Treasury Curve Construction
Treasury Curve Construction
The Treasury yield curve you see published on news sites and financial terminals is not an observed fact; it is a constructed object. The US Treasury issues securities at specific maturities: 3-month and 6-month bills, 2-year notes, 3-year notes, 5-year notes, 7-year notes, 10-year notes, 20-year bonds, and 30-year bonds. These discrete points have actively traded prices. But there are many maturities in between—1.5 years, 2.3 years, 4.7 years—where no Treasury security exists.
Financial institutions and the Treasury Department construct a smooth yield curve from the available data points through a process called bootstrapping. Bootstrapping uses the yields of securities at known maturities to infer the yields at intermediate maturities. The result is a complete curve from 0 to 30 years (or sometimes 0 to 50 years, if inflation-protected securities and very long bonds are included). This constructed curve is used by traders, investors, portfolio managers, and risk managers as the benchmark reference rate.
Understanding how the curve is constructed matters because it tells you where the curve is supported by liquid, heavily traded securities, and where it is interpolated guesswork. If the curve at the 10-year point is backed by billions of dollars of trading volume, the 10-year yield is reliable. If the curve at the 11-year point is pure interpolation between the 10-year and 20-year points, and those bonds are less liquid, the 11-year yield is less reliable. For investors, this means the short end of the curve (2, 5, 10 years) is the most relevant and most reliable; the long end and the very short end have more estimation and are less precise.
Key takeaways
- The Treasury yield curve is constructed from discrete points (2-year, 3-year, 5-year, 10-year, 30-year) using bootstrapping to interpolate intermediate maturities.
- Bootstrapping infers zero-coupon yields (spot rates) from the prices of coupon-bearing securities, then uses those spot rates to build the curve.
- On-the-run Treasury securities (the most recently issued at each maturity) are the primary data points for curve construction because they are most liquid.
- The short end of the curve (2–10 years) is the most reliable; the long end (beyond 20 years) is less liquid and subject to greater interpolation.
- Multiple curve construction methodologies exist (spline, Nelson-Siegel); different sources may publish slightly different curves. The differences are usually minor.
The Role of On-the-Run Securities
The Treasury Department regularly auctions new securities at standard maturities. When a new 10-year Treasury is issued, it becomes the on-the-run 10-year—the most recently issued 10-year security. It is the most liquid point on the curve because it has the highest trading volume and the tightest bid-ask spreads. Traders, investors, and institutions continuously trade the on-the-run 10-year. The price and yield of this security reflect real-time market consensus.
The on-the-run point at each maturity becomes the anchor for the constructed curve. The 2-year on-the-run, the 5-year on-the-run, the 10-year on-the-run, and the 30-year on-the-run are the main reference points. Other securities—older issues at the same maturity (called off-the-run securities), floating-rate notes, TIPS (inflation-protected Treasuries)—provide additional data points that can refine the curve, but the on-the-run securities are the primary drivers.
From these anchor points, mathematicians and traders interpolate the curve. If the 2-year on-the-run yields 3% and the 10-year on-the-run yields 4%, the curve between 2 and 10 years must somehow connect these two points. A simple linear interpolation would put the 5-year yield at 3.5%; a more sophisticated interpolation method (a spline, for instance) might curve the line smoothly, putting the 5-year at 3.6% or 3.4% depending on the curvature. Different interpolation methods can produce slightly different intermediate yields.
Bootstrapping: From Coupon-Bearing to Zero-Coupon Yields
Under the surface, curve construction relies on bootstrapping: converting the yields of coupon-bearing Treasury securities (which pay interest twice per year) into zero-coupon yields, then using those zero-coupon yields to create a smooth curve.
Here is the conceptual process. A 2-year Treasury note issued today has a stated coupon rate—say 4.5% per year. It will pay $22.50 in coupon interest six months from now, another $22.50 in one year, another $22.50 in 1.5 years, and finally $1,022.50 (the final coupon plus principal) at the 2-year maturity. The price of this security is the present value of all these future cash flows.
A zero-coupon bond, by contrast, makes no coupon payments; it is sold at a discount and redeems at face value. A 2-year zero-coupon bond sells for, say, $920 today and redeems for $1,000 in 2 years. The zero-coupon yield is the rate that equates the current price to the future value, compounded over the 2-year period.
