NXT Lab · Research · Bonds

EXPERIMENTALExperimental. The bond maths matches Treasury's own auction prices. What a euro investor ends up with also rests on judgements: how the dollar drifts, what hedging costs, how far real yields wander, and how Slovakia taxes a TIPS. Each is changed on its own in the sensitivity table.

The US 30-year TIPS: 3% above inflation, seen from euros

In February 2026 the US Treasury sold a new 30-year inflation-protected bond with a 2.375% real coupon. Since then real yields have risen, its price has fallen, and a buyer today locks in more than 3% a year above US inflation until 2056.

The February 2056 TIPS since its first auction

Cash price in USD, per 100 of face value The same in EUR

Source: US Treasury real yield curve (30-year point), CPI-U (BLS), ECB EUR/USD; priced with Treasury's TIPS formulanxtdev.sk NXTlab

What this bond is

A TIPS pays a fixed real coupon on a principal that grows with the US consumer price index (CPI-U, with a three-month lag). At maturity you get the inflated principal back, or 100 if prices have fallen, whichever is more. If you hold it to the end and you count in dollars, the real yield you buy at is the real return you get. Nothing else in finance offers that.

Auction	Real yield	Price (real, per 100)	Index ratio	Bid-to-cover	Size

The 2.35% you may have read is roughly the coupon (2.375%), not the yield. The coupon is fixed for 30 years; the yield moves with the price. Today's buyer pays for 100 of real principal and earns above inflation to 2056.
It is a long bond in disguise. Its real duration is years: if real yields rise by one point, the price falls by about . Inflation protection does not protect against that. Hold to maturity and it does not matter; sell in between and it does.
The February buyer is down so far. In dollars, after the August coupon and the inflation uplift: . In euros it is , because the dollar rose from to per euro.

Real yields since 1871

The market has quoted a real yield only since 1997. Before that it has to be built from the nominal long rate and inflation, in two ways. Ex ante takes off the inflation of the past ten years: what a lender could have guessed. Ex post takes off the inflation of the next ten years: what a lender actually earned. The gap between the two lines is the inflation surprise.

From

US real 10-year yield: guessed, earned and traded

Source: Robert Shiller (long rate, CPI since 1871), US Treasury real curves, Cleveland Fed modelnxtdev.sk NXTlab

Real yields were mostly positive, but not for lenders in the 1910s, 1940s and 1970s. Then inflation came after the bonds were bought, and holders of nominal bonds lost up to a year in real terms over ten years (). A TIPS is the insurance against exactly those decades.
The ex-ante real 10-year yield has averaged since 1881. Today's 30-year TIPS yield of is above of those 145 years of months.
Among traded 30-year TIPS yields since 2010 it is the highest, the percentile. In 2021 the same bond class paid : buyers then locked in a real loss.

Expected inflation

The gap between a nominal Treasury and a TIPS of the same maturity is the breakeven: the inflation at which both pay the same. It is the market's forecast, plus a small insurance premium. The Cleveland Fed fits a model to yields, swaps and surveys, and professional forecasters are asked directly.

US inflation: what came, and what was expected

Source: Shiller CPI, US Treasury curves (breakeven = nominal − TIPS), Cleveland Fed, Philadelphia Fed SPFnxtdev.sk NXTlab

Was the forecast right? Each 10-year forecast against the inflation that followed

Realised = CPI over the next 10 years, a year; the line ends ten years agonxtdev.sk NXTlab

10-year inflation forecast	Average miss	Average size of the miss

The real cost of capital, without inflation

Strip inflation out and every investment competes with the same thing: the real yield on a safe bond. That is the real cost of capital. Shares compete with it through their real earnings yield, 1 / CAPE (ten years of inflation-adjusted earnings over today's price): roughly what stocks earn a year above inflation if valuations stay where they are.

Real bond yield against the real earnings yield of US stocks, since 1881

Real bond yield: 10y TIPS from 2003, Cleveland Fed 1982–2002, 10y nominal − past 10y CPI before; 1/CAPE: Shillernxtdev.sk NXTlab

Real yield today	% a year above inflation	What it is

What it pays a euro investor

The TIPS guarantees a real return in dollars, against US prices. A euro investor gets two extra things: the dollar, and euro inflation instead of US inflation. There are two ways to hold it:

Unhedged: you carry the dollar. Over 30 years currencies tend to move with the inflation gap (purchasing-power parity), but year to year EUR/USD swings about 9%.
Hedged: a rolling forward removes the dollar, and costs the gap between US and euro short rates, now a year. That is far more than the inflation gap the TIPS pays you for ().

