Bills, Notes and Bonds: What a Yield Does to a Price

Buy one Treasury security at par on a day in 2026, revalue it on another, and watch the price move. The numbers are Treasury's own daily curves, nominal and inflation-protected.

Worked example — Bills, Notes and Bonds: What a Yield Does to a Price

Price per 100 face	94.28
Change since purchase	−5.72%
Yield move	+38 bp
Modified duration	15.70
Basis points per 1% of price	6
Real yield (TIPS)	2.96%
Breakeven inflation	2.28%

These are the values the calculator shows when the page opens. Change any input above to recompute them.

Loading interactive simulation...

The long end rose least in 2026 and lost the most 🖖

Over the eight months to 4 September the 2-year yield rose 90 basis points and the 30-year rose 38. Buy each at par on 2 January and revalue them on the September curve: the 2-year is worth 98.29 and the 30-year 94.28. The long bond lost 3.35 times as much money from 0.42 times the yield move. Duration is the whole reason, and the tool prints it — 1.92 years against 15.70. Move the security selector down the list and watch the loss grow while the yield move shrinks.

Almost none of it was inflation 🖖

Treasury publishes a second curve, for inflation-protected securities, and the gap between the two is the inflation rate the market is pricing. Of the 38 basis points the 30-year added this year, 33 came from the real yield, which went from 2.63% to 2.96% and touched 3.06% on 17 August. Five came from expected inflation. Fear of inflation is the usual explanation for a high long yield, and here it is doing almost none of the work.

Thirty-year inflation is priced below ten-year inflation, and has been all year 🖖

On 4 September the breakeven was 2.35% at ten years and 2.28% at thirty. That is the wrong way round for anyone expecting inflation to compound away over decades, and it is not one day's quirk: it held on 170 of the 171 sessions in the file. Select the 10-year, read the breakeven card, then select the 30-year.

A price of 94 is not a loss unless you sell 🖖

The 30-year at 94.28 still pays 100 at maturity, and every coupon in between. The loss belongs to a seller. That is why one bank can carry the same bond at 94 and another at 100, depending on whether it is held to maturity, and it is the distinction that decided Silicon Valley Bank in 2023. What the price card shows is what somebody else would pay you today.

Every maturity on the curve now costs more than the debt already pays 🖖

The average interest rate across all interest-bearing federal debt was 3.447% on 31 July. The cheapest point on the 4 September curve is the one-month constant maturity at 3.79%, and the thirty-year is 5.24%. As old debt matures and is reissued the average climbs toward the curve, which happens whether or not a single yield ever moves again.

References (2)

The two curves this tool is built from, and how they are constructed — which is why its figures are closes rather than intraday quotes: U.S. Department of the Treasury, "Interest Rate Statistics" — Daily Treasury Par Yield Curve Rates and Daily Treasury PAR Real Yield Curve Rates.
The long-end intervention the tool's opening section describes, in Treasury's own words: U.S. Department of the Treasury, "Treasury Announces Increased Sizes of Nominal Long-End Liquidity Support Buybacks Beginning September 9", press release, 19 August 2026.

By the 42Math team · Updated 2026-09-08

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

30-year, January to September - A 30-year bought at par on 2 January, when the par yield was 4.86%, revalued on the 4 September curve at 5.24%. The price is 94.28 per 100 of face, a change of −5.72% from a yield move of 38 basis points. Modified duration 15.70.
2-year, same months - The same eight months for a 2-year note. Its yield moved 90 basis points, more than twice as far as the 30-year's, and the price is 98.29 — a change of −1.71%. Modified duration 1.92, which is the whole difference.
13-week bill - A 13-week bill across the same months, where the discount rate went from 3.65% to 3.91% and the price is 99.01 per 100 of face. The change is −0.07%, and a bill has no duration card because it has no coupons to weight.
Revalued at the August high - The 30-year revalued on 17 August, the 2026 high at 5.31%, where the price is 93.28 and the change −6.72%. The real yield that day was 3.06% and the breakeven 2.25%.
Bought at par today - A 30-year bought at par on the 4 September curve, so the yield is 5.24%, the price is exactly 100.00 and nothing has moved yet. The real yield is 2.96% and the breakeven 2.28%.