Treasury Yield Curve Methodology
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This description was revised and updated on December 3, 2007. The Treasury’s yield curve is derived using a quasi-cubic hermite spline function. Our inputs are the Close of Business (COB) bid yields for the on-the-run securities. Because the on-the-run securities typically trade close to par, those securities are designated as the knot points in the quasi-cubic hermite spline algorithm and the resulting yield curve is considered a par curve. However, Treasury reserves the option to input additional bid yields if there is no on-the-run security available for a given maturity range that we deem necessary for deriving a good fit for the quasi-cubic hermite spline curve. In particular, due to Treasury’s discontinuance of 3-year notes, we are adding a composite rate in the 3-year range based on an average of off-the-run securities in that time tranche. In addition, we are also using composites of off-the-run bonds in the 20-year range reflecting market yields available in that time tranche. Previously, a rolled-down 10-year note with a remaining maturity nearest to 7 years was also used as an additional input. That input was discontinued on May 26, 2005. More specifically, the current inputs are the most recently auctioned 4-, 13- and 26-week bills, plus the most recently auctioned 2-, 5-, and 10-year notes and the most recently auctioned 30-year bond, plus the composite rates in the 3- and 20-year maturity ranges. The quotes for these securities are obtained at or near the 3:30 PM close each trading day. The inputs for the three bills are their bond equivalent yields. To reduce volatility in the 1-year Treasury Constant Maturity (CMT) rate, and due to the fact that there is no on-the-run issue between 6-months and 2-years, Treasury uses an additional input to insure that the 1-year CMT rate is consistent with on-the-run yields on either side of it’s maturity range. Thus, Treasury interpolates between the secondary bond equivalent yield on the most recently auctioned 26-week bill and the secondary market yield on the most recently auctioned 2-year note and inputs the resulting yield as an additional knot point for the derivation of the daily Treasury Yield Curve. The result of this step is that the 1-year CMT is generally the same as the interpolated rate. Treasury has used this interpolated methodology since August 6, 2004. Treasury does not provide the computer formulation of our quasi-cubic hermite spline yield curve derivation program. However, we have found that most researchers have been able to reasonably match our results using alternative cubic spline formulas. Treasury reviews its yield curve derivation methodology on a regular basis and reserves the right to modify, adjust or improve the methodology at its option. If Treasury determines that the methodology needs to be changed or updated, Treasury will revise the above description to reflect such changes. Yield curve rates are normally available at Treasury’s interest rate web sites as early as 5:00 PM Eastern Time and usually no later than 6:00 PM Eastern Time each trading day. Office of Debt Management
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