Day Counting: Securities Dated on the 15th of a Month

Day counting: securities dated on the 15th of a month. I am writing in response to your letter of May 26, 1982 in which you inquire as to the correct day count for calculation purposes on a security which is dated on the 15th of a month and pays interest on the first of a following month. In your letter you pose the example of a security dated on June 15, 1982 and paying interest on July 1, 1982, and you inquire whether the July 1, 1982 coupon on such security should have a value of 15 or 16 days of accrued interest.

As you know, Board rule G-33 provides the following formula for use on computations of day counts on securities calculated on a "30/360" day basis:

Number of days = (Y2 - Y1) 360 + (M2 - M1) 30 + (D2 - D1)

In this formula, the variables "Y1," "M1," and "D1" are defined as the year, month, and day, respectively, of the date on which the computation period begins (June 15, 1982, in your example), and "Y2," "M2," and "D2" as the year, month, and day of the date on which the computation period ends (July 1, 1982, in your example). In the situation you present, therefore, the number of days in the period would correctly be computed as follows:

Number of days = (1982 - 1982) 360 + (7 - 6) 30 + (1 - 15)

or

Number of days = (0) 360 + (1) 30 + (- 14)

or

Number of days = 0 + 30 + ( - 14)

or

Number of days = 16 days

If figured correctly, therefore, the coupon for such a period should have a value of 16 days of accrued interest. If the coupon is for a longer period of time, this particular portion of that longer period would still correctly be counted as 16 days (e.g., the day count on a coupon for the period June 15 to September 1 would correctly be figured as 76 days, consisting of 16 days for the period June 15 to July 1, and 30 days each for the months of July and August).

The error of computing the day count for such a period as 15 days apparently arises from an assumption that, on a security dated on the 15th of a month, accrued interest is owed only for the "second half" of that month. In reality, of course, the 15th of a month is not the first day of the "second half" of that month, but rather is the last day of the "first half" of that month (since a 30-day month consists of two 15-day half-months, the first half being from the 1st to the 15th, and the second half being from the 16th to the 30th). Again, it can clearly be seen that the correct day count for such a period is 16 days. MSRB interpretation of June 2, 1982.