Over the next few weeks we’ll be discussing mechanics.  Not the fix-it types down at the local Gas-n-Go, but bond mechanics.  After mastering these topics, your next deal will run like a well-oiled machine.

First, we’ll deconstruct (and inspect, oil and then re-assemble) several important timing and calculation issues that commonly arise in bond deals.

Bond Math and Interest Accrual

How is interest calculated on bonds?

The indenture governing the bonds (or the note itself) will usually contain language similar to the following1:

The issuer will pay interest semi-annually in arrears on January 15 and July 15 of each year, commencing July 15, 2013.  Interest on the bonds will accrue from the most recent date to which interest has been paid or, if no interest has been paid, from the date of issuance.  Interest will be computed on the basis of a 360-day year compromised of twelve 30-day months.  Interest accrued to the interest payment date will be paid to each holder of record as of the record date.

Interest on bonds is almost always payable on the 1st of a month to the holders of record2 on the 15th day of the prior month or on the 15th of a month to the holders of record on the 1st day of such month.  Interest payment dates are typically a function of the maturity date of the bonds – the maturity date is the 1st or 15th of a month and the maturity date is the last semi-annual interest payment date.  If any interest payment date falls on a non-business day, the payment will be made on the next succeeding business day (and such payment will include interest to the original interest payment date only).

How is time measured in bondland?

Bonds generally use a “30/360” convention to determine how interest accrues over time.  This means that interest will be computed on the basis of a 360-day year comprised of twelve 30-day months.  Said a different way, 8.33333% of the annual interest payments on the bonds will accrue during each full month that the bonds remain outstanding (without regard to the actual number of days in the month).  Note that this methodology differs from the “actual/365” convention used in the bank loan market.

When calculating the accrual period, it’s important to know that interest only accrues overnight.  This means, in bondland, you don’t include the end date (i.e., the payment date) when calculating the period within a range of dates, since it is the start date of, and is included in, the next interest accrual period.  For example, during the period “from July 1 to July 24,” a total of 23 nights of interest will accrue.  July 1 counts and July 24 does not.

In bondland, for each calendar month (from the 1st of a month to the 1st of the next month), 30 nights of interest will be deemed to accrue, regardless of the actual number of nights in the month.  Thirty is the magic number.  Note that this produces some interesting results.  For example, the amount of interest accruing during the first 30 nights of a 31-night month is the same as the amount of interest accruing for the entire month (so, no interest accrues on that 31st night).  And the last night of February is a particularly good night for bondholders; during a leap year, two nights of interest accrue during the night of the 29th and, during a normal year, three nights of interest accrue during the night of the 28th.

It gets a bit trickier in the case of a partial calendar month.  Let's first look at a partial calendar month that does not include the last days of the month.  In that case, it's pretty easy—bond interest is computed on the basis of the actual number of nights in the partial month, with 0.27778% of the annual interest charge accruing during each night that the bonds are outstanding in the partial calendar month.  For a partial calendar month that starts on the 1st, the number of nights of interest that have accrued as of a particular date is one less than the date of the calendar month, i.e., as of the 15th, 14 nights of interest will have accrued.

All of the fancy footwork in bond math occurs at the end of a calendar month.  When dealing with a partial calendar month that includes the last days of the month, you must first figure out what the magic number is for that partial month period in order to know how many nights of interest will accrue during that period.  The magic number for the whole calendar month is always 30.  The magic number for a partial calendar month that includes the last days of the month is 30 minus the number of days (nights, really) of interest that have already accrued in that calendar month prior to the commencement of the partial period at the end of the month.  So, for a partial calendar month that commences on the 15th day of that calendar month, there were 14 nights in the calendar month prior to the commencement of our partial month period, and, as a result, the magic number is 16 (30 minus 14 equals 16).  Now that we know the magic number, we proceed the same way we did for a full month, i.e., we count actual days (nights, really) in the partial month period, with each day (night) resulting in a one-day accrual of interest, until we get to the end of the month.  If there are more days (nights) in the period than the magic number, the extra days do not earn interest, and if there are less days (nights) in the period than the magic number, then the last day counts as many times as necessary to get to the magic number.  Piece of cake, right?

Put another way, the adjustments to bring 28-, 29- and 31-night calendar months in line with the 30/360 convention occur at the end of the calendar month, whether we are dealing with a full calendar month or a partial calendar month.

Here are two illustrative examples:

• For bonds with interest payment dates on February 15 and August 15, as of noon on March 3, 2013, even though 16 nights have passed since the last interest payment date, 18/360ths (or 5%) of the annual coupon will have accrued.  This is the math: 16 nights from February 15 to March 1 (14 actual nights, increased by two extra nights on the night of February 28th, to produce a 30-night calendar month), plus 2 nights for the nights of March 1 and 2 = 18.
• For bonds with interest payment dates on January 15 and July 15, as of noon on June 24, 2013, 159/360ths (or 44.17%) of the annual coupon will have accrued, even though 160 nights will have passed since January 15, the last interest payment date.  This is the math: 16 nights from January 15 to February 1 (17 actual nights, reduced by one night to produce a 30-night month); plus four months x 30 nights for the period from February 1 to July 1 (i.e., 120 nights, which, coincidentally, is the same as the 120 nights that actually passed during such period); plus 23 additional nights for the period from June 1 to June 24 = 159.

How is accrued interest calculated in connection with a redemption and who receives the interest payment?

Indentures typically provide that, on the redemption date, the issuer will pay the redemption price for the bonds, as well as the amount of accrued and unpaid interest “from” the last interest payment date “to (but not including)” the redemption date, “subject to the rights of bondholders on the relevant record date to receive interest due on the relevant interest payment date.”  What’s that all about?

If a redemption date occurs during the two-week period after the record date for the next interest payment but prior to the next interest payment date, the issuer is required to pay accrued interest up to the redemption date on the redemption date but that accrued interest will be paid out to the holders of record as of the immediately preceding record date (even if the bondholder on the record date is not the same person as the bondholder on the redemption date).  Obviously, this is a situation ripe for market confusion.  If the interest is paid to a prior owner of the bonds, the new owner on the interest payment date may feel he or she has not gotten a payment to which she was entitled.  Historically, this disconnect was addressed in the bond markets by setting a date after which the bonds will trade ex coupon, i.e., the seller of the bond retained the right to receive interest on the next interest payment date (and the purchase price for the bond was reduced accordingly).  With the advent of electronic settlement through DTC, ex coupon trading of bonds in the U.S. has been nearly eliminated (although it persists in certain other jurisdictions).  As discussed above in footnote #1, there will always be only a single holder of record for bonds settled through DTC’s electronic book-entry system (namely, DTC’s nominee, Cede & Co.), and, if DTC’s interim accounting procedures apply, the DTC participant that holds a beneficial interest in the global note as of the business day prior to the redemption date will receive the interest payment on the redemption date.

So, there are two parallel universes intersecting in bondland – the indenture world and the electronic trading world of DTC.  It’s important to understand both of these worlds in order to grasp the subtleties of bond math.