Three percent real, for thirty years — and a 55% chance it holds

The Probability Desk · Thursday, 3 September 2026 · Universal Asset Owners

The 30-year US real yield has spent sixteen years below 3%. It has closed at or above 3% on seven days, all of them between 31 July and 21 August, and it sits two basis points below it now. The Desk puts the probability that it is still there on 31 December at 55% — and the more interesting number is what a durable 3% real rate does to two pension systems that discount the same future in opposite ways.

Executive summary

On 1 September 2026 the 30-year US Treasury inflation-protected real yield closed at 2.98% (FRED DFII30; identical to the Treasury Daily Par Real Yield Curve 30-year point). In the 4,136 trading days since that series began on 22 February 2010, it has closed at or above 3.00% on seven. All seven fell between 31 July and 21 August 2026. The series high, 3.06%, is seventeen days old.

This is not an inflation story. Realised core PCE inflation ran at 3.34% year-over-year in July 2026, while the 10-year breakeven sat at 2.34% on 2 September and the 5-year-forward-5-year breakeven at 2.33%. The bond market is asserting that the inflation problem gets solved. Every basis point of the long-end sell-off is therefore being paid in real compensation — term premium, fiscal risk, and the price of duration itself.

The Desk's forecast question is whether that compensation survives the year. Our answer, from a 50,000-path block-bootstrap simulation anchored to sixteen years of joint real-yield and breakeven data: P(DFII30 ≥ 3.00% at the 31 December 2026 close) = 55%. The unconditional random-walk base rate is 48%; the same base rate computed inside the 2023–2026 regime is 65%; a zero-drift version of our own simulation returns 46%. We sit at 55% and show, below, every piece of evidence that moved us there.

The allocation consequence is larger than the forecast. A 3% thirty-year real yield is a risk-free, inflation-linked, thirty-year hurdle rate of 3% — the highest available to a long-horizon owner since TIPS at that maturity were reintroduced. Against it, the compensation for taking risk has rarely been thinner: investment-grade credit was paying 81 basis points over Treasuries on 2 September and high yield 266 basis points, with the VIX at 15.2. The Desk's highest-conviction observation is not about the level of rates. It is that the risk-free real rate and the risk premium have moved in opposite directions for long enough that, for a large number of institutional portfolios, the marginal dollar of risk is no longer paid for.

Desk view, one paragraph. We probability-weight a plateau, not a break. The most likely world (55%) is one in which the 30-year real yield ends 2026 between 2.75% and 3.25% — high, stable, and quietly repricing every discount rate in institutional finance. We give a decisive upside break above 3.25% a 25% weight, driven by fiscal supply and the withdrawal of Japanese duration demand; we give a relief rally back below 2.75% a 15% weight and a genuine growth-shock dislocation below 2.40% only 5%, because nothing in credit or volatility is currently pricing the recession that historically delivers one. The asymmetry that matters for universal owners is not in the yield. It is in the fact that corporate defined-benefit plans, which mark their liabilities to a market rate, have already banked the gain — while public plans, which discount at an assumed return, have banked none of it and are carrying the asset-side mark instead.

The Trigger

Two dated events from the same session on Tuesday, and one data print from this morning.

First. On Tuesday 1 September 2026, Japan's benchmark 10-year government bond yield reached 3% for the first time since 1996, per Reuters — which dates the last 3-handle to September 1996, while Kyodo dates it to October 1996; both are published and the two wires have not been reconciled — "pushed higher by investor concerns about inflation, fiscal health and mounting pressure on the central bank to raise interest rates faster." The 10-year traded to 3.005% in the afternoon session; the two-year reached a 31-year peak of 1.81% as markets priced a near-certainty that the Bank of Japan raises at its meeting this month. Reuters described the move as occurring "amid a deepening global debt selloff." Japan is the world's largest exporter of duration demand. A domestic long bond that finally pays changes the arithmetic for every Japanese life insurer, bank and pension that has spent three decades buying somebody else's.

Second. The same session, the US 30-year real yield closed at 2.98% and the 30-year nominal at 5.27% (FRED, 1 September). Brent closed at $96.02 and WTI at $91.48 — the oil-driven inflation impulse Reuters named as one driver of the global move is visible in the price, though not, notably, in US breakevens.

The driver Reuters names. The same wire attributes the global move to a live conflict, not to a rate cycle: "With no end in sight for the U.S.-Iran conflict and elevated oil prices, bond yields across the United States, Germany and France jumped to multi-year highs of late," and "the Middle East crisis stoking inflation fears globally." Brent at $96.02 is that conflict, priced. This matters for the forecast in a specific and uncomfortable way: our central claim is that the long-end sell-off is being paid in real compensation rather than inflation compensation, and an escalation that lifts Brent through $110 is the single cleanest way that claim stops being true. We hold the claim as it stands because breakevens have not moved — the 10-year at 2.34% and the 5y5y at 2.33% — but we name the exposure rather than leaving it out.

Third, this morning. Freddie Mac's 30-year fixed mortgage rate printed 6.71% on 3 September 2026 — the real economy's live read on the same long-end repricing, and the transmission channel through which a 3% real rate reaches housing, construction and the household balance sheet.

Sitting behind all three: on 19 August 2026 the US Treasury announced it is at least doubling the size of its liquidity-support buyback operations in the 10-to-20-year and 20-to-30-year sectors, from a $2 billion maximum per operation to at least $4 billion, effective 9 September 2026 and running through 4 November. Treasury framed it as a response to "consistent strong sponsorship." It is also, in effect, an official bid arriving in the exact part of the curve this report is about, six days from now.

