OFCFACTORS
Updated: 31 May 2014
Use the tablevalued function OFCFACTORS to return the components used in the calculation of price and yield for a bond with an odd first coupon. OFCFACTORS supports odd first coupon bonds with up to 2 quasicoupon periods.
Syntax
SELECT * FROM [wctFinancial].[wct].[OFCFACTORS](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@Issue, datetime,>
,<@FirstCoupon, datetime,>
,<@Rate, float,>
,<@Price, float,>
,<@Yield, float,>
,<@Redemption, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>)
Arguments
@Settlement
the settlement date of the security. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Maturity
the maturity date of the security. @Maturity is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Issue
the issue date of the security; the date from which the security starts accruing interest. @Issue is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@FirstCoupon
the first coupon date of the security. The period from the issue date until the first coupon date defines the odd interest period. All subsequent coupon dates are assumed to occur at regular periodic intervals as defined by @Frequency. @First_coupon is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Rate
the securityâ€™s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Price
the price of the bond. @Price is an expression of type float or of a type that can be implicitly converted to float.
@Yield
the securityâ€™s annual yield. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the securityâ€™s redemption value per 100 face value. @Redemption is an expression of type float or of a type that can be implicitly converted to float.
@Frequency
the number of coupon payments per year. For annual payments, @Frequency = 1; for semiannual, @Frequency = 2; for quarterly, @Frequency = 4; for bimonthly @Frequency = 6; for monthly, @Frequency = 12. For bonds with @Basis = 'A/364' or 9, you can enter 364 for payments made every 52 weeks, 182 for payments made every 26 weeks, 91 for payments made every 13 weeks, 28 for payments made every 4 weeks, 14 for payments made every 2 weeks, and 7 for weekly payments. @Frequency is an expression of type float or of a type that can be implicitly converted to float.
@Basis
is the type of day count to use. @Basis is an expression of the character string data type category.
@Basis

Day count basis

0, 'BOND'

US (NASD) 30/360

1, 'ACTUAL'

Actual/Actual

2, 'A360'

Actual/360

3, 'A365'

Actual/365

4, '30E/360 (ISDA)', '30E/360', 'ISDA', '30E/360 ISDA', 'EBOND'

European 30/360

5, '30/360', '30/360 ISDA', 'GERMAN'

30/360 ISDA

6, 'NL/ACT'

No Leap Year/ACT

7, 'NL/365'

No Leap Year /365

8, 'NL/360'

No Leap Year /360

9, 'A/364'

Actual/364

10, 'BOND NONEOM'

US (NASD) 30/360 nonendofmonth

11, 'ACTUAL NONEOM'

Actual/Actual nonendofmonth

12, 'A360 NONEOM'

Actual/360 nonendofmonth

13, 'A365 NONEOM'

Actual/365 nonendofmonth

14, '30E/360 NONEOM', '30E/360 ICMA NONEOM', 'EBOND NONEOM'

European 30/360 nonendofmonth

15, '30/360 NONEOM', '30/360 ISDA NONEOM', 'GERMAN NONEOM'

30/360 ISDA nonendofmonth

16, 'NL/ACT NONEOM'

No Leap Year/ACT nonendofmonth

17, 'NL/365 NONEOM'

No Leap Year/365 nonendofmonth

18, 'NL/360 NONEOM'

No Leap Year/360 nonendofmonth

19, 'A/364 NONEOM'

Actual/364 nonendofmonth

Return Type
RETURNS TABLE (
[E] [float] NULL,
[DSC] [float] NULL,
[N] [int] NULL,
[NCF] [int] NULL,
[A1] [float] NULL,
[DFC1] [float] NULL,
[NLF1] [float] NULL,
[A2] [float] NULL,
[DFC2] [float] NULL,
[NLF2] [float] NULL,
[Nqf] [float] NULL,
[quasistart] [datetime] NULL,
[quasicoup] [datetime] NULL,
[C] [float] NULL,
[FC] [float] NULL,
[P] [float] NULL,
[AI] [float] NULL,
[Y] [float] NULL
)
Column

Description

E

Number of coupon days in the quasicoupon period in which the settlement date falls.

DSC

Number of days from the settlement date to the next quasicoupon date.

N

Number of coupons between the first coupon date and the maturity date.

NCF

Number of quasicoupon periods in the odd period (1 or 2).

A1

Number of accrued days in the first quasicoupon period.

DFC1

Number of accrued days from the issue date to the next quasicoupon date.

NLF1

Normal length of the first quasicoupon period.

A2

Number of accrued days in the second quasicoupon period.

DFC2

Number of accrued days from the quasicoup date to to the first coupon date.

NLF2

Normal length of the period from the quasicoup date to the first coupon date.

Nqf

Number of whole coupons between the settlement date and the first coupon date.

quasistart

Implied previous coupon date with respect to the issue date.

quasicoup

Implied next coupon date with respect to the issue date when NCF = 2.

C

Coupon amount

FC

First coupon amount

P

Price. If @Yield is NOT NULL then P is calculated from the inputs otherwise P is the value entered in @Price.

AI

Accrued interest as of the settlement date.

Y

Yield. If @Yield is NOT NULL then Y is the value entered in @Yield otherwise Y is calculated from the inputs.

