CD Equivalent Yield
The CD equivalent yield (also called the money market equivalent yield)
makes the quoted yield on a bank discount basis more comparable to
yield quotations on other money market instruments that pay interest
on a 360-day basis. It does this by taking into consideration the price of
the discount security (i.e., the amount invested) rather than its face
value. The formula for the CD equivalent yield is
CD equivalent yield =360Yd/(360 – t(Yd))
To illustrate the calculation of the CD equivalent, suppose a 91-day
Treasury bill has a yield on a bank discount basis is 5.56%. The CD
equivalent yield is computed as follows:
CD equivalent yield = 360(0.0556)/(360 – 91(0.0556))=0.05639 = 5.639%
Actual/360
Actual/360 is the second type of day count convention. Specifically,
Actual/360 specifies that each month has the same number of days as
indicated by the calendar. However, each year is assumed to have 360
days regardless of the actual number of days in a year. Actual/360 is the
day count convention used in U.S. money markets. Let’s illustrate the
Actual/360 day count with a 26-week U.S. Treasury bill which matures
on March 7, 2002. The Bloomberg Security Display (DES) screen for this
security is presented in Exhibit 2.3. From the “Security Information” box
on the left-hand side of the screen, we see that the day count is specified
as “ACT/360.” Suppose this Treasury bill is purchased with a settlement
date on September 11, 2001 at a price of 98.466. How many days does
this bill have until maturity using the Actual/360 day count convention?
Once again, the question is easily answered using Bloomberg’s DCX
(Days Between Dates) function and specifying the two dates of interest.
This screen is presented in Exhibit 2.4. We see that with a settlement date
of September 11, 2001 there are 177 calendar days until maturity on
March 7, 2002. This can be confirmed by examining the Bloomberg’s YA
(Yield Analysis) screen in Exhibit 2.5. We see that with a settlement date of
September 11, 2001 this Treasury bill has 177 days to maturity. This information
is located just above the “Price” box in the center of the screen.
Actual/Actual
Treasury notes, bonds and STRIPS use an Actual/Actual (in period) day
count convention. When calculating the number of days between two
dates, the Actual/Actual day count convention uses the actual number of
calendar days as the name implies. Let’s illustrate the Actual/Actual day
count convention with a 3.625% coupon, 2-year U.S. Treasury note with
a maturity date of August 31, 2003. The Bloomberg Security Display
(DES) screen for this security is presented in Exhibit 2.1. In the “Security
Information” box on the left-hand side of the screen, we see that the day
count is specified as “ACT/ACT.” From the “Issuance Info” box on the
right-hand side of the screen, we see that interest starts accruing on
August 31, 2001 (the issuance date) and the first coupon date is February
28, 2002. Suppose this bond is traded with a settlement date of September
11, 2001. How many days are there between August 31, 2001 and
September 11, 2001 using the Actual/Actual day count convention?
To answer this question, we simply count the actual number of days
between these two dates.3 To do this, we utilize Bloomberg’s DCX (Days
Between Dates) function presented in Exhibit 2.2. The function tells us
there are 11 actual days between August 31, 2001 and September 11,
2001.4 In the same manner, we can also determine the actual number of
calendar days in the full coupon period. A full 6-month coupon period can
only have 181, 182, 183 or 184 calendar days. For example, the actual
number of days between August 31, 2001 and February 28, 2002 is 184.