The Forecast Question

Will the 30-year US Treasury inflation-indexed constant-maturity real yield (FRED series DFII30, equivalently the 30-year point of the Treasury Daily Par Real Yield Curve) close at or above 3.00% on 31 December 2026?

Horizon: 83 US business days from the 1 September 2026 close. (The simulation uses 83; the SIFMA calendar on which DFII30 is published gives 82 — 87 gross business days less Labor Day 7 Sep, Columbus Day 12 Oct, Veterans Day 11 Nov, Thanksgiving 26 Nov and Christmas 25 Dec. The one-day difference moves P(≥3.00%) by under half a point and the base-rate windows use the same 83, so the comparison is internally consistent. Not re-run.) (The simulation uses 83; the SIFMA calendar on which DFII30 is published gives 82 — 87 gross business days less Labor Day 7 Sep, Columbus Day 12 Oct, Veterans Day 11 Nov, Thanksgiving 26 Nov and Christmas 25 Dec. The one-day difference moves P(≥3.00%) by under half a point and the base-rate windows use the same 83, so the comparison is internally consistent. Not re-run.)
Resolution: the published DFII30 value for the final business day of 2026. A print of exactly 3.00 resolves YES.
Current reading: 2.98% (1 September 2026).
Desk probability: 55%.
What would change it: a Federal Reserve pivot that drags the two-year below the effective funds rate; a credit event that widens high-yield spreads through 400bp; a Treasury refunding on 4 November that shifts issuance decisively toward bills; or a Japanese policy surprise in either direction.

This question is chosen because it is the single input that reprices the largest number of institutional balance sheets simultaneously, and because it is cleanly gradeable on a date certain from a public series.

Source Ledger

Thirty-six inspected sources. Every figure used in this report appears below with the date it was read and the confidence assigned.

Market and macro data (FRED, Federal Reserve Bank of St. Louis — inspected 3 September 2026)

#	Series	Reading	As of	Confidence	Why it matters	Moves the model?
1	`DFII30` 30y TIPS real yield	2.98%	2026-09-01	H	The forecast variable	Yes — it is the variable
2	`DFII30` full history	4,136 obs from 2010-02-22; 7 closes ≥3.00%, all 2026-07-31 to 2026-08-21; high 3.06% on 2026-08-17	2026-09-01	H	The level base rate	Yes — prior
3	`DFII20` 20y real	2.78%	2026-09-01	H	Curve shape in real space	Context
4	`DFII10` 10y real	2.44%	2026-09-01	H	Real curve slope	Yes
5	`DFII5` 5y real	2.18%	2026-09-01	H	Front real rate	Context
6	`DGS30` 30y nominal	5.27%	2026-09-01	H	Implies 30y breakeven 2.29%	Yes
7	`DGS20` 20y nominal	5.27%	2026-09-01	H	20s/30s flat	Context
8	`DGS10` 10y nominal	4.79%	2026-09-01	H	Benchmark	Yes
9	`DGS5` 5y nominal	4.55%	2026-09-01	H	Belly	Context
10	`DGS2` 2y nominal	4.39%	2026-09-01	H	Prices the policy path	Yes
11	`EFFR` effective fed funds	3.63%	2026-09-02	H	2y sits 76bp above it	Yes
12	`T10YIE` 10y breakeven	2.34%	2026-09-02	H	The move is real, not inflationary	Yes
13	`T5YIE` 5y breakeven	2.35%	2026-09-02	H	Flat breakeven curve	Context
14	`T5YIFR` 5y5y forward breakeven	2.33%	2026-09-02	H	Long-run expectations anchored	Yes
15	`PCEPILFE` core PCE index	130.658, +3.34% y/y	2026-07-01	H	Realised inflation 100bp above expected	Yes
16	`CPILFESL` core CPI index	336.789	2026-07-01	H	Corroborates	Context
17	`BAMLC0A0CM` IG OAS	81bp	2026-09-02	H	Risk premium near cycle tights	Yes
18	`BAMLH0A0HYM2` HY OAS	266bp	2026-09-02	H	at or tighter on 5.5% of days since 2023-09; strictly tighter on 3.7%	Yes
19	`VIXCLS`	15.20	2026-09-02	H	No stress priced	Yes
20	`DCOILBRENTEU` Brent	$96.02	2026-09-01	H	The named inflation impulse	Yes
21	`DCOILWTICO` WTI	$91.48	2026-09-01	H	Corroborates	Context
22	`MORTGAGE30US` (Freddie Mac PMMS)	6.71%	2026-09-03	H	Today's real-economy transmission	Yes
23	`DPRIME` bank prime	6.75%	2026-09-01	H	Short-rate corroboration	Context
24	`DTWEXBGS` broad dollar	118.75	2026-08-28	H	Reserve-manager context	Context
25	`DEXJPUS` USD/JPY	159.97	2026-08-28	H	Japan repatriation channel	Yes
26	`DEXUSEU` EUR/USD	1.1598	2026-08-28	H	Cross-market	Context
27	`DEXCHUS` USD/CNY	6.726	2026-08-28	H	Cross-market	Context
28	`GFDEGDQ188S` / `FYGFGDQ188S` federal debt / GDP	122.59% gross (total public debt outstanding); 98.71% held by the public	2026-Q1	H	The supply anchor of term premium — the held-by-the-public figure is the marketable one	Yes
29	`A091RC1Q027SBEA` federal interest outlays	$1,247.0bn SAAR	2026-Q2	H	3.84% of nominal GDP	Yes
30	`GDP` nominal GDP	$32,486.1bn SAAR	2026-Q2	H	Denominator for #29	Yes
31	`FYFSGDA188S` federal deficit / GDP	−5.77%	FY2025	H	Ongoing supply	Yes
32	`UNRATE`	4.1%	2026-07-01	H	No labour-market break	Yes

