منحنی بازده وزارت خزانه داری آمریکا: 1961 تا به امروز

The discount function, which determines the value of all future nominal payments, is the most basic building block of finance and is usually inferred from the Treasury yield curve. It is therefore surprising that researchers and practitioners do not have available to them a long history of high-frequency yield curve estimates. This paper fills that void by making public the Treasury yield curve estimates of the Federal Reserve Board at a daily frequency from 1961 to the present. We use a well-known and simple smoothing method that is shown to fit the data very well. The resulting estimates can be used to compute yields or forward rates for any horizon. We hope that the data, which are posted on the website http://www.federalreserve.gov/pubs/feds/2006 and which will be updated quarterly, will provide a benchmark yield curve that will be useful to applied economists.

Interest rates are one of the basic ingredients of applied work in macroeconomics and finance. Having a long time series of properly measured high-frequency yield curves will therefore facilitate research in these areas. Towards that end, this paper fits a yield curve to off-the-run Treasury notes and bonds at the daily frequency for the entire maturity range spanned by outstanding Treasury securities, from 1961 to 2006. The resulting yield curve can be expressed in terms of zero-coupon yields, par yields, instantaneous forward rates, or n×mn×m forward rates (that is, the m-year rate beginning n years ahead) for any n and m. Several authors have produced time series estimates of U.S. Treasury yield curves. Perhaps the most commonly used among these are the Fama–Bliss (1987) yields. Commonly available Fama–Bliss yields are month-end measures of yield curves going out to five years in maturity. The yield curve estimates that we present more information than the Fama–Bliss yields in three ways. First, we provide daily estimates, facilitating high-frequency studies. Second, we present estimates going out to the longest available maturity—for example, we provide more than 35 years of 10-year yields. Lastly, the estimates presented in this paper will be updated quarterly, keeping the data current. Section 2 of the paper briefly reviews the fundamental concepts of the yield curve. Section 3 describes the specific methodology that we employ to estimate the yield curve, and Section 4 discusses our data and some of the details of the estimation. Section 5 shows the results of our estimation, including an assessment of the fit of the curve, and Section 6 demonstrates how the estimated yield curve can be used to calculate the yield on “synthetic” Treasury securities with any desired maturity date and coupon rate. As an application of this approach, we create a synthetic off-the-run Treasury security that exactly replicates the payments of the on-the-run 10-year Treasury note, allowing us accurately to measure the liquidity premium on that particular issue. Section 7 concludes. The data are posted as an appendix to the paper on the FEDS website.

In this paper we have estimated the U.S. Treasury yield curve using a simple and parsimonious approach. The approach is quite effective at capturing the general shape of the yield curve while smoothing through the idiosyncratic variation in the yields on individual securities. As such, the results should prove useful for understanding the general macroeconomic and other factors that have broad effects on the shape of the yield curve. The estimated yield curve can be expressed in a variety of ways, including zero-coupon yields, par yields, and forward rates. Our yield curve fills a void in the academic literature. To our knowledge, no estimated yield curve is available on a daily basis back to the early 1960s. The data set of Fama and Bliss (1987) (which has been updated) is monthly, and only provides estimates out to five-year maturities, while the data set of McCulloch and Kwon (1993) is also monthly and only provides estimates out to 10-year maturities. Our data set has the advantages of being available on a daily basis, extending back to 1961, providing estimates for all maturities that are feasible given the distribution of outstanding securities, and being updated on a regular basis. The full data set is available to be downloaded from http://www.federalreserve.gov/pubs/feds/2006/200628/feds200628.xls and will be updated quarterly.