Remarks
Â· If @Settlement is NULL then @Settlement = GETDATE().
Â· If @Rate is NULL then @Rate = 0.
Â· If @Redemption is NULL then @Redemption = 100.
Â· If @Frequency is NULL then @Frequency = 2.
Â· If @Basis is NULL then @Basis = 0.
Â· If @Frequency is any number other than 1, 2, 4, 6 or 12, or for @Basis = 'A/364' any number other than 1, 2, 4, 6, or 12 as well as 7, 14, 28, 91, 182, or 364 OFCFACTORS returns an error.
Â· If @Basis invalid (see above list), OFCFACTORS returns an error.
Â· If @Maturity is NULL then an error is returned.
Â· If @Issue is NULL then an error is returned.
Â· If @FirstCoupon is NULL then an error is returned.
Â· If @Settlement >= @FirstCoupon then nothing is returned.
Â· The first quasicoupon period is always the quasicoupon period in which the issue date occurs.
Â· The previous coupon date for the first quasicoupon period is calculated using @Frequency, @Basis, and @Maturity. This is the value returned in quasistart.
Â· If there is only one quasicoupon period then quasicoup is NULL. Otherwise the preivous coupon date for the second quasicoupon period is calculated using @Frequency, @Basis, and @Maturity.
Â· If there are 2 quasicoupon periods then DFC2 = NLF2.
Examples
This bond has an odd short first coupon (meaning that the first coupon period is shorter than a normal coupon period) and settles on the issue date.
SELECT
*
FROM
wct.OFCFACTORS(
'20140501', @Settlement
'20340615', @Maturity
'20140501', @Issue
'20140615', @FirstCoupon
0.025, @Rate
NULL, @Price
0.0276, @Yield
100, @Redemption
2, @Frequency
1 @Basis
)
This produces the following result (which has been reformatted for ease of viewing).
E

DSC

N

NCF

A1

DFC1

NLF1

A2

DFC2

NLF2

Nqf

182

45

40

1

0

45

NULL

NULL

NULL

NULL

0

quasistart

quasicoup

C

FC

P

AI

Y

12/15/2013

NULL

1.25

0.309065934

96.00756311

0

0.0276

This bond has odd long first coupon (meaning that the first coupon period is longer than a normal coupon period) and settles on the issue date.
SELECT
*
FROM
wct.OFCFACTORS(
'20140501', @Settlement
'20340615', @Maturity
'20140501', @Issue
'20141215', @FirstCoupon
0.025, @Rate
NULL, @Price
0.0276, @Yield
100, @Redemption
2, @Frequency
1 @Basis
)
This produces the following result (which has been reformatted for ease of viewing).
E

DSC

N

NCF

A1

DFC1

NLF1

A2

DFC2

NLF2

Nqf

182

45

39

2

0

45

182

0

183

183

1

quasistart

quasicoup

C

FC

P

AI

Y

12/15/2013

6/15/2014

1.25

1.559065934

96.00337029

0

0.0276

Here we calculate the factors for a bond with an odd long first coupon with semiannual coupons payable on March 30^{th} and September 30^{th}.
SELECT
*
FROM
wct.OFCFACTORS(
'20140915', @Settlement
'20340930', @Maturity
'20140301', @Issue
'20140930', @FirstCoupon
0.0257, @Rate
98.116208, @Price
NULL, @Yield
100, @Redemption
2, @Frequency
11 @Basis
)
This produces the following result.
E

DSC

N

NCF

A1

DFC1

NLF1

A2

DFC2

NLF2

Nqf

184

15

40

2

29

29

181

169

184

184

0

quasistart

quasicoup

C

FC

P

AI

Y

9/30/2013

3/30/2014

1.285

1.490883978

98.116208

1.3861285431

0.02692185

Here's an example with a negative yield.
SELECT
*
FROM wct.OFCFACTORS(
'20140315', @Settlement
'20240930', @Maturity
'20140301', @Issue
'20140330', @FirstCoupon
0.0157, @Rate
NULL, @Price
0.00235, @Yield
100, @Redemption
2, @Frequency
10 @Basis
)
This produces the following result.
E

DSC

N

NCF

A1

DFC1

NLF1

A2

DFC2

NLF2

Nqf

180

15

21

1

14

29

NULL

NULL

NULL

NULL

0

quasistart

quasicoup

C

FC

P

AI

Y

9/30/2013

NULL

0.79

0.126472222

119.2767915

0

0.00235

This is an example of a bond paying interest every 26 weeks.
SELECT
*
FROM
wct.OFCFACTORS(
'20141004', @Settlement
'20291212', @Maturity
'20140326', @Issue
'20141231', @FirstCoupon
0.1250, @Rate
NULL, @Price
0.1100, @Yield
100, @Redemption
182, @Frequency
9 @Basis
)
This produces the following result.
E

DSC

N

NCF

A1

DFC1

NLF1

A2

DFC2

NLF2

Nqf

182

88

30

2

98

98

182

94

182

182

0

quasistart

quasicoup

C

FC

P

AI

Y

20140101

20140702

6.25

9.615384615

110.8424329

6.593406593

0.11

See Also