Documents

#	Source	Date	Data point used	Confidence
33	US Department of the Treasury, press release, "Treasury Announces Increased Sizes of Nominal Long-End Liquidity Support Buybacks Beginning September 9" (home.treasury.gov/news/press-releases/sb0607)	2026-08-19	Buyback maximum in the 10–20y and 20–30y sectors rises from $2bn to at least $4bn per operation, effective 9 Sep, through 4 Nov 2026	H — primary
34	US Treasury, Daily Treasury Par Real Yield Curve Rates, 2026 (TextView)	inspected 2026-09-03	30-year real: 3.03% (31 Jul), 3.06% (17 Aug), 3.00% (21 Aug), 2.92% (27 Aug) — matches `DFII30` exactly	H — primary
35	Reuters, "Japan's benchmark bond yield rises to 3% for first time in 30 years," via Investing.com (link), published 1 Sep 2026 02:33, updated 13:54	2026-09-01	10y JGB at 3.005%, first since Sep 1996; 2y at a 31-year peak of 1.81%; "deepening global debt selloff"; record initial budget requests reported by domestic media	H
36	Milliman, Pension Funding Index July 2026, Zorast Wadia (milliman.com), published 7 Jul 2026	data as of 2026-06-30	Milliman 100 corporate DB funded ratio 109.5%, surplus $114bn, PBO $1.208tn, discount rate 5.61%; published two-sided forecast: 5.91% discount rate paired with 10.61% annual asset returns → 116% funded by end-2026; 5.31% paired with 2.61% returns → 105%	H
37	Milliman / Business Wire, "Public pension funded ratio slips again, to 88.2% as of July 31" (businesswire.com)	2026-08-27	Milliman PPFI (100 largest US public DB plans) 88.2% funded at 31 Jul, from 88.7%; liabilities $6.911tn; asset-liability gap widened to $816bn; July return −0.1%; 2026 YTD return 6.1%; 11 of 100 plans below 60% funded	H
38	Milliman / Business Wire, multiemployer plans reach 106% funded at midyear 2026, highest in study history (businesswire.com)	2026-08-14	Third US pension cohort, same direction as corporate DB	M
39	Invesco Global Sovereign Asset Management Study 2026 (invesco.com)	2026	90 sovereign wealth funds and 54 central banks, ~$29tn; equity allocation fell to 30% from 32%	M
40	Milliman 2026 Corporate Pension Funding Study (milliman.com), published 21 Apr 2026	2026-04-21	Expected FY2025 monthly investment return 0.53% (6.61% annualised) — the return assumption the 3% real rate now competes against	H

Deliberately excluded. One aggregator page we checked for Japanese long-end yields returned data current to September 2025 and was discarded. The 30-year figure is nonetheless sourced: the Reuters wire at ledger #35 reports the 30-year yield "poised for a record high closing level of 4.18%," the 20-year touching 3.885%, "a level not seen since 1996," and the 5-year at a record 2.265%. Likewise, a widely repeated figure putting the Milliman 100 funded ratio at 112.1% on a 6.02% discount rate as of 31 July could not be verified against Milliman's own page; we use only the June figure Milliman published (109.5% / 5.61%).

Prior and base rates

The naive base rate is a trap, and it is worth walking into it deliberately.

Reference class A — the level. DFII30 has closed at or above 3.00% on 7 of 4,136 days: 0.17%. Taken at face value this says the answer is almost certainly no. It is the wrong reference class, and obviously so: the series is non-stationary. Its annual means are 1.82 (2010), 0.56 (2012), −0.20 (2021), 0.76 (2022), 1.80 (2023), 2.15 (2024), 2.51 (2025), 2.72 (2026 to date). Five consecutive years of a higher mean. Asking how often a variable has historically been at a level it has never sustained tells you about the past regime, not the next four months. We state it because a probability desk that hides its least convenient number is not one.

Reference class B — the change. The right question is: given the level today, how do 83-business-day changes in this series distribute? Over the full 2010–2026 history, 83-day changes have a mean of +1.7bp and a standard deviation of 35bp, and the probability of a change of at least +2bp (what it takes to reach 3.00% from 2.98%) is 47.8%. That is the honest prior: 48%, essentially a coin flip, which is what a random walk starting 2bp below a threshold should give you.

Reference class C — the change, inside the regime. Restricting to 2023-09-01 onward, 83-day changes have a mean of +7.9bp, a standard deviation of 23bp — lower volatility, positive drift — and the probability of clearing +2bp is 65.0%.

Historical analogues.

