U.S. Treasury Securities

Invoice Price

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The Invoice Price of a Note or Bond is the “actual price” that a buyer pays the seller when
 a trade is settled. Though the calculation of this price is really quite simple, it requires some background knowledge of the underlying characteristics and conventions used in Note and Bond calculations.

Let’s start with the background information first, which we will need to work through an example of an invoice price calculation:

  • Date Definitions
  • Price Quote Conventions
  • Day Count Conventions

Date Definitions

There are a number of important dates to understand when dealing with U.S. Treasury Securities.

Announcement Date

This is the date that the Department of Treasury, through the Bureau of Public Debt based in Washington D.C., releases an announcement describing the details of a pending auction of a specific Treasury security.

Because the Treasury has a well-organized and regular schedule for the issuance of its securities, the auctions are generally anticipated. Investors pay particular attention to the size of the issuance (that is, how much of the security will be auctioned).

The Treasury makes the announcement to the press at an earlier time, but the press cannot release the announcement to the general public until the Treasury has also posted it on its website.

Auction Date

This is the date of the actual auction of the securities. The auction announcement also provides the times at which bids are due.

Competitive bids are due from primary dealers (the dealers authorized by the Federal Reserve to purchase securities directly from the Treasury).

Non-competitive bids are due from the public through TreasuryDirect, the Treasury’s online auction website for general investors and TAAPS (Treasury Automated Auction Processing System), its auction site for institutional investors.

The closing time for competitive bids is typically one hour later than the closing time for non-competitive bids. Shortly after the auction, the Treasury releases the clearing price and other details of the results.

Issue Date

A few days after the auction, the Treasury delivers securities to the auction winners and receives payment in return; this occurs on the Issue Date. From this point on, the Treasury simply needs to pay coupons (semi-annually) and retire the debt (pay off the principal) at its maturity.

Original Issue Date

Often, the Treasury securities being auctioned aren’t part of a completely new issue; rather, they are a “reopening” of an outstanding issue.

The concept of the “reopened” security is best understood by example.  The 13- and 26-week Treasury Bills are auctioned every week. After 13 weeks have elapsed, the old 26-week T-Bill has 13 weeks left to mature. The Treasury is also having its regular auctions of 13- and 26-week bills. Instead of creating a new 13-week bill, the Treasury “reopens” the original 26-week bill, with an effective maturity of 13 weeks, and simply auctions more of it.

In this case, the issue date of the newly created 13-week Bill follows the second auction in the example. But its “Original Issue Date” is when the original 26-week bill was issued.

Confused? Not to worry—though you may want to look over this section again, the original issue date is never involved in any of the financial calculations. In the event that it differs from the regular issue date, it is simply there to let you know that the security was “reopened.”

Dated Date

The date on which the security begins accruing interest is called the  “Dated Date.” Today, this is the same as the Issue Date for all U.S. Treasury securities. In some unusual cases in the past, however, bonds began accruing interest after their issue dates.

Maturity Date

On the Maturity Date, the last coupon is paid and the face value (or principal, or “corpus”) of the Note or Bond is repaid. After these final transfers, all future obligations of the Treasury to the security holder are extinguished.

Dates Applicable to the Secondary Market

After the Treasuries are issued, owners of the securities may sell them to dealers or other investors in the secondary market. A network of banks and dealers facilitate the trading of Treasuries among other investors (their clients). They may also sell them on to other dealers in the interdealer broker market or hold the securities in inventory for themselves.

Two other dates are meaningful in the secondary market: trade and settlement.

Trade Date

When institutional investors trade U.S. Treasury securities with dealers in the secondary market, or when dealers trade with other dealers in the interdealer market, they first negotiate the quantity and price of the trade. The trade is considered “done” when both parties have consented, verbally or electronically, to its terms in a kind of gentlemen’s agreement. This all happens on the Trade Date.

