Par Rate

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.

The par curve is derived by the Treasury from actively traded securities using a cubic spline model fitted to the most liquid on-the-run issues. This produces a smooth curve across all maturities from 1 month to 30 years.

Par rates are the starting point for:

• Bootstrapping: extracting the zero-coupon (spot) curve from par yields
• Forward rate calculation: implied future rates derived from the spot curve
• Relative value analysis: comparing actual bond yields to the fitted par curve to find cheap or rich issues

Par rates are quoted as annualized percentages with semiannual compounding, consistent with U.S. Treasury coupon conventions.