The 2013 taper tantrum. DFII30 averaged 0.56% in 2012 and peaked at 1.66% in 2013 — a real-rate repricing of roughly 110bp inside a year, driven by a change in expected official demand rather than by inflation. Why relevant: it is the closest precedent for a real-rate move caused by supply-and-demand for duration rather than by the inflation outlook, which is precisely today's configuration. Why possibly misleading: it retraced. The 2014 and 2015 annual means were 1.11 and 1.00. Implication for the prior: a move of this kind can overshoot and give back; it argues against extrapolating the 2026 trend.
The 2022–2023 regime break. The annual mean rose from 0.76 to 1.80 in a single year and has risen every year since. Why relevant: it establishes that the level is not mean-reverting to a post-GFC anchor. Why possibly misleading: the initial move was a policy-rate shock; the current move is not — the Fed is already at an effective 3.63%. Implication: supports a positive drift term but not one as large as 2022–23's.
2010–2011, the last time the series was "high." Means of 1.82 and 1.47, followed by a decade below. Why relevant: the cautionary case. Long real rates that look structurally high have historically been the top, not the floor. Why possibly misleading: that decade contained roughly $4tn of central-bank duration absorption and a debt-to-GDP ratio far below 122.6%. Implication: the mechanism that pulled real rates down then is not currently operating.

Prior adopted: 48% (reference class B). Class C's 65% is treated below as evidence, not as the prior — using it as the starting point would import the conclusion.

Evidence-update table

No probability appears in this report without the evidence that moved it. Each row cites a dated source from the ledger.

#	Evidence	Source (ledger #)	Direction	Strength	Impact	Running posterior
—	Prior: 83-day random walk from 2.98%	2	—	—	—	48%
1	Five consecutive years of rising annual mean real yield; the same 83-day base rate computed inside the 2023–26 window is 65.0%	2	↑	Moderate	+6pp	54%
2	Core PCE +3.34% y/y (Jul) against a 10y breakeven of 2.34% and 5y5y of 2.33%: disinflation is already assumed, so a nominal rally has to come from the real leg	12, 14, 15	↑	Weak	+1pp	55%
3	EFFR at 3.63% with the 2-year at 4.39% — 76bp above it. The market prices a higher policy path, not cuts; a duration rally has no front-end engine as priced	10, 11	↑	Moderate	+3pp	58%
4	Gross debt at 122.6% of GDP (98.7% held by the public), interest outlays $1,247bn (3.84% of $32,486bn nominal GDP), FY2025 deficit 5.77% of GDP	28, 29, 30, 31	↑	Moderate	+2pp	60%
5	Japan's 10y at 3.005% on 1 Sep, first 3-handle since 1996; 2y at a 31-year peak of 1.81%; 5y at a record 2.265%; 20y at 3.885%, unseen since 1996; 30y poised for a record close of 4.18%; markets pricing a BOJ hike this month as close to certain (Reuters). The whole JGB curve now pays, and the largest foreign source of duration demand has a domestic alternative across every tenor	35	↑	Moderate, size uncertain	+2pp	62%
6	Treasury doubles long-end liquidity-support buybacks to ≥$4bn per operation from 9 Sep to 4 Nov — a deliberate official bid inside the horizon	33	↓	Weak-to-moderate	−3pp	59%
7	Level effect: at 2.98% real, price-insensitive liability buyers (insurers, closed DB plans, LDI mandates) are paid to lock 30-year real cash flows for the first time in the series' history. Demand for this asset rises with its yield	1, 36	↓	Moderate	−3pp	56%
8	IG OAS 81bp, HY OAS 266bp, VIX 15.2, unemployment 4.1%: the recession that historically delivers a fast real-rate decline is not being priced anywhere	17, 18, 19, 32	↑	Weak (removes a path down rather than adding one up)	+1pp	57%
9	Model-uncertainty haircut. Our own simulation returns 55.4% as run and 46.4% with the sampled drift removed. The window choice is doing real work and we give some of it back	Simulation, below	↓	Moderate	−2pp	55%

Desk probability: 55%. Rounded to the nearest 5%. It sits 7pp above the unconditional base rate and 10pp below the in-regime one. It also lands on the as-run simulation — but that agreement is not independent confirmation and should not be read as any. Evidence row 1 awards +6pp for regime persistence; the simulation's 60/40 window mixture imports the same regime persistence as +7.4bp of drift, worth roughly +9pp. Two methods that share an assumption will agree about it. Row 9's −2pp haircut is the only place we pay for that.

The scenarios

Four scenarios, defined as non-overlapping, collectively exhaustive bands of the resolution variable — DFII30 at the 31 December 2026 close. Weights sum to 100% and are rounded to 5%.

Scenario	Band (`DFII30`, 31 Dec 2026)	Weight	Simulation frequency
Plateau (base case)	2.75% ≤ y < 3.25%	55%	53.3%
Break	y ≥ 3.25%	25%	27.8%
Relief	2.40% ≤ y < 2.75%	15%	16.1%
Dislocation	y < 2.40%	5%	2.9%

Note the arithmetic that ties the scenarios to the headline: the 55% probability of finishing at or above 3.00% is not the base case weight. In the simulation it is the Break band (27.8%) plus the upper portion of the Plateau band (27.6%) — 55.4%. The published weights place Break at 25% rather than the 30% a 5% grid would give, for the reason logged in the worksheet; the published 55% headline is the Desk's, and it is 27.8 + 27.6 in the simulation that informs it.

Plateau — 55%

The 30-year real yield ends the year within 25bp of 3%. The Fed does not deliver the front-end move a duration rally needs; supply and the term premium keep the long end anchored high; Treasury's enlarged buybacks and steady liability-driven demand keep it from breaking higher. Nothing dramatic happens, and that is the point — the market simply agrees, for a fourth consecutive quarter, that 3% real is the clearing price for thirty-year duration.

This is the most consequential world precisely because it is the least eventful. A yield that stays is a yield that gets built into assumptions. Actuaries adopt it. Investment committees rebuild capital-market assumptions around it. Private-market general partners find that the hurdle they must clear has risen by roughly 250bp of real return since 2021 without any change in their fee structure. The repricing that a spike would force in a week, a plateau forces over three valuation cycles.