Bootstrapping uses the prices of coupon-bearing securities to infer the zero-coupon yields at each maturity. Given the price and coupon schedule of the 2-year note, you can solve for the 2-year zero-coupon yield. Given the zero-coupon yields at 2 years and the price and cash flows of the 5-year note, you can solve for the 5-year zero-coupon yield. This step-by-step process is bootstrapping.
Once you have zero-coupon yields (also called spot rates) at each maturity, you have a complete picture of the term structure of discount rates. Any intermediate maturity can be interpolated. An investor trying to price a bond or a portfolio can now discount each cash flow at the appropriate zero-coupon rate.
Sources of Curve Data
Different financial institutions publish Treasury curves. The Federal Reserve publishes an official curve daily. Bloomberg, Reuters, and other data providers publish curves based on their own methodologies and data feeds. The differences between these curves are usually small (a few basis points) but can occasionally be larger (10+ basis points) if the underlying data or interpolation methods differ significantly.
For most investors, the published curve from a reputable source (the Fed, Bloomberg, or the Treasury Department's website) is reliable for decision-making. The curve will shift throughout the day as new transactions occur. The 10-year yield might move from 4.1% to 4.15% in the course of an hour, for instance. These changes reflect real trading and changing market conditions. The curve published at 4 p.m. Eastern Time will be different from the curve published at 9 a.m. Eastern Time.
Individual investors typically use the end-of-day Treasury curve published by the Treasury Department or reported by financial news sites. This is sufficient for weekly or monthly portfolio rebalancing decisions. Traders and portfolio managers may use real-time curves updated continuously throughout the day. For a three-fund investor buying an aggregate bond fund (BND or AGG) or Treasury funds (IEF, TLT), the exact curve construction methodology is transparent; you do not need to worry about how the curve was built. The fund company handles that.
Why Curve Construction Matters
Understanding curve construction helps you interpret curve data accurately. When you see that the 10-year Treasury yields 4.2%, you know that yield is based on actual trading of the on-the-run 10-year security. When you see that the 11-year maturity yields 4.18%, you know that point is interpolated and less reliable; there is no 11-year Treasury security. This distinction matters if you are trying to identify relative value along the curve.
It also matters when the curve is distorted by supply or demand imbalances. If there is an excess supply of 10-year Treasuries and a shortage of 5-year Treasuries, the 10-year yield might be pushed up artificially (making 10-years look cheap), while the 5-year yield is pushed down (making 5-years look expensive). An interpolation of intermediate yields might not capture this distortion well, giving you a false sense of value. Experienced traders study not just the smooth curve but also the actual trading levels at each on-the-run point to identify supply-driven distortions.
Additionally, different Treasury securities have different liquidity characteristics. The 10-year on-the-run is extremely liquid; bid-ask spreads are tight. The 30-year on-the-run is much less liquid; spreads are wider. A 20-year off-the-run bond (an older issue) is less liquid still. When constructing a curve, these liquidity differences should ideally be accounted for. Some curves weight on-the-run securities more heavily (because they reflect more reliable real-time pricing) than off-the-run securities or alternative data sources.
Flowchart: How the Treasury Curve Is Constructed
Construction and Real-World Implications
If you are building a Treasury ladder (buying individual Treasury securities across maturities), you do not need to understand bootstrapping in detail. You can simply look at the published yields on the Treasury Department's website and buy securities along the ladder. But if you are comparing relative value across the curve—asking whether 5-year Treasuries are cheap relative to 10-years—understanding that the 10-year is an on-the-run point (backed by heavy trading) and more reliable helps you avoid overweighting noise.
If you are holding a Treasury ETF or bond fund, the fund manager uses the published yield curve to mark bond prices daily. The curve's construction affects how each bond in the portfolio is priced, which affects the fund's NAV and your returns. For index funds (which mark to market based on published prices), this is transparent. For actively managed funds, the fund manager might use their own internal curve construction to identify mispricings relative to the published curve and trade accordingly.
Next
The curve we see in the financial media is built from discrete Treasury securities and constructed through bootstrapping to fill in the missing maturities. But behind this constructed curve is an even more fundamental idea: the zero-coupon yield curve, sometimes called the spot rate curve. Zero-coupon yields are the "true" risk-free discount rates and are the foundation of all bond valuation.