Lesson 7 of 8
The yield curve
The real US Treasury curve for 11 September 2026, read properly: what each point is, what the slope contains, and the forward rate hidden inside two of them.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A yield curve is one issuer's yields plotted against maturity on one day, and nothing else.
- The published par curve is not a set of spot rates. Turning one into the other is called bootstrapping.
- Two points on the curve imply a forward rate, which is arithmetic rather than a forecast.
A curve is a photograph of one day. It holds the credit quality constant, varies only the maturity, and lets you read the price of time on its own. The Treasury publishes its own every business day, which makes it the cleanest such picture that exists.
US Treasury par yields, 11 September 2026
- Par yield
Show the numbers
| Par yield | |
|---|---|
| 1M | 3.93% |
| 3M | 4.07% |
| 6M | 4.12% |
| 1Y | 4.35% |
| 2Y | 4.63% |
| 3Y | 4.69% |
| 5Y | 4.78% |
| 7Y | 4.87% |
| 10Y | 4.96% |
| 20Y | 5.38% |
| 30Y | 5.35% |
What each point is
The published series is a par curve: for each maturity, the coupon rate at which a new Treasury of that maturity would price at exactly face value. It is built by fitting through actual traded securities, which is why it is a curve rather than a list.
A spot rate is different. It is the yield on a single payment at one date, with no coupons in the way. Spot rates are what you actually need to discount a dated cash flow, and they are not published.
Bootstrapping is the procedure that turns one into the other. Take the shortest maturity, where par and spot agree because there is only one payment. Use it to strip the first coupon out of the two-year par bond, which leaves the two-year spot rate. Repeat down the curve. Each step uses only rates already solved, which is why the order matters and why it is called bootstrapping.
Reading the slope
On this day the curve rises almost all the way out: 3.93 percent at one month and 4.96 at ten years, a difference of 1.03 points. Then it rises again to 5.38 at twenty years and comes back down to 5.35 at thirty.
That final step down is real, and it is the kind of detail a smoothed chart hides. A thirty-year yield three basis points below a twenty-year one is a small inversion at the long end of the curve, on one day.
The forward rate
Two points on a curve imply a third number. If one year pays 4.35 percent and two years pays 4.63 percent, then lending for two years must equal lending for one and relending for the second.
Working it: 1.0463 squared is 1.09474. Divide by 1.0435 and you get 1.04911. The one-year rate, one year forward, implied by this curve is 4.91 percent.
That number is arithmetic, not a prediction. It is what the curve's own two points require of each other on this one day. Whether the one-year rate a year from now turns out to be 4.91 percent is a separate question, and the curve does not answer it. Read a forward rate as the rate at which the two maturities are indifferent, which is exactly what it is.
What a curve does not contain
It does not contain a forecast, a policy intention or a recession signal that can be read off directly. It contains yields, on one issuer, on one day. Everything else said about a curve is interpretation laid on top, and the interpretation changes while the numbers do not.
Check yourself
The published Treasury curve is a par curve. What does that mean?
- Every bond on it trades at par today
- Each point is the coupon at which a new bond of that maturity would price at face value
- It shows the yield on a single payment at each date
Show the answer
Answer: B.
Par yields describe hypothetical new issues priced at face. A yield on a single dated payment is a spot rate, which has to be bootstrapped out of the par curve.One year yields 4.35 percent and two years yields 4.63 percent. What does the curve imply for the one-year rate starting in a year?
- 4.63 percent
- About 4.91 percent
- 4.35 percent
Show the answer
Answer: B.
1.0463 squared divided by 1.0435 is 1.04911. The second year has to carry the extra return that makes two one-year investments equal one two-year investment.On 11 September 2026 the thirty-year Treasury yielded 5.35 percent and the twenty-year 5.38. What is that?
- A data error, since longer always yields more
- A small inversion at the long end of the curve on that day
- Evidence that rates will fall
Show the answer
Answer: B.
Curves are not required to rise everywhere. It is a three basis point inversion between two long maturities on one session, and it is what the published series says.Sources
- US Department of the Treasury, Daily Treasury Par Yield Curve Rates, session of 11 September 2026. Every yield in this lesson is from that day's published table. ValueScreener stores the ten-year figure for the same session and it agrees to the basis point.
- Damodaran, Investment Valuation: the use of a government yield curve as the risk-free term structure in valuation.
What this leaves out
- A curve is one day. The figures here describe 11 September 2026 and no other date, and they will not be the figures on the day you read this.
- Par yields are a fitted series, not the traded yield of any particular security.
- A forward rate is what two points on a curve require of each other. It is not a forecast, and this lesson makes no claim about future rates.
- Nothing here is advice about any security.