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XLeratorDB/financial Documentation

SQL server bond duration function


RPIDURATION

Updated: 05 May 2014


Use RPIDURATION to calculate the duration for a bond that pays regular periodic interest. The duration is calculated as the first derivative of the price of the bond with respect to yield multiplied by -1, divided by the dirty price of the bond multiplied by 1 plus the yield divided by the frequency.

XLeratorDB regular periodic interest duration formula for RPIDURATION function for SQL Server
Syntax
SELECT [wctFinancial].[wct].[RPICONVEXITY](
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@Rate, float,>
 ,<@Yld, float,>
 ,<@Redemption, float,>
 ,<@Frequency, float,>
 ,<@Basis, nvarchar(4000),>)
Arguments
@Settlement
the settlement date occurring within a coupon period of the bond. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Maturity
the maturity date of the bond. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Rate
the bond’s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yld
the yield for the maturity date passed into the function. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the redemption value of the bond assuming a par value of 100. @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.
@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 NON-EOM'
US (NASD) 30/360 non-end-of-month
11, 'ACTUAL NON-EOM'
Actual/Actual non-end-of-month
12, 'A360 NON-EOM'
Actual/360 non-end-of-month
13, 'A365 NON-EOM'
Actual/365 non-end-of-month
14, '30E/360 NON-EOM', '30E/360 ICMA NON-EOM', 'EBOND NON-EOM'
European 30/360 non-end-of-month
15, '30/360 NON-EOM', '30/360 ISDA NON-EOM', 'GERMAN NON-EOM'
30/360 ISDA non-end-of-month
16, 'NL/ACT NON-EOM'
No Leap Year/ACT non-end-of-month
17, 'NL/365 NON-EOM'
No Leap Year/365 non-end-of-month
18, 'NL/360 NON-EOM'
No Leap Year/360 non-end-of-month
19, 'A/364 NON-EOM'
Actual/364 non-end-of-month
Return Type
float
Remarks
·         If @Maturity <= @Settlement 0 is returned.
·         If @Settlement is NULL, @Settlement = GETDATE()
·         If @Rate is NULL, @Rate = 0
·         If @Yld is NULL, @Yld = 0
·         If @Frequency is NULL, @Frequency = 2
·         If @Basis is NULL, @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 RPIDURATION returns an error.
·         If @Basis is invalid (see above list), RPIDURATION returns an error.
·         @Rate is entered as a decimal value; 1.0% = 0.01
·         @Yld is entered as a decimal value; 1.0% = 0.01
Examples
In this example we calculate the duration for a bond maturing on 2034-06-15. The settlement date is 2014-05-01, the yield is 2.76%, the coupon rate is 2.50%, the redemption value is 100, the coupon is paid twice-yearly, and the bais code is 1.
SELECT wct.RPIDURATION(
   '2014-05-01', --@Settlement
   '2034-06-15', --@Maturity
   0.025,         --@Rate
   0.0276,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as DURATION
This produces the following result
              DURATION
----------------------
      15.6780086644317


In this example, we calculate the duration of a zero-coupon bond.
SELECT wct.RPIDURATION(
   '2014-05-01', --@Settlement
   '2044-06-15', --@Maturity
   0.00,          --@Rate
   0.0301,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as DURATION
This produces the following result.
              DURATION
----------------------
      30.1236728174663


In this example we know the price of the bond (99.9875), but not the yield.
SELECT wct.RPIDURATION(
   '2014-05-01', --@Settlement
   '2024-09-15', --@Maturity
   0.0190,        --@Rate
   wct.YIELD(
      '2014-05-01',
      '2024-09-15',
      0.0190,
      99.9875,
      100,
      2,
      1
      ),          --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as DURATION
This produces the following result.
              DURATION
----------------------
      9.44057846789297


In this example we calculate the duration of a bond settling in the final coupon period.
SELECT wct.RPIDURATION(
   '2014-05-01', --@Settlement
   '2014-07-15', --@Maturity
   0.0190,        --@Rate
   0.0005,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   0              --@Basis
   ) as DURATION
This produces the following result.
              DURATION
----------------------
     0.205585814877239


This is an example of a bond paying interest every 26 weeks.
SELECT wct.RPIDURATION(
      '2014-10-01',     --@Settlement
      '2023-03-13',     --@Maturity
      0.1250,           --@Rate
      0.1100,           --@Yield
      100,              --@Redemption
      182,              --@Frequency
      9                 --@Basis
      ) as DURATION
This produces the following result.
              DURATION
----------------------
      5.56584970656666

 

See Also

 



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