Treasury Bills are securities traded in the U.S. Treasury market. Reported Treasury Bill yields are used to construct different mortgage (ARM) indexes, including Treasury Bill indexes.

Treasury Bills are traded in primary and secondary markets. Originally, they are auctioned directly by the U.S. government. This is their primary market (the market in which Treasury Bills are first issued). They are subsequently traded among investors in the secondary market. These markets determine a price for each Treasury Bill.

Treasury Bill quotes are provided either in the form of an annualized discount rate percentage relative to the par value and a 360-day year, called the Discount Yield, or as a bond equivalent yield, which is relative to the price and a 365-day year*.

* Some of these terms can be confusing. The Discount Yield is an annualized rate of return based on the par value of the bills and is calculated on a 360-day basis. The other name for the Discount Yield is: Discount Rate. The Bond Equivalent Yield is calculated on a 365-day basis and is an annualized rate based on the purchase price of the bills and reflects the actual yield to maturity. The other names for the Bond Equivalent Yield are: Investment Yield, Coupon-Equivalent Yield or Investment Rate.

Conversion Formulas (for bills of not more than 6 months to maturity)

Convert Price (P) to Discount Rate (d): d=((100-P)/100)*(360/r)

Convert Price (P) to Coupon Equivalent Yield (i): i=((100-P)/P)*(y/r)

Convert Discount Rate (d) to Price (P): P=100*(1-d*r/360)

Convert Discount Rate (d) to Coupon Equivalent Yield (i): i=y/(360/d-r)

Convert Coupon Equivalent Yield (i) to Discount Rate (d): d=360/(y/i+r)

P = Price d = Discount Rate r = Days to Maturity y = Days in Year i = Bond Equivalent Yield

Example:

Term:	91-Day Bill
High Rate:	3.495%
Investment Rate:	3.575%
Price:	99.116542
Issue Date:	09/01/2005
Maturity Date:	12/01/2005
CUSIP:	912795WC1

Conversion Results:

Convert Price (P) to Discount Rate (d): d=((100-99.116542)/100)*(360/91)=0.03495

Convert Price (P) to Coupon Equivalent Yield (i): i=((100-99.116542)/99.116542)*(365/91)=0.03575

Convert Discount Rate (d) to Price (P): P=100*(1-0.03495*91/360)=99.11654

Convert Discount Rate (d) to Coupon Equivalent Yield (i): i=365/(360/0.03495-91)=0.035751

Convert Coupon Equivalent Yield (i) to Discount Rate (d): d=360/(365/0.03575+91)=0.034949

The following mortgage (ARM) indexes are constructed using the 13- and 26-Week Treasury Bill Auction results and the secondary market prices of the 13- and 26-Week Treasury Bills:

• Weekly 3-Month T-Bill (Auction High)
• Weekly 6-Month T-Bill (Auction High)
• Weekly 3-Month T-Bill (Secondary Market)
• Weekly 6-Month T-Bill (Secondary Market)
• Weekly 3-Month CMT
• Weekly 6-Month CMT
• Monthly 3-Month T-Bill (Secondary Market)
• Monthly 6-Month T-Bill (Secondary Market)
• Monthly 3-Month T-Bill (Auction High)
• Monthly 6-Month T-Bill (Auction High)
• Monthly 3-Month CMT
• Monthly 6-Month CMT

Each of these indexes can be used to calculate the new interest rate on ARM loans.

What is the difference between the Weekly and the Monthly 6-Month T-Bill (Auction High)?

The Weekly 6-Month T-Bill (Auction High) is the discount rate for the 26-week Treasury Bill bought at original issue, at the most recent auction of U.S. Treasury bills.

The Monthly 6-Month T-Bill (Auction High) is the average of the past month's weekly 6-Month T-Bill (Auction High) values.

What is the difference between the Weekly and the Monthly 6-Month T-Bill (Secondary Market)?

The Weekly 6-Month T-Bill (Secondary Market) is the average of the past week's daily secondary market 6-Month T-Bill rates.

The Monthly 6-Month T-Bill (Secondary Market) is the average of the past month's daily secondary market 6-Month T-Bill rates.

What is the difference between the Weekly 6-Month T-Bill (Auction High), the Weekly 6-Month T-Bill (Secondary Market) and the Weekly 6-Month CMT?

The Weekly 6-Month T-Bill (Auction High) is the discount rate for the 26-week Treasury Bill bought at original issue, at the most recent auction of U.S. Treasury bills. The Weekly 6-Month T-Bill (Secondary Market) is the average of the past week's daily secondary market 6-Month T-Bill rates.

Rate quotes for T-Bills are provided in the form of an annualized discount rate percentage relative to the par value of the bills and a 360-day year.

