ODDLYIELD
Updated: 30 June 2014
Use ODDLYIELD to calculate the yield of a security with an odd last coupon period. If the settlement date is less than the last coupon date there is no closed-form solution for calculating the yield; the solution is found by iteration. If the settlement date is greater than or equal to the last coupon date then the formula for yield is:
Where
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RV
|
=
|
redemption value
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|
C
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=
|
100 * rate/frequency
|
|
F
|
=
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frequency
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|
P
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=
|
price
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NLC
|
=
|
the number of quasi-coupons from the last coupon date to the quasi-maturity date
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|
DLCi
|
=
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the number of from the previous coupon date to the lesser of the next coupon date and the maturity date in the ith quasi-coupon period
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|
NLLi
|
=
|
the normal length in days of the full ith quasi-coupon period in the odd last period
|
|
DSCi
|
=
|
number of days from the settlement date (or beginning of the quasi-coupon period) to the next quasi-coupon within odd period (or to redemption date) for the ith quasi-coupon period
|
|
Ai
|
=
|
number of accrued days for the ith quasi-coupon within odd period counting forward from the last interest date before redemption
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Syntax
SELECT [wctFinancial].[wct].[ODDLYIELD] (
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@Last_interest, datetime,>
,<@Rate, float,>
,<@Pr, 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.
@Last_interest
the last coupon date of the security prior to the maturity. The period from the last interest date until the maturity date defines the odd interest period. All previous coupon dates are assumed to occur at regular periodic intervals as defined by @Frequency. @Last_interest is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Rate
the security’s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Pr
the price of the security. @Pr is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the security’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 semi-annual, @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.
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@Basis
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Day count basis
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|
0, 'BOND'
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US (NASD) 30/360
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1, 'ACTUAL'
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Actual/Actual
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2, 'A360'
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Actual/360
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3, 'A365'
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Actual/365
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4, '30E/360 (ISDA)', '30E/360', 'ISDA', '30E/360 ISDA', 'EBOND'
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European 30/360
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5, '30/360', '30/360 ISDA', 'GERMAN'
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30/360 ISDA
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6, 'NL/ACT'
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No Leap Year/ACT
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7, 'NL/365'
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No Leap Year /365
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8, 'NL/360'
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No Leap Year /360
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9, 'A/364'
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Actual/364
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10, 'BOND NON-EOM'
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US (NASD) 30/360 non-end-of-month
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11, 'ACTUAL NON-EOM'
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Actual/Actual non-end-of-month
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12, 'A360 NON-EOM'
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Actual/360 non-end-of-month
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13, 'A365 NON-EOM'
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Actual/365 non-end-of-month
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14, '30E/360 NON-EOM', '30E/360 ICMA NON-EOM', 'EBOND NON-EOM'
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European 30/360 non-end-of-month
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15, '30/360 NON-EOM', '30/360 ISDA NON-EOM', 'GERMAN NON-EOM'
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30/360 ISDA non-end-of-month
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|
16, 'NL/ACT NON-EOM'
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No Leap Year/ACT non-end-of-month
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17, 'NL/365 NON-EOM'
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No Leap Year/365 non-end-of-month
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18, 'NL/360 NON-EOM'
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No Leap Year/360 non-end-of-month
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19, 'A/364 NON-EOM'
|
Actual/364 non-end-of-month
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Return Types
float
Remarks
· If @Settlement is NULL then @Settlement = GETDATE().
· If @Rate is NULL then @Rate = 0.
· If @Redemption is NULL then @Redemption = 100.
· If @Frequency is NULL then @Frequency = 2.
· If @Basis is NULL then @Basis = 0.
· 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 ODDLYIELD returns an error.
· If @Basis is invalid (see above list), ODDLYIELD returns an error.
· If @Maturity is NULL then an error is returned.
· If @Last_interest is NULL then an error is returned.
· If @Price is NULL than an error is returned.
Examples
This is a bond with an odd short last coupon period where the settlement date in the last coupon period.
SELECT
wct.ODDLYIELD(
'2014-10-01', --@Settlement
'2014-12-15', --@Maturity
'2014-09-15', --@Last_interest
0.0225, --@Rate
100.445329, --@Price
100, --@Redemption
2, --@Frequency
1 --@Basis
) as Yield
This produces the following result.
Yield
----------------------
0.00100000580324695
This is a bond with an odd long last coupon period with a settlement date in the last coupon period.
SELECT
wct.ODDLYIELD(
'2014-10-01', --@Settlement
'2014-12-15', --@Maturity
'2014-03-15', --@Last_interest
0.0225, --@Rate
100.445096, --@Price
100, --@Redemption
2, --@Frequency
1 --@Basis
) as Yield
This produces the following result.
Yield
----------------------
0.00100000422761388
This is a bond with an odd short last coupon with a settlement date prior to the last coupon date.
SELECT
wct.ODDLYIELD(
'2014-10-01', --@Settlement
'2034-12-15', --@Maturity
'2034-09-15', --@Last_interest
0.0425, --@Rate
103.443238, --@Price
100, --@Redemption
2, --@Frequency
1 --@Basis
) as Yield
This produces the following result.
Yield
----------------------
0.039999999949176
This is a bond with an odd long last coupon period with a settlement date prior to the last coupon date.
SELECT
wct.ODDLYIELD(
'2014-10-01', --@Settlement
'2034-12-15', --@Maturity
'2034-03-15', --@Last_interest
0.0425, --@Rate
103.433687, --@Price
100, --@Redemption
2, --@Frequency
1 --@Basis
) as Yield
This produces the following result.
Yield
----------------------
0.0400000001216811
This is an example of a bond paying interest every 26 weeks.
SELECT
wct.ODDLYIELD(
'2014-10-04', --@Settlement
'2014-12-15', --@Maturity
'2014-06-01', --@Last_interest
0.1250, --@Rate
100.198974906573, --@Price
100, --@Redemption
182, --@Frequency
9 --@Basis
) as Yield
This produces the following result.
Yield
----------------------
0.110000000000015
See Also