Trigger: the status quo, extended. Tripwire that confirms it: DFII30 prints inside 2.85–3.15% at the 4 November refunding and the 2-year stays above the effective funds rate. What would falsify it: either tripwire in the sections below firing.

Break — 25%

The real yield clears 3.25% and the series high of 3.06% is left well behind. The mechanism is supply meeting a shrinking pool of price-insensitive buyers: a 4 November refunding that lifts coupon sizes at the long end, Japanese institutions repatriating at the margin as the BOJ tightens into a 3%-plus domestic 10-year, and a term premium that widens because gross federal debt at 122.6% of GDP — 98.7% of it held by the public, which is the part that has to clear the market — carrying $1.25tn of annual interest is a fact investors are re-underwriting rather than a forecast.

In this world the nominal 30-year trades above 5.50% — our simulation puts that at 35.2% — the mortgage rate follows past 7%, and an equity market content to insure itself at a VIX of 15 looks like the mispricing of the year.

Trigger: an above-consensus long-end coupon increase at the 4 November refunding, or a BOJ hike accompanied by evidence of foreign-bond selling. Tripwire: DFII30 closes above 3.10% for five consecutive sessions. Falsifier: the Treasury buyback programme visibly absorbing supply — sustained operation sizes at the new $4bn maximum with the 20s/30s sector richening.

Relief — 15%

The real yield falls back to the 2.40–2.75% range it occupied as recently as March 2026 (2.48% on 3 March). The route is a genuine front-end repricing: labour-market data that turns the 2-year's 76bp premium over effective funds into a discount, plus a term-premium compression as the buyback programme proves larger than expected and the refunding leans on bills.

Note what this scenario is not: it is not a crisis. It is the ordinary business of a central bank being believed. Core PCE at 3.34% is the obstacle — this scenario effectively requires the July inflation print to have been the peak.

Trigger: two consecutive soft payroll reports with core PCE decelerating below 3%. Tripwire: the 2-year trades below EFFR. Falsifier: core PCE reaccelerating with Brent above $100.

Dislocation — 5%

Below 2.40%. This requires a genuine growth or credit shock — the historical mechanism by which long real yields fall fast. We weight it low not because it is impossible but because nothing is pricing it: IG at 81bp, HY at 266bp (at or tighter on 5.5% of days since September 2023, and strictly tighter on only 3.7%), VIX at 15.2, unemployment at 4.1%. A universal owner should nonetheless hold the scenario in mind, because it is the one in which the long-duration asset that hurt the portfolio all year becomes the only thing that works.

Trigger: high-yield spreads widening through 400bp inside a month, or a funding-market accident. Tripwire: HY OAS above 350bp with VIX above 25. Falsifier: the absence of both by 4 November.

The Monte Carlo — simulation results

A real simulation was run. The code ships alongside this report as mc.py; the full output is in mc-results.json and the fan chart is mc-fan.png.

Design. 50,000 paths, 83 US business days, fixed-length (moving) block bootstrap with a 10-day block length. We resample joint daily changes in DFII30 and in the 30-year breakeven (DGS30 − DFII30) using the same day index, which preserves the empirical contemporaneous correlation between the real and inflation legs (measured at −0.03 daily) without assuming a copula. The nominal 30-year is reconstructed as real plus breakeven, so it is internally consistent rather than modelled separately. Block bootstrapping (rather than i.i.d. draws) preserves volatility clustering and short-horizon autocorrelation, both of which are present in this series. (Fixed 10-day blocks, drawn i.i.d. and concatenated. This is the moving-block bootstrap, not the Politis–Romano stationary bootstrap, which randomises block length geometrically; we name the difference because the code ships.) (Fixed 10-day blocks, drawn i.i.d. and concatenated. This is the moving-block bootstrap, not the Politis–Romano stationary bootstrap, which randomises block length geometrically; we name the difference because the code ships.)

Sampling window. 60% of paths draw from the 2023-09-01 → 2026-09-01 regime window (daily σ 4.13bp for the real leg, 1.89bp for the breakeven), 40% from the full 2010–2026 history (4.43bp and 2.83bp). No drift is imposed; the mixture nonetheless inherits an implied 83-day drift of +7.4bp from the sampled means. This is a modelling choice with consequences and we report both sides of it.

Results — DFII30 at the 31 December 2026 close

Percentile	P5	P10	P25	P50	P75	P90	P95
Real 30y	2.48%	2.61%	2.82%	3.04%	3.28%	3.49%	3.62%
Nominal 30y	4.60%	4.77%	5.04%	5.33%	5.63%	5.90%	6.06%

Threshold probabilities

Threshold	≥2.40%	≥2.75%	≥3.00%	≥3.25%	≥3.50%	≥3.75%
Probability	97.1%	81.1%	55.4%	27.8%	9.6%	2.4%

Additional outputs: the probability of touching 3.00% at any point before year-end is 93.6% (the threshold is 2bp away, so this is close to a certainty and should not be confused with the resolution probability). The 95th-percentile maximum draw-up from here is +73bp. The probability the nominal 30-year finishes at or above 5.50% is 35.2%.

Robustness — the number that matters most. Re-running with the sampled daily changes demeaned (a true zero-drift random walk) returns P(≥3.00%) = 46.4%, a median of 2.967% and a P25–P75 of 2.745–3.197%. The 9-point gap between the as-run and demeaned versions is entirely the inherited drift. The honest statement is therefore: the answer is between 46% and 65% depending on how much weight you place on the 2023–2026 regime persisting, and the Desk's 55% is a deliberate position inside that range, not an output.

