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Ease is important, but not to the degree it is for Operations. Understanding the methods means understanding the conflicts and making decisions. The first decision is the period s you want to keep interest constant over. Constant Interest Period There are basically three alternatives for the period for which you can have a constant interest increment.

This implies that the coupon payments and total annual income are not constant, because of leap years. Daily by coupon period Interest is constant for each day of a given coupon period, and each period has the same coupon payment. Payments are also constant by year.

On the other hand, one day's interest may vary between periods. Monthly All months, and thus coupon payments, are constant, but the days aren't. Determining Daily Interest Bonds are quoted on an annual interest basis, e. The next step is to determine the daily interest rate. For the "Daily" alternative above, the most common approaches are to divide the quoted interest rate by or You could use any fixed number even For "Daily by coupon" you first divide the quoted rate by the number of coupon periods in a year.

You then divide that result by the number of days in the particular period e.

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For "Monthly" you divide the quoted rate by and take a standard 30 days per month. For argument's sake you could use with 29 days per month, but in practice only with 30 are used. Note that none of these approaches take compounding into account. The following table summarizes the discussion to this point.

We discuss the meaning of "Split" below. The amount per month is not constant, though the amount per coupon period and year is. But there is a problem with handling daily interest. The problem, of course, is that you want to have constant monthly interest, but the number of days per month is not constant. One approach would be to divide the quoted annual interest rate by 12 to get a constant monthly rate, and then divide that rate by the actual number of days in the month.

The problem with this approach is operational: The approach used in practice is to assign 30 days to each month. If the month has more or fewer days, an adjustment is made at the end of the month so that each month gets exactly 30 days of interest. We consider two common methods used in practice to handle that "adjustment", reflecting conflicting emphases on interest bought and on interest earned.

These are illustrated in the table below. In the table we ignore the effects of non-settlement days and month-ends that were discussed above. June 1st is a coupon payment date, so there is no interest on that day. The next two blocks of rows show daily interest again in days of interest and month-to-date interest.

In all cases the interest bought on the second day of the month is one higher than on the first day, with each day increasing until the adjustment point is reached. For months with less than 31 days the approaches are identical, so we discuss only months with 31 days below. Interest bought increases each day until the last day of the month, with the 31st being unchanged from the 30th. It then goes up on the first of the next month by one day.

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Under the US approach, it goes up through the 31st, and the first of the next month has the same value as the 31st, before it starts increasing again on the 2nd day of the following month. Under the ICMA it increases through the 29th, stays unchanged on the 30th, and then goes up again on the 31st. Given the relation of interest earned to the following day's interest bought discussed in an earlier section, this situation is unavoidable.

You can't have both intuitive interest bought and intuitive month-to-date interest income. Remarks We started this discussion of day count conventions by emphasizing the utility of understanding the reasons the various conventions were first developed. They were all developed to be suitable for a particular purpose not just to confuse programmers! If you understand the reasons, you should be able to develop the algorithms from scratch.

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As to why there aren't more, there are. It's a balance among the goals of those involved in the marketplace. It's a dynamic process.

It is also important to remember that these methods were developed before computers were available. Finally, bond coupons do not exist in an investment vacuum. Dividend Comparison Dividends are very similar to coupon payments at an architectural level. These are the only differences: Declaration date is effectively the bond issue date, as the dates and amounts are described in the bond prospectus.

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