumptions in the article. They are not model output and they are not confidence intervals. The escalation range for Q4 2026 and Q1 2027 is above the 90th percentile of past changes, though inside the largest rises on record.
Term premium: two models
| Estimate | February 27 | September 25 | Change |
|---|---|---|---|
| Kim-Wright (Federal Reserve Board, FRED THREEFYTP10) | 0.46 | 1.02 | +0.56 |
| Adrian-Crump-Moench (New York Fed) | 0.59 | 0.77 | +0.18 |
The 10-year yield rose about 1.2 points over the same dates. One model attributes close to half of that to the term premium and the other about a sixth. The New York Fed estimate was 0.90 on October 1. Both are model estimates, not traded prices, and both can be revised. Because they disagree, the article gives the term premium a direction in each scenario and not a number.
Market pricing
- CME FedWatch, as reported by CNBC on October 2: about a 17% chance of an increase at the October 28 meeting, and the same report said traders still expected the Fed to raise rates in December.
- I have not pulled the futures contracts directly, so I do not show meeting-by-meeting implied rates.
- Fed funds futures price the Fed's rate. They are not forecasts of the 10-year yield and not probabilities for my scenarios.
Mortgage spreads
Each day's Optimal Blue average minus the same day's 10-year Treasury yield, on the 151 days from February 27 to October 1, 2026 when both were published. The average is a simple average of those daily spreads.
| Loan | Average | Low | High | October 1 | Used in the article |
|---|---|---|---|---|---|
| 30-year conventional conforming | 1.98 | 1.90 | 2.13 | 2.13 | 2.0 |
| 30-year FHA | 1.77 | 1.64 | 1.89 | 1.86 | 1.8 |
| 30-year VA | 1.61 | 1.47 | 1.80 | 1.76 | 1.7 |
All three spreads were at or near their highs for the period on October 1. If they stay there, mortgage rates would run about 0.1 point above the figures in the article. The mortgage figures are mechanical additions to the 10-year ranges.
- The VA spread used in the article (1.7) is rounded up from the 1.61 average toward the 1.76 reading on October 1.
- Sensitivity: the spreads are held fixed, so a spread 0.5 point wider raises every mortgage estimate by 0.5 point, and a narrower spread lowers it by the same amount. This is a sensitivity check, not a probability.
- The Optimal Blue indexes are built from rate locks for each loan type, and the Freddie Mac weekly average uses a different loan population and collection method. Differences between the averages do not show what one borrower would be offered on each loan type.
- The Freddie Mac comparison in the article runs from the February 26 release (5.98%) to the October 1 release (7.28%).
Supply calculations
- Debt outstanding (Treasury Debt to the Penny, total public debt): $38.77 trillion on February 27 and $40.26 trillion on October 1. Change: $1.49 trillion over 216 days, or about $210 billion per 30.4-day month.
- Deficit (Monthly Treasury Statement): $1.97 trillion for October 2025 through August 2026.
- Not included: net marketable borrowing, gross issuance and longer-term auction sizes.
Source records. Debt to the Penny, total public debt outstanding: $38,769,805,982,273.81 on February 27, 2026 and $40,260,641,972,390.03 on October 1, 2026. Monthly Treasury Statement deficit in $ billions: October 284, November 173, December 145, January 95, February 308, March 164, April surplus of 215, May 293, June 120, July 432, August 167.
The $38.77 trillion and $40.26 trillion figures are gross debt. They include debt held within the federal government. Debt held by the public was $31,186,965,290,815.89 on February 27 and $32,433,790,394,253.86 on October 1, a rise of about $1.25 trillion. Neither figure is a measure of new marketable Treasury issuance.
Payrolls (BLS, FRED series PAYEMS), monthly change in thousands: July -10, August +133, September +29. Three-month average: about 51. Four-week average of initial claims (FRED IC4WSA): 200,000 for the week ending September 26.
Change log
| Item | Before | Now | Why |
|---|---|---|---|
| Stalemate, Q4 2026 | 5.4% to 5.7% | 5.2% to 5.7% | No model beat no-change, markets already expect a December increase, and oil flows have improved. |
| Stalemate, Q1 2027 | 5.3% to 5.8% | 5.1% to 5.8% | Same. |
| Term premium share of the rise | Close to half | About a sixth to about half | The second model disagrees with the first. |
| Aaa corporate spread as a safety premium proxy | Included | Removed | Maturity mismatch, and not needed for the estimates. |
| Claim that debt changes too slowly to affect daily yields | Included | Removed | Issuance expectations can move yields before debt is sold. |
| Federal interest payments figure | Included | Removed | Accounting basis not confirmed. |
| Oil flow table and shipping detail | Included | Cut to scenario assumptions | Reports conflict and do not measure the same thing. |
| FHA and VA mortgage ranges | Not in the bond version | Added | Combined article. |
Final correction pass, October 4:
- VA funding fee wording corrected. The earlier draft said most VA loans carry the fee. It now says the fee applies unless the borrower is exempt.
- Historical band described as the middle 80% of past changes, not a probability forecast. Escalation comparison corrected by horizon.
- Mortgage scale removed from the Treasury chart. The mortgage chart carries the loan-type estimates.
- Fixed-spread assumption and a spread sensitivity added under the mortgage chart.
- Section renamed from Other forecasts to Fed pricing. The unfinished survey comparison was removed from the article.
- Disclaimer added at the end.
Last check, October 4:
- The two one-year escalation outcomes are now labeled no recession and recession. Inflation pressure persists in both.
- The payroll reading now matches the rule: a three-month average of about 51,000. The claims rule is now a four-week average.
- Debt is labeled gross debt, with debt held by the public shown alongside.
- Forecast dates carry the year, and the January 2 estimate is checked against the January 4 reading.
Revision, October 4, after publishing:
- Horizon labels changed from day counts (90, 180 and 365 days) to quarter ends (Q4 2026, Q1 2027 and Q3 2027). The ranges are unchanged. Each estimate is now checked against the last trading day of its quarter.
- The disclaimer now says historical relationships may not hold in the future.
What remains untested
- Real-time data vintages (ALFRED).
- A yield-curve factor model.
- Futures-implied policy path by meeting.
- Survey of Professional Forecasters comparison.
- The monitoring thresholds for oil, claims and credit spreads.
- Auction and net borrowing data.