Primary and Secondary Markets for U.S. Treasury Securities
The debt of the United States government consists of both marketable and nonmarketable securities, in near equal proportions. Marketable securities consists of bills, notes, bonds, Treasury Inflation Protected Securities (TIPS), and STRIPS. Nonmarketable securities consists of United States Savings Bonds, Domestic, Foreign, REA, SLGS, GAS and Other securities. These securities include special securities issued only to state and local governments and Federal trust funds such as Social Security. Nonmarketable securities are nontransferable securities issued by the government and registered to the owner, and are payable only to the person(s) or entities to whom they are registered. They cannot be sold in the financial market, but they can be redeemed at any time after they've been held for one year.
Primary Market
Marketable Treasury securities are sold in the primary market through sealedbid single price auctions (aka uniformprice auctions), sometimes called Dutch auctions, which are announced several days in advance of the auction by Department of the Treasury press releases, detailing the offering amount, type of security, and its term. Most bids — both competitive and noncompetitive — are submitted electronically to a Federal Reserve Bank or an authorized financial institution, or to the Bureau of the Public Debt.
Treasury auctions consists of competitive bids placed by primary dealers, that include HSBC, J.P. Morgan, and Citigroup, and noncompetitive bids, which are bids submitted by everyone else. Primary dealers are required to bid at Treasury auctions.
The yield is set by the competitive bidding to the lowest level, known as the stopout yield that allows the entire offering of marketable securities, minus the noncompetitive bids, to be sold. Competitive bidders that bid higher than the stopout price only have to pay the stopout price, but competitive bidders who bid below the stopout price are not filled. Noncompetitive bidders always pay the stopout price and are always filled.
TreasuryDirect
TreasuryDirect is the best way for individuals to buy and hold marketable Treasury securities.
Marketable securities are those securities that can be bought and sold in the secondary market at prevailing market prices after original issue. The following marketable securities are available in TreasuryDirect: 4, 13, and 26week Bills; Notes with maturities of 2, 5, and 10 years; 5, 10, and 20year TIPS, and 30year Bonds. The mix of securities offered may change, as the Treasury's borrowing needs change.
Purchases of marketable issues in TreasuryDirect are allowed on a noncompetitive basis in increments of $100. Purchasers receive their securities at the same price and yield awarded to competitive bidders in the auctions. Recurring purchases of Treasury securities can also be set up to five years in advance.
Treasury Automated Auction Processing System (TAAPS)
The Treasury Automated Auction Processing System (TAAPS) is an electronic trading platform for financial institutions that provides direct access to U.S. Treasury auctions. This system electronically receives and processes tenders sent to U.S. Treasury auctions, thus allowing institutions to purchase marketable securities directly from the desktop.
Primary Dealers
A large part of the Treasury offerings is sold to authorized primary government securities dealers, which have a special account with the Federal Reserve Bank of New York, and include major financial institutions and domestic and foreign securities dealers. They are required to maintain a minimum of capital, and to participate significantly in the auctions, and to provide market information to the Fed.
No one, even the primary dealers, are permitted to buy more than 35% of any issue.
Reopenings
On some of its securities, the Treasury has reopenings where additional amounts of a previously issued security are sold. The securities have the same coupon interest rate and maturity, but different issue date and price. Accrued interest may have to be paid, but is paid back on the 1^{st} interest payment. The following table shows the current reopening schedule.
Security Type  Original Issue  Reopening  Comment 

10year note  February May August November  March June September December  The 10year note is reopened 1 month after original issuance. 
30year bond  February August  May November  The issuance of the 30year bond resumed in February 2006. 
5year TIPS  April  October  Reopened 6 months after original issuance. 
10year TIPS  January July  April October  Reopened 3 months after original issuance. 
20year TIPS  January  July  Reopened 6 months after original issuance. 
Buybacks
Sometimes the Treasury, during budget surpluses, buys back some of its securities through a reverse auction on the secondary market to limit the average maturity of its debt and to increase the liquidity of the Treasury market. The 1^{st} debt buyback program was in the 1920s, to use the tax surpluses during the booming economic times to pay off the debt from World War I. The current debt buyback program was initiated in January 2000, again using the surpluses of the booming economy. The last was in April 2002, using the surplus tax receipts.
