U.S. Department of the Treasury

Overview of the Two Methodologies:

• Historically, Treasury has used a quasi-cubic hermite spline (HS) method for yield curve construction. 
• The HS method directly uses secondary market yields as inputs to create a yield curve that is assumed to be a par curve.
• Implementation of the HS method has traditionally required modifications to the input points in maturity ranges where Treasury did not issue, or ceased issuing, securities when deemed necessary for deriving a good fit for the quasi-cubic hermite spline curve.  That is, modifications were made to avoid distortions in the HS curve that could result in rates outside of the range of those available in the market.  Some examples:
  • Composite points consisting of “off-the-run” bonds in the 10- to 30-year range to serve as proxies for market yields in the 20-year maturity range prior to the re-introduction of the 20-year bond on May 20, 2020
  • Interpolated yields
  • Rolled down securities 
• The monotone convex (MC) method for yield curve construction is a more theoretically robust technique.
• The MC method begins with secondary market prices converted to yields and used to bootstrap the instantaneous forward rates at the input maturity points so that these instruments are sequentially priced without error.  The initial step is followed by a monotone convex interpolation performed on forward rates midway between the input points to construct the entire interest rate curve.  This fitting minimizes the price error on the initial price input points, resulting in a true par curve.
• The MC method eliminates the need to routinely monitor and potentially modify curve inputs due to changes in the maturity sectors of Treasury security issuance.
  • While Treasury does not anticipate modifying the MC curve inputs, Treasury retains the right to modify or change inputs to the MC yield curve when needed, as determined in its sole discretion.

Differences in Treasury Yield Curve Rates Resulting from the Change in Methodology:

• The new MC methodology does not materially affect the Constant Maturity Treasury (CMT) Rates, published on the Treasury website and in the Federal Reserve’s H.15 Statistical Release.
  • The average differences between MC and HS CMT rates from October 1, 2020 to September 30, 2021 ranged from -0.1 to 0.5 basis points.
  • Standard deviations ranged from 0.2 to 1.0 basis points.
• The impact on the real CMT (RCMT) points, is somewhat greater, affected in part by the greater time between original issues of TIPS securities compared to nominal securities.
  • The average difference between MC and HS RCMT rates from October 1, 2020 to September 30, 2021 ranged from -2.7 to -0.6 basis points.
  • Standard deviations ranged from 0.9 to 4.1 basis points.
• Historical rates obtained using the two methodologies are available in CSV format.

Application of the New MC Methodology:

• Historically, the HS method has been used for all official Treasury yield curves used to determine interest rates as specified by statute or regulation for government borrowing, lending and investment programs, as well as other purposes, as appropriate.
• The new MC method will replace the HS method everywhere the HS method was previously used, effective with implementation of the MC method in early December 2021. When the new methodology is implemented, Treasury will update the information on the Daily Treasury Yield Curve Rates web page to reflect the effective date.
• All Treasury yield curve rates derived from yield curves that used the HS methodology - prior to implementation of the MC method in early December 2021 - remain official. 
• Any Treasury-determined interest rates that use as inputs CMT rates from dates both before and after the implementation of the MC yield curve methodology in early December 2021 will consist of rates produced by both methods.