The Weekly 6-Month CMT is the average of the past week's daily 6-Month Constant Maturity Treasury rates. Each Constant Maturity Treasury is a "theoretical" security based on the most recently auctioned "real" securities: 1-, 3-, 6-month bills, 2-, 3-, 5-, 10-year notes, and also the 'off-the-runs' in the 7- to 20-year maturity range. Yields on Treasury securities at "constant maturity" are interpolated by the U.S. Treasury from the daily yield curve, which is based on the closing market bid yields on actively traded Treasury securities in the over-the-counter market.

Rate quotes for CMT indexes are provided in the form of an investment yield, or coupon-equivalent yield, are calculated on a 365-day basis and reflect the actual yield to maturity.

Example:

On 9/16/2005 the Weekly 6-Month T-Bill (Auction High) was: 3.67, the Weekly 6-Month T-Bill (Secondary Market) was: 3.66 and the Weekly 6-Month CMT was: 3.78 (as per the H.15 Federal Reserve Statistical Release and the Treasury Bill, Note, and Bond Auction History).

How to compute the Weekly 3-Month T-Bill ARM index (Auction High)?

1. Download the most recent auction results of the 13-Week Treasury Bills (91-Day Bill).

You can use the the U.S. Treasury website (www.ustreas.gov). The 13-Week Treasury Bills are auctioned every Monday. The resulting figures are released to the public the next day.

2. Convert Price to Discount Rate, or use the published Discount Rate ('High Rate').

Formula: d=((100-P)/100) * (360/r)

where:
d: Discount Rate
P: Price
r: Days to Maturity

Example:

13- and 26-Week Treasury Bill Auction Results (08/29/2005):

Term:	91-Day Bill	182-Day Bill
High Rate:	3.495%	3.705%
Investment Rate:	3.575%	3.828%
Price:	99.116542	98.126917
Issue Date:	09/01/2005	09/01/2005
Maturity Date:	12/01/2005	03/02/2006
CUSIP:	912795WC1	912795WR8

d=((100-99.116542)/100) * (360/91)=0.03495

d (Discount Rate) = 3.495%

3. Round the Discount Rate ('High Rate') to 2 digits.

In our example: Weekly 3-Month T-Bill ARM index = 3.50% (Week Ending: 9/2/05).

What was the Monthly 6-Month T-Bill on Wednesday, October 5 2005? How to compute it? Please Explain.

You need the September value for the Monthly 6-Month T-Bill ARM index. It was 3.68.

Monthly 6-Month T-Bill ARM Index Calculation.

1. Download the 26-Week Treasury Bill (182-Day Bill) Auction results. The Issue Date should be between 9/1/2005 and 9/30/2005.

Term:	91-Day Bill	182-Day Bill
High Rate:	3.495%	3.705%
Investment Rate:	3.575%	3.828%
Price:	99.116542	98.126917
Issue Date:	09/01/2005	09/01/2005
Maturity Date:	12/01/2005	03/02/2006
CUSIP:	912795WC1	912795WR8
Term:	91-Day Bill	182-Day Bill
High Rate:	3.435%	3.570%
Investment Rate:	3.513%	3.686%
Price:	99.131708	98.195167
Issue Date:	09/08/2005	09/08/2005
Maturity Date:	12/08/2005	03/09/2006
CUSIP:	912795WD9	912795WS6
Term:	91-Day Bill	182-Day Bill
High Rate:	3.450%	3.670%
Investment Rate:	3.529%	3.791%
Price:	99.127917	98.144611
Issue Date:	09/15/2005	09/15/2005
Maturity Date:	12/15/2005	03/16/2006
CUSIP:	912795WE7	912795WT4
Term:	91-Day Bill	182-Day Bill
High Rate:	3.495%	3.715%
Investment Rate:	3.575%	3.839%
Price:	99.116542	98.121861
Issue Date:	09/22/2005	09/22/2005
Maturity Date:	12/22/2005	03/23/2006
CUSIP:	912795WF4	912795WU1
Term:	91-Day Bill	182-Day Bill
High Rate:	3.440%	3.745%
Investment Rate:	3.518%	3.870%
Price:	99.130444	98.106694
Issue Date:	09/29/2005	09/29/2005
Maturity Date:	12/29/2005	03/30/2006
CUSIP:	912795WG2	912795WV9

2. Add the Discount Rate values (rounded to 2 digits) for the 182-Day Bill together.

Original values: 3.705, 3.570, 3.670, 3.715, 3.745

Rounded values: 3.71 + 3.57 + 3.67 + 3.72 + 3.75 = 18.42

3. Divide the result by the number of auctions.

18.42 / 5 = 3.684

4. Round it to 2 digits.

The Monthly 6-Month T-Bill ARM index = 3.68 (September 2005)

Historical Graphs

The following graphs reflect the movement of the 3-, and 6-Month monthly Treasury Bills (secondary market):

If you need historical data prior to 1990, please visit the U.S. Treasury website (www.ustreas.gov). Secondary market T-bill rates are contained in the H.15 Federal Reserve Statistical Release.

Back to Mortgage Indexes