Balance-sheet translation (linear duration, convexity ignored). Applying the simulated change in real yield to a 30-year TIPS at a modified duration of 20.5, real return over the horizon distributes P10 −9.5%, P50 −0.3%, P90 +8.6% — real carry plus the duration effect, excluding inflation accrual on the principal, which would add roughly a point of nominal return over four months at the current core rate. Applied to a mature defined-benefit liability at a 12-year effective duration discounted off the long real curve, the present value of liabilities changes P10 −6.1%, P50 −0.7%, P90 +4.4% — a reminder that the left tail of the asset is the right tail of the liability.

Limitations, stated plainly. (1) The bootstrap assumes the future resembles a mixture of two past windows; a regime break of a kind not present in 2010–2026 is not in the distribution. (2) No macro variables drive the path — this is a reduced-form model of the yield itself, not a structural model of the economy. (3) Duration effects above are linear; at these yields convexity would improve the reported left tail for the TIPS position by roughly 100–200bp at the extremes. (4) The 60/40 window mixture is a judgement, and the robustness run above shows exactly how much that judgement is worth (9 percentage points). (5) Overlapping 83-day windows were used for the base-rate calculation, which understates the standard error on that estimate. (6) No multi-agent simulation was run and none is claimed. (7) The TIPS figures above are real returns; inflation accrual on the indexed principal is excluded and would raise the nominal equivalents by roughly 1% over the horizon. (7) The TIPS figures above are real returns; inflation accrual on the indexed principal is excluded and would raise the nominal equivalents by roughly 1% over the horizon.

Market pricing versus the Desk view

Instrument	Market pricing (2 Sep unless noted)	Desk view
30y real yield	2.98% (1 Sep)	Fairly priced for the plateau; we see 55% odds it holds ≥3.00%
30y nominal	5.27% (1 Sep)	35% odds ≥5.50% at year-end — the options market's implied distribution looks thin in that tail
10y breakeven	2.34%	The clearest mispricing in the complex. Core PCE is running at 3.34%; the market is pricing a full 100bp of disinflation as done. Long breakevens are cheap relative to realised inflation, and cheaper still against Brent at $96
IG credit	81bp OAS	Underpaid. At a 2.98% real risk-free rate, 81bp is a rounding error for taking corporate risk
High yield	266bp OAS	Underpaid. At or tighter on 5.5% of days since Sep 2023; strictly tighter on 3.7%, at the same time the risk-free real alternative is at a series high
Equity volatility	VIX 15.2	Complacent given the Break scenario at 25%
Front end	2y at 4.39% vs EFFR 3.63%	Consistent with our view; this is the one place the market and the Desk clearly agree

Highest-conviction mispricing: long-dated breakevens against realised inflation. What consensus is missing: that the corporate and public pension systems are receiving opposite signals from the same rate, and only one of them is required to notice. What would prove the Desk wrong: a Q4 in which core PCE decelerates below 3%, the 2-year falls through the effective funds rate, and DFII30 closes 2026 below 2.75%. In that world our Plateau weight was too high and our Relief weight far too low.

Universal-owner portfolio map

Direction and magnitude band by asset class, under each scenario. This is strategic mapping, not advice.

Asset class	Relief (<2.75%)	Plateau (2.75–3.25%)	Break (≥3.25%)
Long nominal government bonds	↑↑ strong (+8–12%)	→ flat to slightly negative	↓↓ strong (−8–12%)
Long TIPS / index-linked	↑↑ strong	→ flat (P50 −0.3% over the horizon)	↓↓ strong (P10 −9.5%)
Corporate DB liabilities (marked)	↑ liabilities rise, funded ratio falls	→ stable near record surplus	↓ liabilities fall, funded ratio rises further
Public DB (assumed-return discounting)	↑ modest asset relief, liability unchanged	↓ slow bleed: assets marked, liabilities not	↓↓ asset drawdown, liability still unchanged
Investment-grade credit	↑ moderate	→ carry-positive, spread-neutral	↓ moderate; 81bp is thin protection
High yield / private credit	↑ moderate	→ carry-positive	↓↓ the refinancing cost of a 5.5%+ base rate compounds
Global equities	↑ moderate	→ multiple compression pressure, earnings-dependent	↓ moderate-to-strong; discount-rate-sensitive growth worst hit
Listed & unlisted infrastructure	↑ moderate	↓ moderate — cap rates follow real rates with a lag	↓↓ strong; the asset class was underwritten at a sub-1% real rate
Core real estate	↑ moderate	↓ moderate; cap-rate expansion continues	↓↓ strong
Private equity	→ lagged	↓ hurdle-rate compression of the equity risk premium	↓↓ exit multiples and leverage cost together
Insurance / annuity writers	↓ reinvestment yield falls	↑↑ the single best environment in a generation	↑↑ stronger still, subject to unrealised-loss optics
Sovereign / reserve managers	→	↑ a 3% real risk-free asset restores the fixed-income leg	↑ but with mark-to-market pain in transition
Gold and reserve diversifiers	↑	→	↓ higher real carry cost
EM local debt	↑↑	→	↓↓ dollar and real-rate squeeze together

The asymmetry to internalise. Milliman's 100 largest corporate DB plans closed June 2026 109.5% funded with a $114bn surplus on a 5.61% discount rate. Milliman's 100 largest public plans closed July 88.2% funded with an $816bn gap on liabilities of $6.911tn — and that gap widened by $38bn during a month when long rates were near their highs, because public plans discount at an assumed return and therefore capture none of the liability relief while taking the full asset mark. Multiemployer plans, at 106% funded at midyear, sit with the corporates. Same rate. Opposite sign. The difference is entirely a discounting convention.