At this point, each party “books” the trade into its internal systems, and the respective back offices begin the post-trade processing cycle so that they can confirm the details and eventually settle the trade.

Settlement Date

The Settlement Date is the date on which the seller is obligated to deliver the security to the buyer (this is typically a book entry, not a physical transfer). The buyer must also wire funds (equal to the invoice price) to the seller to pay for the securities.

Trades in U.S. Treasury securities are generally settled one business after they are made. This is known as “T+1” settlement (“trade date plus one business day”).

Occasionally, counter-parties will agree to same day settlement. But this is a rare occurrence because it puts a great deal of pressure on the back offices.


The Bureau of the Public Debt, on behalf of the Department of the Treasury announced the following 5-Year Note to be issued on June 23, 2011 at 11:00 AM EST:

  • Term and Type of Security: 5-Year Note
  • Offering Amount: $35,000,000,000
  • Currently Outstanding: 0
  • CUSIP: 912828QR4
  • Auction Date: June 28, 2011
  • Original Issue Date: June 30, 2011
  • Issue Date: June 30, 2011
  • Maturity Date: June 30, 2016
  • Dated Date: June 30, 2011
  • Series: Z-2016
  • Yield: Determined at Auction
  • Interest Rate: Determined at Auction
  • Interest Payment Dates: December 31 and June 30
  • Premium or Discount: Determined at Auction

Price Quoting Conventions

The price quoting conventions of U.S. Treasury Notes and Bonds are somewhat quirky. Historically, treasuries were quoted in fractions such as halves, quarters, and eighths. As the market became more competitive, the
 fractions became smaller and smaller, until most market participants agreed to quote Notes and Bonds in 32nds of a percent.

Yet Treasury markets have become even tighter, further narrowing spreads, and dealers and interdealer brokers now quote Treasuries in fractions of 32nds, a convention that is very confusing to outside observers. The best way to explain is through example.

On August 2, 2011, Bloomberg (a very popular market data service, used by financial professionals), listed the 5-Year Treasury (UST 5Y 1.500 of 7/31//2016) at a price of “101-11+” at the close.

The quoted price is “101-11+” in percent of face value; here’s how to interpret it.

To left of the dash (“-“) is a whole decimal number in percent. The next two digits to the right of the dash are in 32nds of a percent. The third character (here, the plus sign (“+”)) to
 the right of dash is in fractions of a 32nd of a percent. The plus sign indicates ½ of a 32nd. So mathematically, “101-11+” is equivalent to:

101 + 11/32 + (1/2)/32 percent, or 101.359375 percent

If the third character to the right of the dash is a digit (1, 2, 3, 5, 7), it is in 8ths of a 32nd of a percent. For example, a price of “101-113” would be equivalent to:

101 + 11/32 + (3/8)/32 percent, or 101.35546875 percent

Notice that “4” was not included in the above list of possible digits. 4/8 of a 32nd is equivalent to ½ of a 32nd, which, from the first example, you know is represented by a plus sign.

If there is no 3rd character after the dash, the first two digits are still  in 32nds. So a quote of “101-11” would be equal to:

101 + 11/32 percent, or 101.343750 percent

Finally, a “0” as the first digit in front of the dash simply serves as a placeholder. For example, a quote of “101-02” is just 101 and 2/32 of a percent.

Day Count Convention

Trades of U.S. Treasury Notes and Bonds use what is called an “Actual versus Actual” calendar (often written as “Actual/Actual” or “ACT/ACT”). Interest rates are typically calculated based on the number of days interest is accrued against a base period.

For example: let’s assume you deposit $1,000.00 on January 1, 2011 at a bank that pays an annual simple interest rate of 5% (yes, there was a time when interest rates were this high). If you were to close the account on January 1, 2012, you would expect to get your $1,000.00 back and $50.00 of interest (5% of $1,000.00).

