In grfiv/ustreasuries: Treasury Data Download, Fixed-Income Models and Derivative Analyses

The ustreasuries package provides a CMTrates function which downloads the daily CMT rates from 1960 to the most-recently completed business day. Also provided is an APY function which converts CMT rates to APY.

CMT Yield Definition

Constant-Maturity Treasury (CMT) yields are derived from a 'quasi-cubic hermite spline function' proprietary to the US Treasury Department.

At the end of business each day the bid yields for on-the-run securities (which trade close to par) are input as the knot points and splines are used to derive a continuous curve. The yields for the exact maturity points are read from this curve, which are the yields available from the CMTrates function.

Yields on all Treasury securities are based on actual day counts on a 365- or 366-day year basis, not a 30/360 basis, and the yield curve is based on securities that pay semiannual interest; the yields at any point on the yield curve are consistent with a semiannual coupon security with that amount of time remaining to maturity.

All yield curve rates are considered "bond-equivalent" yields.

The yield curve is considered a Par Yield Curve.

APY Definition

CMT yields represent "bond equivalent yields" for securities that pay semiannual interest, expressed on a simple annualized basis. This is consistent with market practices for quoting bond yields in the market and makes the CMT yields directly comparable to quotations on other bond market yields. As such, these yields are not effective annualized yields or Annualized Percentage Yields (APY), which include the effect of compounding.

To convert a CMT yield to an APY the following formula is applied:

                                      APY = (1 + i/2)**2 - 1

Where i is the CMT rate expressed in decimals.

For example, if the 5-year CMT rate was 8.00%, then the annualized effective yield, or APY, would be:

                                      APY =  (1 + .0800/2)**2 - 1 
                                      APY =  1.081600 - 1 
                                      APY =  0.081600

And, expressed as a percent:

                                      APY =  8.16%

References

Daily Treasury Yield Curve Rates
https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield

Interest Rates - Frequently Asked Questions
https://www.treasury.gov/resource-center/faqs/Interest-Rates/Pages/faq.aspx

Treasury Yield Curve Methodology
https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/yieldmethod.aspx

Selected historical average rates are available from the FRB at
http://www.federalreserve.gov/datadownload/Choose.aspx?rel=H15

Most-recently viewed on 01/25/2016

grfiv/ustreasuries documentation built on May 17, 2019, 8:36 a.m.