Milliman publishes a two-sided end-2026 forecast, and it is worth reading precisely: the optimistic case pairs a 5.91% discount rate with 10.61% annual asset returns and reaches 116% funded; the pessimistic case pairs 5.31% with 2.61% returns and falls to 105%. The eleven-point band is a joint rate-and-return swing, not a pure rate sensitivity. On our own arithmetic the discount rate does most but not all of the work: 30bp on a $1.208tn PBO at roughly 12-year duration is about four points of funded status, with the return assumption supplying the rest.

Second- and third-order effects

The hurdle rate resets, silently. A durable 3% real risk-free rate means every private-market underwriting model built on a 0–1% real rate is carrying an embedded 200–300bp of unearned excess return. This does not show up as a loss. It shows up as a decade of realised returns that fall short of the assumptions used to justify the allocation.
Liability-driven investment becomes rational again, at scale. For the first time in the series' history a closed DB plan or an annuity writer can defease thirty-year real liabilities at a 3% real yield. Expect corporate DB de-risking and pension risk transfer to accelerate — which mechanically removes long-duration buyers from equities and private markets and adds them to the long end. This is self-limiting: the de-risking bid caps the Break scenario.
Public plans face a governance question, not a market one. An $816bn gap that widens while the risk-free real rate hits a record is a discount-rate-assumption problem. The pressure to lower assumed returns will grow, and every 10bp reduction raises reported liabilities on a $6.9tn base by roughly $80–100bn at typical durations.
Japan's repatriation is the slow variable. If a 3% domestic 10-year persists, Japanese life insurers and banks face a decade-long rebalancing out of foreign duration. This is not a September event; it is a multi-year drain on the marginal demand for US and European long bonds. USD/JPY at 159.97 makes the currency-hedged calculus worse still.
Fiscal reflexivity. $1,247bn of annual federal interest at 3.84% of GDP is itself a source of the deficit that is a source of the term premium. Every 100bp of additional long-end yield eventually adds to the supply that produced it. This loop is slow and it is not self-correcting on a four-month horizon.
Housing and the real economy. A 6.71% mortgage rate (3 September) with a 2.98% thirty-year real yield means housing affordability is now a real-rate problem, not a policy-rate problem. Front-end easing on its own would do little to change it.
Insurance capital gets a windfall and an optics problem. Higher reinvestment yields improve economics substantially while unrealised losses on legacy books look worse. Regulatory and rating-agency treatment of that divergence becomes a live issue.
The equity risk premium compresses arithmetically. With a 3% real risk-free rate, an equity market must deliver materially higher real earnings growth to justify the same multiple. Concentration in a small number of high-duration growth names makes this a concentrated, not a diversified, exposure to the discount rate.
Sovereign allocators get their fixed-income leg back. Invesco's 2026 study reports sovereign equity allocations falling to 30% from 32% across 90 SWFs and 54 central banks managing ~$29tn. A 3% real risk-free rate is a coherent reason for that drift to continue.
Stewardship and long-horizon capital. Higher real discount rates penalise long-payback investment — grid, transmission, decarbonisation capex, and the physical build-out behind AI infrastructure — precisely the assets universal owners have been increasing. The governance question for an owner of the whole market is whether to accept a higher hurdle on projects whose systemic value accrues to the portfolio rather than to the project.

Watch dashboard

#	Indicator	Current	Source	Threshold that changes the model	Direction
1	`DFII30` 30y real yield	2.98% (1 Sep)	FRED	5 consecutive closes >3.10% → Break; <2.75% → Relief	The variable
2	2y less EFFR	+76bp (4.39 / 3.63)	FRED	Turns negative → Relief odds rise sharply	↓ real yields
3	10y breakeven	2.34% (2 Sep)	FRED	>2.60% → the move stops being purely real	Mixed
4	Core PCE y/y	3.34% (Jul)	FRED	<3.00% → Relief; >3.50% → Break	Two-sided
5	Treasury buyback operation sizes	≥$4bn max from 9 Sep	Treasury SB0607	Consistent full-size operations with 20s/30s richening → caps Break	↓ real yields
6	Quarterly Refunding, 4 Nov 2026	scheduled	Treasury	Long-end coupon increase → Break	↑ real yields
7	HY OAS	266bp (2 Sep)	FRED	>350bp → Dislocation live	↓ real yields
8	IG OAS	81bp (2 Sep)	FRED	>120bp → risk premium normalising	↓ real yields
9	VIX	15.2 (2 Sep)	FRED	>25 with HY >350bp → Dislocation	↓ real yields
10	10y JGB	3.005% (1 Sep)	Reuters	Sustained >3.25%, or a BOJ hike with evidence of foreign-bond selling → Break	↑ real yields
11	USD/JPY	159.97 (28 Aug)	FRED	<145 → repatriation accelerating	↑ US real yields
12	30y fixed mortgage	6.71% (3 Sep)	Freddie Mac / FRED	>7.25% → real-economy strain, two-sided	Two-sided
13	Brent	$96.02 (1 Sep)	FRED	>$110 → breakeven repricing; <$80 → Relief support	Two-sided
14	Unemployment rate	4.1% (Jul)	FRED	>4.5% → Relief/Dislocation odds rise	↓ real yields
15	Milliman PPFI funded ratio	88.2% (31 Jul)	Milliman	<85% → public-plan discount-rate pressure becomes a policy story	Governance
16	US–Iran conflict / Strait of Hormuz throughput	Active; partial flows	Wire + shipping data	Escalation lifting Brent >$110 → breakevens reprice and the "real, not inflationary" framing breaks; a durable ceasefire with full transit → Relief support	Two-sided
16	US–Iran conflict / Strait of Hormuz throughput	Active; partial flows	Wire + shipping data	Escalation lifting Brent >$110 → breakevens reprice and the "real, not inflationary" framing breaks; a durable ceasefire with full transit → Relief support	Two-sided