But let’s say you had to withdraw the money on February 14, 2011 to buy a nice gift for your loved one on Valentine’s Day. How much interest should you get? First you need to calculate the number of days for which you deserve to collect interest; here, it is from January 1st to February 14th, or 44 days. The base period on the 5% term is from January 1, 2011 to January 1, 2012, or 365 days. The bank held your money for 44/365 of the base period, so it should pay you:

(5/100) * (44 days/365 days) * $1,000, which is $6.03.

In this example, you used an “Actual/Actual  Day Count” because you calculated the actual number of days for which you should accrue interest (the numerator) and divided it by the actual number of days in the base period of the interest payment (the denominator).

Note that this same calculation would be different if the $1,000.00 term were from January 1, 2012 to January 1, 2013 because 2012 is a leap year; the denominator for the base year would be 366 as opposed to 365.

Invoice Price

Now that we’ve explained the many date definitions, price quote conventions, and day count conventions, we are ready to describe Invoice Price, the main topic of this article.

 The Invoice Price of a Bond is defined as follows:

Invoice Price = Quoted Price + Accrued Interest

We’ll use our 5-Year Treasury example. The 5 Year has a coupon of 1.5% and matures on June 30, 2016. On August 2nd, the Trade Date if the Note was purchased that day, the quoted price was “101-11+”.

The invoice price is sometimes referred to as the “dirty price” because it takes into accounted accrued interest, which changes every day. The quoted price is also called the “clean price” and is what Wall Street uses to quote Notes and Bonds.

Note that, by convention, the invoice price is rounded to six decimal places.

Quoted Price

We explained the quoted price earlier:

Quoted Price = 101 + 11/32 + (1/2)/32 = 101.359375

Accrued Interest

Calculating  accrued interest takes a little more work. The Trade Date was Tuesday, August 2, 2011; therefore the Settlement Date is Wednesday, August 3, 2011, one business day later. Though the seller agreed to sell the security to the buyer on August 2nd, he still technically owns it until August 3rd. Therefore he should accrue interest until this later date.

The base period in which the interest is earned is from 6/30/2011 to 12/31/2011, which is 184 days. Remember, Notes and Bonds pay coupons semi-annually, so the owner of the security earns half the annual coupon over each period. Here, the coupon is 1.5%; this means that 0.075% is earned semi-annually. The interest should accrue from 6/30/2011 until 8/3/2011, which is 34 days. Using this information and the Actual/Actual day count convention, we get:

Accrued Interest = (1.5 * ½) * (34/184) = 0.13858696

Putting it Altogether

Plugging these intermediate results of Quoted Price and Accrued Interest into the equation, we get:

Invoice Price = Quoted Price + Accrued Interest = 101.359375 + 0.13858696 = 101.497620

So if $1,000,000 Face Value of the 5-Year Treasury was traded at “101-11+” on August 2, 2011, then on August 3, 2011 the buyer would have to wire an amount equal to the Invoice Price in percent multiplied by the Amount of Face Value of the Note.

Invoice Amount = $1,000,000 * 101.497620 / 100 = $1,014,979.62


Traders don’t typically care about invoice prices because they trade securities with their counterparties using quoted prices. But the back office and accounting areas of the firm do care, because they have to settle the trade.

Generally speaking, the back offices of both buyer and seller calculate the invoice price and the total invoice amount independently. If they disagree they must reconcile. But this rarely happens in the U.S. Treasury markets since these calculations and definitions are standardized and well understood. Furthermore, there are analytical systems that can perform these calculations; Bloomberg is considered the definitive reference source.


Written by Larry Ng

August 2, 2011 at 8:19 PM

One Response

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  1. Historically, bond prices were quoted in fractions. As the markets became more liquid and competitive, the divisor became smaller and smaller. What was 8ths, became 16ths, then eventually 32nds. Today, the first two decimal places are in 32nds. The 3rd decimal place is an 1/8th of a 32nd or 1/256th of a percent.

    Larry Ng

    November 21, 2014 at 5:36 PM

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