APY function - grfiv/ustreasuries GitHub Wiki

APY Definition

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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%

Example Code

> library(ustreasuries)
> CMT = c(7.87, 7.92, 7.91, 7.92, 7.92, 7.92)
> APY(CMT, percent=TRUE)
[1] 0.08024842 0.08076816 0.08066420 0.08076816 0.08076816 0.08076816

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