Buybacks can increase the liquidity of new issues when deficits are declining by allowing Treasury officials to continue a series without shrinking newissue sizes and can smooth weektoweek fluctuations in Treasury bill offerings. Buybacks actively promote the liquidity of the newissue markets by regularly repurchasing outstanding debt and funding the purchases with new debt offerings. Buybacks also limit the accumulation of large Treasury cash balances, which usually occurs in late April and early May, when most taxpayers pay their income taxes.
Liquidity also provides current market information about the riskfree rate, which is used in many investment decisions.
Secondary Market
The trading of already issued securities by investors and primary market participants constitutes the secondary market, which is the largest security market in the world, with very narrow bidask spreads.
Central banks, both the Federal Reserve and foreign central banks, hold large reserves and trade actively. The main trading centers are in New York, London, and Tokyo. Although trading can occur 24 hours, most of it is done during the New York business day, since the Federal Reserve of New York is the largest holder and trader of Treasury securities.
The primary dealers act as market makers in the secondary market, with standing bid/offer quotes, in the overthecounter market (OTC).
Interdealer Brokers
Primary dealers trade among themselves by using an electronic platform provided by an interdealer broker, which lists the best bid/ask prices and the quantity. The minimum bid or offer is $5 million for Tbills and $1 million for notes and bonds.
Interdealer brokers provide anonymity for the traders, some of which are nonprimary dealers, and provide the latest transaction prices and quantities on their trading platform.
Some interbroker dealers include:
 BrokerTec (acquired by ICAP)
 Cantor Fitzgerald/eSpeed
 GarbanIntercapital
 Hilliard Farber
 Tullett Liberty.
Federal Reserve
The Federal Reserve buys and sells large amounts of securities through its open market operations to fulfill the monetary policies of the Federal Open Market Committee (FOMC). The money supply is expanded when the Federal Reserve buys Treasury securities on the secondary market, and contracted when the central bank sells them.
OnTheRun, OffTheRun, and WhenIssued Treasury Securities
Although Treasury securities trading is the most active and liquid market, less than 200 recent issues constitute most of the trading activity. The most recent issues of a given maturity are called ontherun securities, in contrast to the older, much more numerous, but less actively traded offtherun securities.
Whenissued securities are securities announced for auction, but not yet issued . Dealers often take orders for whenissued securities to gauge the yield of the new issues and to be able to bid with lesser risk. Although most trades for Treasuries settle the following day, whenissued securities settle on the day of issue.
Quoting Conventions
There is a convention to how the prices of Treasuries are quoted.
Treasury Bills
Bills are sold at a discount from their face value. When a bill matures, the investor receives the face value. The difference between the purchase price and the face value equals the interest earned. The purchase price can be determined from the following formula:
TBill Price  =  Face Value  ×  (  1    d × t 360  ) 
d = Discount Rate t = Days till Maturity 
For example, if a $1,000 26week bill sells at auction for a 3.80% discount rate, the purchase price would be $980.79, a discount of $19.21.
The discount rate differs from usual calculation of an investment return because it is based on the face value of the security rather than the actual amount invested, and yields are calculated using a 360day year— a banker's year.
Applying the equation to the above example:
P = 1000 (1 (.0380 × 182)/360) = $ 980.79
Tbills are usually quoted to 2 decimal places in the secondary market, or, for more active issues, to 3 decimal places, if the last digit is a 5.
Treasury Bill Yields: the Discount Yield and the Investment Yield
Shortly after the auction, the U.S. Treasury reports the high, low, and average prices of the Tbills sold. It also reports the yield, which is annualized so that it can be easily compared to other investments.
There are 2 methods for determining the annualized yield on Tbills, both of which are reported by the U.S. Treasury:
 The discount yield is the annualized yield on the face value of the Tbill, which allows its yields to be more easily compared to coupon Treasuries. The discount yield uses a banker's year of 360 days to calculate its yield.
