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Odd Coupon Periods

Some bonds have a first or last coupon payment that differs from the standard coupon amount. The amount paid on these coupon payment dates may be either greater than or less than the standard coupon, depending on the length of time between the dated date and the first coupon date (for odd first coupons) or the length of time between the penultimate coupon date and the maturity date (for odd last coupons).

In order to demonstrate the manner in which the first coupon amount is calculated, consider the two examples presented in the following table:

 

Type of Odd First Coupon

Short

Long

 

Dated Date

25 April 2000

12 January 1999

Maturity Date

20 March 2006

15 May 2009

First Coupon Date

20 March 2001

15 November 1999

Coupon Frequency

Annual

Semi-Annual

Coupon Rate

7%

5.5%

Normal Coupon Cycle

20 March

15 May, 15 Nov

Accrual Basis

Actual/Actual (actual)

Actual/Actual (actual)

 

 

 

Both the long and short first coupon calculation are effectively dealt with using the same approach, and this approach is used when the settlement date falls between the bond's dated date and first coupon payment date. The procedure is set out below:

1.

 

Compute the nominal coupon payment dates by cycling back from the maturity date. A 'nominal' coupon date is a date on which a coupon payment would be paid if there were no odd first coupon. The first nominal date in the series must precede the bond's dated date. For bonds with a long first coupon payment, there will be one nominal payment date on which no payment is made.

2.

The nominal coupon schedule, along with the dated date and first payment date, can then be used to determine whether we are dealing with a long or short first period.

3.

Based on the nominal coupon payment schedule, both a long and short first coupon period will include a short stub period at the beginning. The 'accrued' interest for this period is computed as a function of the accrual basis and the period length. The relevant dates and period lengths for the bonds in the example are:

 

 

 

Short First Coupon

Long First Coupon

 

 

 

First Nominal Coupon Date

20 March 2000

15 November 1998

 

Second Nominal Coupon Date

20 March 2001

15 May 1999

 

Actual First Coupon Date

20 March 2001

15 November 1999

 

Dated Date

25 April 2000

12 January 1999

 

Accrual Days in Stub First Period

329
(20/3/01 25/04/00)

123
(15/05/99 12/01/99)

 

Total Days in First Coupon Period

365
(20/3/01 20/03/00)

181
(15/05/99 15/11/98)

 

 

4.

The first period coupon amount is then computed as the accrued interest for the stub first period (for short first coupons) plus the normal coupon payment for the second nominal coupon period (for long first coupons).

For the examples, the coupon values are computed as follows:

 

 

 

Short First Coupon

Long First Coupon

 

 

 

 

Proportional Length of Stub First Period

329/365

123/181

 

Coupon Payment for Stub First Period (PPH)

6.3095890411

1.86878453039

 

 

 

 

 

Total First Coupon Payment

6.3095890411

4.61878453039

 

 

 

 

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