The convention for quoting bids and offers in the secondary market is different for Treasury bills and Treasury coupon securities. Bids/offers on bills are quoted in a special way. Unlike bonds that pay coupon interest,Treasury bill values are quoted on a bank discount basis, not on a price basis. The yield on a bank discount basis is computed as follows:
Yd = annualized yield on a bank discount basis (expressed as a decimal)
D = dollar discount, which is equal to the difference between the face value and the price
F = face value
t = number of days remaining to maturity
For example, Exhibit presents the PX1 Governments screenfrom Bloomberg. Data for the most recently issued bills appear in the upper left-hand corner. The first and second columns indicate the security and its maturity date. In the third column, there is an arrow indicating an up or down tick for the last trade. The fourth column indicates the current bid/ask rates. A bond-equivalent yield (discussed later) using the ask yield/price is contained in column 5. The last column contains the change in bank discount yields based on the previous day’s closing rates as of the time posted. Exhibit presents the same information for all outstanding bills (page PX2). The current/when issued bills’maturity dates are highlighted. Other important market indicators are contained in the lower right-hand corner of the screen.
Given the yield on a bank discount basis, the price of a Treasury billis found by first solving the formula for Yd to obtain the dollar discount(D), as follows:
D = Yd × F × (t/360)
The price is then
price = F − D
Bloomberg Current Governments Screen
Sorce: BloombergFinancial Market
Bloomberg Screen of All Outstanding Bills
Sorce: Bloomberg Financial Market
Using the information in Exhibit, for the current 28-day bill with a face value of $1,000, if the offer yield on a bank discount basis is quoted as 1.76%, D is equal to
D = 0.0176 × $1,000 × 28/360 = $1.3689
price = $1,000 − $1.3689 = $998.6311
The quoted yield on a bank discount basis is not a meaningful measure of the potential return from holding a Treasury bill, for two reasons. First,the measure is based on a face-value investment rather than on the actual dollar amount invested. Second, the yield is annualized according to a 360-day rather than a 365-day year, making it difficult to compare Treasury bill yields with Treasury notes and bonds, which pay interest on a 365-daybasis. The use of 360 days for a year is a money market convention for some money market instruments, however. Despite its short comings as a measure of return, this is the method that dealers have adopted to quote Treasury bills. Many dealer quote sheets and some other reporting services provide two other yield measures that attempt to make the quoted yield comparable to that for a coupon bond and other money market instruments.
CD Equivalent Yield
The CD equivalent yield (also called the money market equivalent yield)makes the quoted yield on a Treasury bill more comparable to yield quotationson other money market instruments that pay interest on a 360-daybasis. It does this by taking into consideration the price of the Treasurybill (i.e., the amount invested) rather than its face value. The formula for the CD equivalent yield is
For example, using the data from Exhibit for the 28-day bill that matures on April 11, 2002, the ask rate on a bank discount basis is1.76%. The CD equivalent yield is computed as follows:
Because of the low rate, the CD equivalent yield is the same as the yield on a bank discount basis.
The measure that seeks to make the Treasury bill quote comparable to coupon Treasuries is called the bond-equivalent yield. This yield measure makes the quoted yield on a Treasury bill more comparable to yields onTreasury notes and bonds that use an actual/actual day count convention. In order to convert the yield on a bank discount to a bond-equivalent yield, the following formula is used:
where T is the actual number of days in the calendar year (i.e., 365 or 366).As an example, using the same Treasury bill with 28 days to maturity and a face value of $1,000 that would be quoted at 1.76% on a bank discount basis, the bond-equivalent yield is calculated as follows:
This number matches the bond-equivalent yield given by the Bloomberg screen in Exhibit .There are a couple of points to note in this calculation.First, we used 365 in the numerator because the year 2002 is a non-leap year.Second, the formula for the bond-equivalent yield presented above assumes that the current maturity of the Treasury bill in question is 182 days or less.
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