How Treasury Constant Maturity Yields Are Interpolated and Quoted

Summary

The document explains that a Treasury constant maturity yield is a rate for a theoretical bond with a fixed remaining term, rather than necessarily the yield on one particular security. As existing bonds age and their maturities move away from the desired point on the yield curve, the Treasury uses cubic spline interpolation to estimate the rate at that constant maturity. The stated example describes the constant maturity rate as representing a hypothetical newly issued bond with the specified term on that date.

The quoted yield follows a par yield convention and is expressed as a bond-equivalent yield with semiannual compounding; it is not a zero-coupon yield. This distinction matters when interpreting historical yield series or comparing them with rates derived under other conventions. The answer is a concise description of the construction and convention, not a full account of the Treasury’s curve inputs, interpolation procedure, or how to reproduce the published series independently.

Key ideas

• A constant maturity rate refers to a theoretical bond at a fixed term on a given date.
• The quoted rate may not equal the yield of any individual Treasury security.
• Cubic splines are used to interpolate the yield curve at the target maturity.
• The published figure uses a par yield convention with bond-equivalent yield and semiannual compounding.
• A constant maturity yield is not the same as a zero-coupon yield.

Tags

# How is the “constant maturity” 10 year treasury calculated?


# How is the “constant maturity” 10 year treasury calculated?












The Fed’s historical chart of the 10 year treasury yield is titled “10-Year Treasury Constant Maturity.” How exactly is the yield calculated?

## Answer by wgajate (score 3)

https://quant.stackexchange.com/a/63179

From the US Treasury FAQ:

"CMT rates are read from fixed, constant maturity points on the curve and may not match the exact yield on any one specific security ... For example, the 20-year daily yield curve rate (i.e., the 20-year CMT) represents the yield for a new theoretical 20-year bond as of that date."

Due to aging of the 10 year and 20 year bonds, the Treasury employs cubic splines to interpolate the exact 10 year bond yield value and quotes using a par yield convention (Bond Equivalent Yield/Semi-Annual Compounding), not zero coupon yield.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.