The par rate (or par yield) for a given maturity is the coupon rate that makes a bond's price equal to its face value (par, or 100). The U.S. Treasury publishes daily par yield curve rates, and these are the yields displayed throughout this site.
Par rates differ from spot rates because a coupon-bearing bond receives intermediate cash flows, each discounted at a different rate. The par rate blends these discount rates into a single number. When the yield curve is upward-sloping, par yields are lower than spot rates at longer maturities because early coupon payments are discounted at the lower short-term rates.
Par rates are the starting point for:
The U.S. Treasury publishes a daily par yield curve constructed by fitting a cubic spline to prices of on-the-run and recently off-the-run issues. The methodology removes idiosyncratic richness or cheapness from any single security and produces a smooth, continuous curve across the full maturity spectrum.
The published maturities are: 1M, 2M, 3M, 4M, 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 20Y, and 30Y. These rates are available daily at treasury.gov and serve as the primary data source for yieldcurvepro.pro. Every yield displayed on the yield curves page traces back to this published series.
Because the curve is fitted to liquid on-the-run issues, it reflects the market's consensus view of the risk-free rate at each tenor rather than the yield of any individual security. This matters for relative value work: a bond's yield must be compared to the fitted curve, not to an adjacent on-the-run issue.
Assume a simple upward-sloping curve: the 1-year par rate is 4.00% and the 2-year par rate is 4.40%.
The 1-year spot rate equals the 1-year par rate exactly: 4.00%. There is only one cash flow at maturity, so no blending occurs.
For the 2-year par bond, coupons are 4.40 / 2 = 2.20 per period, paid semiannually. Discounting those cash flows at the 6-month spot rate (approximately 3.80%) and the 1-year spot rate (4.00%), then solving for the 2-year spot rate that equates the bond's present value to 100 produces a 2-year spot rate of approximately 4.42%. The spot rate exceeds the par rate by about 2 basis points.
The pattern generalizes: on an upward-sloping par curve, spot rates exceed par rates at every maturity beyond the shortest tenor. On an inverted curve, the relationship reverses. Bootstrapping formalizes this extraction process, iterating maturity by maturity from short to long.
When an individual bond's yield exceeds the par curve at its maturity, that bond is "cheap" relative to the curve. It delivers more spread than the fitted market implies. When its yield falls below the curve, the bond is "rich."
Primary dealers and asset managers run this comparison daily across their inventories. A corporate bond spread, for instance, is often quoted as the difference between the bond's yield and the interpolated par rate at the same maturity, not versus a single benchmark Treasury.
On yieldcurve.pro, the curves page lets you visualize the par curve across dates, which makes it straightforward to spot regime changes in the level and shape of the benchmark curve before performing relative value comparisons.
U.S. Treasury par rates are quoted as annualized rates with semiannual compounding, consistent with the bond equivalent yield (BEY) convention. A stated par rate of 4.40% means 2.20% per semiannual period.
To convert to an annual effective rate (AER), apply:
AER = (1 + par_rate / 2)^2 - 1
For a par rate of 4.40%, the AER is (1 + 0.0220)^2 - 1 = 4.448%. The difference is small at low yields but grows as rates rise. Comparing yields across instruments that use different compounding conventions requires this conversion. OIS rates, for example, use daily compounding, while par yields use semiannual compounding. Mixing them without adjustment introduces systematic error in duration-weighted spread calculations.
What is the par rate? The par rate for a given maturity is the coupon rate at which a newly issued bond would price at exactly 100 (par). It represents the market's required yield, expressed as a single blended discount rate across all of a bond's cash flows.
Why does the par curve differ from the spot curve? Par rates blend the discount rates applied to each coupon payment and the final principal into one number. Spot rates apply a single discount rate to a single cash flow at one maturity. On an upward-sloping curve, spot rates exceed par rates beyond the short end because the early coupons are discounted at relatively lower rates, pulling the blended par rate down.
Where does yieldcurve.pro get its par rate data? From the U.S. Treasury's daily constant maturity yield series, published at treasury.gov. The Treasury fits a cubic spline to on-the-run and recently off-the-run issues each business day and reports rates at 13 standard maturities. These form the backbone of every chart and data table on this site.