Red team — how this could be wrong

1. We may have laundered a trend into a probability. The most serious criticism of this report is internal: our simulation returns 55.4% as run and 46.4% with the drift removed, and we chose a 60/40 window mixture that inherits +7.4bp of drift. If the 2023–2026 rise in real yields was a level adjustment that has completed rather than a trend that continues, the correct answer is nearer 46% and our base case should have been Relief-weighted. We have disclosed the exact size of this dependency rather than burying it, but disclosure is not the same as being right. And the criticism is broader than the window: the +6pp we award for regime persistence in the evidence ladder and the +9pp of drift the simulation inherits are the same belief, counted in two places and then described as corroborating each other. And the criticism is broader than the window: the +6pp we award for regime persistence in the evidence ladder and the +9pp of drift the simulation inherits are the same belief, counted in two places and then described as corroborating each other. What would falsify our call: DFII30 below 2.85% by the 4 November refunding.

2. The buyback may be much bigger than we credit. We assigned Treasury's doubling of long-end buybacks a −3pp impact. If the operations run consistently at the new $4bn maximum from 9 September through 4 November, that is a materially larger official bid in the 10–30 year sector than a −3pp adjustment implies, and Treasury has signalled it will discuss further sizing at the November refunding. A Desk that under-weights the issuer's own demand for its own long bonds has made an elementary error. Falsifier: 20s/30s richening against the 10-year through October.

3. The Japan channel is a mechanism, not a measurement. We have a Reuters-sourced 10-year JGB print at 3.005% and a 2-year at a 31-year high. We do not have verified data on Japanese cross-border bond flows, and we were unable to corroborate a widely repeated 30-year JGB figure — the aggregator we checked returned September 2025 data. Our +2pp for the Japan channel is therefore a judgement about a plausible mechanism, not an inference from observed flows. It could be worth zero on this horizon. It could also be worth considerably more.

4. The base case may be too wide to be interesting. A 50bp band around 3% catching 55% of the distribution is close to what a random walk with this volatility would deliver anyway. A reader is entitled to ask what the Desk is adding beyond the arithmetic. Our answer is the conditional structure — the tripwires and the mechanisms — rather than the headline number, and readers should weight the report accordingly.

5. Second-order claims are directional, not quantified. The transmission from a 3% real rate to infrastructure cap rates, private-equity exit multiples and public-plan discount-rate policy is real but its timing and magnitude are contested. We have given directions and magnitude bands, not point estimates, because the honest state of the evidence does not support point estimates.

6. Public-plan liabilities and real yields are not directly linked. Our sharpest framing — that corporate and public plans receive opposite signals from the same rate — is correct as to mechanism but should not be read as saying that public plan liabilities respond to DFII30. They do not respond to market rates at all; that is the entire point, and it is why the divergence is a governance issue rather than a market one.

7. We have written a real-rate report during a shooting war and not named it. Our own primary source attributes the global bond move to the US–Iran conflict and elevated oil prices. We have used the Brent print and omitted its cause. If the conflict escalates, the term-premium story we tell becomes an inflation story we did not price, and evidence row 2 (+1pp for "disinflation is already assumed") inverts. If it de-escalates, Brent falls, breakevens hold and Relief gets cheaper than our 15%. Either way the omission was ours, not the market's.

Methodology box

The Probability Desk builds each scenario from three inputs and one aggregation rule. Base rate: the historical frequency of the relevant change in the resolution variable, stated with its reference class and period (here: 83-business-day changes in DFII30, 2010-02-22 to 2026-09-01, n = 4,053 overlapping windows). Evidence: dated, cited items that move the prior, each with its direction, strength and probability impact shown in the evidence-update table. Simulation: where a forecast variable admits one, a real Monte Carlo whose code, seed and outputs ship with the report (mc.py, seed 20260903, 50,000 paths, mc-results.json). Aggregation: the posterior is the prior adjusted by the tabulated evidence impacts, cross-checked against the simulation, then placed on a 5% grid, subject to the four weights summing to 100. Where the simulation and the adjusted prior disagree, the disagreement is reported rather than reconciled silently.

The MiroFish multi-agent engine was not run for this report and no multi-agent inputs are claimed. All market data is from FRED (Federal Reserve Bank of St. Louis) and the US Treasury, read on 3 September 2026. One widely circulated figure — a Milliman 100 funded ratio of 112.1% on a 6.02% discount rate as of 31 July — was checked, could not be corroborated against Milliman's own published page, and is excluded; only the verified 30 June figure is used.

Disclaimer. This report is for informational and research purposes only and does not constitute investment, legal, tax, or financial advice. Editorial scenario analysis only. Not investment, actuarial, or geopolitical advice.

The Probability Desk · Universal Asset Owners · 3 September 2026. Scenario resolves 31 December 2026 and will be graded in the public calibration log.

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Produced and edited by the UAO editorial desk. Not investment advice.