 Discount Yield = (Face Value  Price Paid)/Face Value × 360/(Term Length in Days)
 The investment yield is the annualized yield of the actual investment, which is the discounted price paid for the Tbill. Because this yield is based on a lower price than the discount yield and is based on the calendar year of 365 days (366 for a leap year), which is the actual number of days in the year rather the banker's year, the investment yield will always be slightly higher. Investment yield is the term used by the Treasury, but it is called the bond equivalent yield (BEY).
Interest Rate Per Term  Number of Terms per Year  
BEY  =  Face Value  Price Paid Price Paid  ×  Actual Number of Days in Year Term Length in Days 
Note that neither the discount yield or the investment yield is compounded. The following example shows how to find the compounded interest rate of a Tbill. The following solution shows yet another way of calculating the interest rate per term of a Tbill.
Formula for Finding the Annualized Effective Compounded Rate of Interest for a TBill
If you bought a 4week Tbill for $996.50 and receive $1,000 4 weeks later, what is the effective annual compounded interest rate earned?
Solution: A disadvantage to either the discount or investment yield is that neither is compounded. To find the effective rate for 4 weeks, you divide the face value of $1,000 divided by the amount that you paid, then subtract 1 for the interest rate over 4 weeks :
$1,000/$996.50  1 = 1.0035 1 = .0035 (rounded) = 0.35%
This is the interest rate for the 4 weeks, but what is the interest rate per year, if compounded (since you can reinvest the money after it matures), so that you can compare it to other investments?
Since there are 13 4week periods in a year, $1 compounded 13 times would equal: (1.0035)^{13}  1 = 1.046  1 = 4.6% (rounded)
(See how the future value of a dollar is calculated to understand the reasoning better.)
You can use this formula for calculating the yields of any money market instrument sold at a discount.
Notes and Bonds
No commission is charged when buying or selling treasury securities in the secondary market. A bond dealer makes money through the spread — the difference between the bid price, which is what the dealer is willing to pay for a security, and the ask price, which is what the dealer is selling it for. To keep the spread further apart, prices are generally listed in 1/32 increments of a point, or a higher multiple, although some Treasuries have price differentials as low as 1/64. (Another reason for this convention is that a point is not equal to a dollar, but a decimal base would still be more convenient.) The pricing convention is to list the point after a dash. Thus, a price listed as 10204 is equal to 102 + 4/32 = 102 + 1/8 = 102.125% of par value. If this listed price were for a $1,000 facevalue Treasury note, then this price would be equal to $1,021.25. The integer point value, in this case 102, is known as the handle. When traders negotiate, the handle is usually known and not expressed. So a trader might say that he'll offer 2 for the security, meaning the handle + 1/16 (= 2/32).
Because the trading volume in Treasuries is much greater than for other bonds, Treasuries sometimes trade in 1/64 increments. A 1/64 increment is denoted by a plus next to the listed price. So a U.S. Treasury note with a $1,000 face value that is listed as 1011+ = 101 + 1/32 + 1/64 = 101 + 3/64 = 101.04875, so the note's price = 101.04875% × 1,000 = $1010.49 (rounded). 1,000 of these securities would cost $1,010,487.50.
Investment Yields on Treasury Notes and Bonds
Calculating investment yields is more complicated for Treasury notes and bonds, but, if the security is held till maturity, the investment yield can be approximated by the following formula:
Investment Yield  =  Coupon Rate  +  Face Value – Price Paid Term Length in Years 
(Face Value + Price Paid) / 2 
Example
What is the investment yield of a 7year Treasury note issued at a price of $99.709, with an annual Treasury announced coupon of 7 7/8, payable semiannually?
Coupon Rate = 7 7/8 = 7.875
Face Value = $100
Price Paid = $99.709
Maturity in Years = 7
Investment yield =  7.875 + [(100  99.709)/7] (100 + 99.709)/2 
Investment yield = (7.875 + .0415714) / (99.8545)
Investment yield = 7.9165714 / 99.8545
Investment yield = .0792810 = 7.93%
Microsoft Excel Functions for TBills: TBILLEQ, TBILLPRICE, and TBILLYIELD
Microsoft Office Excel offers several functions specifically for Tbills. The function TBILLEQ converts the discount yield of a Tbill to its investment yield (bond equivalent yield). TBILLPRICE calculates the price of a Tbill if the discount yield is known, and TBILLYIELD calculates the discount yield if the Tbill price is known. All of these functions use the Date function with format Date(year,month,day), since the MS Excel Help states that there may be problems if entered as text. Cell references that contain valid dates can also be used for the date arguments.
