govtwork / faq / Computing the investment rate for Treasuries

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Referenced Treasury file: ofsec09.pdf
Readers will want Acrobat pages 28 and 33-35
of the 43-page Section 9 PDF

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WASHINGTON, DC 20239-0001

July 26, 2000

Mr. Joel R. Anderson

Dear Mr. Anderson:

This is in response to your letter dated May 18, 2000,
regarding your concern about computing the investment rates
for Treasury Securities. I apologize for the late response.

In answer to your question number one regarding Treasury bills:

The quote you referenced on our website is not specific as
to when the 366-day period begins and ends. The complete
formulas for calculating the purchase price, discount rate,
and investment rate are published in the Uniform Offering
Circular for the Sale and Issue of Marketable Book-Entry
Treasury Bills, Notes, and Bonds (31 CFR Part 356, as
amended). This circular can be found on our website by going
to and
scrolling down and clicking on Section 9, "Uniform Offering
Circular (Treasury Auction Rules)". The formulas are located
in Appendix B, beginning on page 357. Please note the
Uniform Offering Circular is in pdf format. Adobe Acrobat
Reader must be installed on your PC to view files in pdf
format. The Acrobat Reader is included in many Web browsers,
but if your browser does not read Acrobat's pdf files, you
can obtain Acrobat Reader for free at

I have enclosed copies of pages 370 and 371 from this
circular, which give the formula for calculating the
investment rates for Treasury bills. As highlighted, the
definition of "y" is the number of days in the year following
the issue date--normally 365; but if the year following the
issue date includes February 29, then "y" is 366.

To participate competitively in a bill auction, a
competitive bid must be expressed as a discount rate with
three decimals in increments of .005 percent. For cash
management bills (CMBs), a competitive bid must show the
discount rate bid expressed with two decimals in increments
of .01 percent. CMBs traditionally have a very short period
to maturity. If three-decimal bidding is used for bills with
a very short maturity, you will not get a unique price for
each bid. For example, bids of 5.123% and 5.124% may result
in the same calculated price, but bids of 5.12% and 5.13%
will more likely have different prices. To avoid the
confusion of having a single price apply to multiple bids,
we use two-decimal bidding for short-term bills.


                                          (unnumbered page 2)

In answer to your question number two regarding Treasury
notes and bonds:

The Treasury does not use formulas that calculate the yield
from a price because auctions of Treasury notes and bonds
are conducted only on a yield basis. The formula for the
conversion of a price from a yield is found on page 364 of
the Uniform Offering Circular.

In all auctions of Treasury notes and bonds, there is a
relationship among the given security's yield (which is
determined in the auction), its corresponding interest rate,
and its purchase price. The higher the security's yield is
in relation to its interest rate, the lower the price for
that security. The reverse is also true in that the lower a
security's yield is in relation to its interest rate, the
higher the price.

In auctions of all notes and bonds, investors are awarded
their securities at the highest yield accepted from the
competitive bidders in the auction. This yield and the
interest rate will be roughly equivalent. Accordingly, the
investor's purchase price usually is under but relatively
close to par, and the amount returned to the investor does
not constitute a significant portion of the return on his

However, in the case of a reopened security such as the 29-
1/2-year Treasury bond (912810FH6) referenced in your
letter, the yield determined in the auction can be either
higher or lower than the already-established interest rate.
If the yield determined in the auction is significantly
higher than the security's interest rate, the purchase price
will be significantly less than par, and the amount of
discount returned to investors will actually be, along with
future interest payments, a major component of the return on
their investment. If the yield is significantly lower, the
purchaser will pay a premium (par plus an additional
amount). In either case, the yield to maturity will
correspond to the current market price.

I hope this information is of help.


Michael W. Sunner
Deputy Assistant Commissioner