Currency

EUR 100 in the TIPS today, to maturity in 2056

Median path Middle half of paths 1 in 20 / 19 in 20 Euro AAA 30-year bond at today's yield

Model: tips-eval, paths; coupons taxed at 13% and re-investednxtdev.sk NXTlab

Outcomes by holding period

Currency Tax

Held for	Expected a year	Median a year	Real median a year	Worst 1 in 20 a year	Chance of loss	Beats euro AAA	Median worst fall

Return above euro inflation a year, held to 2056, every path

UnhedgedHedged

Share of paths; EUR, coupons taxed at 13%, deflated by 2% a year euro inflationnxtdev.sk NXTlab

What the answer depends on

Each row changes one assumption and re-runs the paths. Coupons taxed at 13%; "real" means above 2% euro inflation.

Change	Unhedged		Hedged
Change	5y expected a year	To 2056, real median a year	5y expected a year	To 2056, real median a year

Price against real yield

The real clean price per 100 today at other real yields, and the change in value that would mean (index ratio unchanged).

Real yield	Price per 100	Change from today

2046 or 2056? The same real yield, ten years apart

Side by side, per USD 1,000 of face value

Bought at Treasury's closing price, held to maturity, US inflation at a flat rate you choose. "Re-invested" puts each coupon back into the same bond at today's yield; "not re-invested" leaves it as cash that earns nothing. Coupon tax is the 13% Slovak rate; the worst case also taxes the whole gain at 19% at maturity.

US inflation to maturity

Item	TIPS Feb 2046	TIPS Feb 2056

The same finish line

The two returns above cover different spans. To compare them fairly, run both to the same date. To 2046: the 2056 is sold in February 2046, ten years before it matures, at whatever 10-year real yield the market then pays. To 2056: the 2046's money is re-invested for the last ten years at that yield. Real return a year, before tax, coupons re-invested.

Real yield in Feb 2046	To Feb 2046		To Feb 2056
Real yield in Feb 2046	2046 held	2056 sold	2046, then re-invested	2056 held

In euros: the Monte Carlo for each

The same model as above, run once per bond from its own price and yield: euro value, coupons taxed at 13% and re-invested. "Real" means above 2% euro inflation; the euro AAA hurdle is the 20-year yield for the 2046 and the 30-year for the 2056.

Currency

EUR result	TIPS Feb 2046	TIPS Feb 2056

Which one to buy

Buy the 2046 if

Buy the 2056 if

Tax in Slovakia

How Slovakia taxes a directly held TIPS has not been tested in practice. Treat this section as questions to settle with your tax adviser.

Coupons: we tax them at 13% when paid, the rule our Bund model uses for bond coupons from 2026.
The inflation uplift and price gains: on a listed security held for more than a year they are exempt. But Treasuries trade over the counter, and the uplift may count as bond income at maturity. The "income" case taxes the whole euro gain at 19% at the end. That taxes inflation itself, and costs a year to 2056 (unhedged).
An accumulating UCITS TIPS fund avoids both: no coupon tax, and exempt after a year. But such funds hold all maturities (duration about 7 years, not 20), so they lock in today's 30-year yield only in part.

Strong and weak sides of this model

What it gets right

The bond maths is exact. It reproduces Treasury's February and August auction prices and index ratios.
One world per path. Real yields, US inflation and the dollar are cut from the same months of 2000–2026, so 2008 and 2022 arrive whole.
Neutral on yields. The expected real yield stays at today's level; the model does not bet on falling yields.
Long history checks the story. 150 years of real yields show how unusual 3% is, and when lenders without inflation protection lost.

What it cannot see

The dollar's drift is a judgement. Inflation gap or rate gap moves the unhedged answer by 1.4 points a year to 2056, more than anything else.
The hedge cost is held fixed. In reality it moves with US and euro short rates, and with US inflation.
US inflation, not euro inflation. A euro inflation shock that the dollar does not offset is not insured.
Before 1997 the real yield is reconstructed, not traded. The Treasury's 30-year curve point is used as the yield of this bond, which matures six months earlier.

What to watch

The Fed and the ECB. Every cut in US rates relative to euro rates makes the hedge cheaper, and narrows the gap between the hedged and unhedged answers.
The February 2027 auction of the next 30-year TIPS, and this bond's reopening in August 2027. A weak bid-to-cover would mean a lower price and a higher yield for a later buyer.
Breakevens. At the market expects close to 2% US inflation for 30 years. Inflation has run at over the past year. If you think it stays higher, a TIPS beats a nominal Treasury.

Method

Sources: TreasuryDirect auction results (CUSIP 912810US5); US Treasury daily par and real yield curves and long-term real average; BLS CPI-U; Robert Shiller's monthly data (shillerdata.com); Federal Reserve Bank of Cleveland inflation expectations; Philadelphia Fed Survey of Professional Forecasters; ECB euro-area AAA yield curve and EUR/USD reference rates. Not investment advice.