4. TBILLEQ, TBILLPRICE, and TBILLYIELD Microsoft Excel Functions. 

Bond Equivalent Yield (Investment Yield) = TBILLEQ(settlement,maturity,discount yield)
TBill Price = TBILLPRICE(settlement,maturity,discount yield)
TBill Yield = TBILLYIELD(settlement,maturity,price)

Using Microsoft Office Excel for Calculating TBill Prices and Discounts
The following basic facts — where they apply or are not changed in the individual examples — will be used for each of the example calculations for a 26week Tbill:
 Settlement date = 1/10/2008
 Maturity date = 7/10/2008
 Discount yield = 2%
 Price (per $100 of face value) = 98.99
 At this price, a $1,000 Tbill will cost you $989.90.
 Previously, $1,000 Treasuries were the smallest denomination that could be purchased, but nowadays, TreasuryDirect.com allows you to purchase Treasuries in $100 increments, so you could actually pay just $98.99 for a $100 Tbill.
What is the bond equivalent yield (investment yield) of a Tbill with an annualized discount yield of 2%?
Investment Yield = TBILLEQ(Date(2008,1,10),Date(2008,7,10),0.02) = 0.020484903 = 2.05%
The difference between the interest rate argument and the interest rate result is because of the 2 differences between the formulas for the discount yield and the investment yield:
 The investment yield uses the actual number of days in a year to calculate the yield rate, whereas the discount yield uses a banker's year of 360 days.
 The discount yield per term is as a percent of face value, whereas the investment yield per term is calculated as a percentage of price paid.
Remember also that only the discount yield should be used in this function. If you already know the investment yield, you don't need this function.
To more clearly see this, note the following for a 6month Tbill costing $99 (the term length of this Tbill is 182 days) with the same settlement and maturity dates as above and using the discount yield and investment yield formulas shown previously:
Discount Yield = (100  99)/100 × 360/182 = .01 × 1.978 = 0.01978 = 1.98%
Investment Yield = (100  99)/99 × 366/182 = 0.020313 = 2.03%
TBILLYIELD = TBILLYIELD(Date(2008,1,10),Date(2008,7,10),99) = (100  99)/99 × 360/182 = 0.01998 = 2.00%
 Note that the Microsoft Excel function TBILLYIELD uses neither the discount yield nor the investment yield formula, but rather an intermediate value. It combines the 1^{st} term of the investment yield formula with the 2^{nd} term of the discount yield formula. This would seem to be an incorrect result, since it does not correspond to established formulas! The MS Excel Help documentation does not specify what kind of yield TBILLYIELD calculates.
TBILLEQ = TBILLEQ(Date(2008,1,10),Date(2008,7,10),0.01978) = 0.020258 = 2.03%.
Note the following:
 When the discount yield is used for the discount argument in TBILLEQ, the result is very close to the investment yield, and is equal when rounded to 2 decimal places. Hence, using the investment yield for the argument in TBILLEQ would overstate the investment yield.
 Since 2008 is a leap year, there are 366 days in 2008, which is used in the investment yield formula.
What is the price of a Tbill selling for a discount yield of 2%?
Here again we use the discount yield, not the investment yield.
TBill Price = TBILLPRICE(Date(2008,1,10),Date(2008,7,10),0.02) = 98.98888889 = $98.99
What is the TBILLYIELD of a Tbill selling for $99?
TBill Discount Yield = TBILLYIELD(Date(2008,1,10),Date(2008,7,10),99) = 0.01998 = 2.00%
Note that this does not correspond to either the discount yield nor the investment yield.
Note: The above calculations were made using Microsoft Office Excel 2007. These functions are also available in earlier versions of Excel. Note also the following:
 All dates are entered using the MS Excel's Date function — format Date(year, month, day)— since the Help states that there may be problems if it is entered as text.
 The different results match closely, but they are not exact because of rounding errors.
 Remember to use the discount yield in the functions' arguments.