SQL Server DURATION Function

Updated 2024-02-23 14:11:37.860000

Description

Use the scalar function DURATION to calculate the Macaulay duration (in years) of a security with regular, periodic interest payments. DURATION assumes a redemption value of 100. The formula for DURATION is:

\mathrm{D=\frac{\Sigma_{i=1}^NCF_i\times{t_i}\times{DF^{t_i}}}{\Sigma_{i=1}^NCF_i\times{DF^{t_i}}}}

Where

D = Duration

CF_i = i^th future cash flow

t_i = time, in coupon periods, to the i^th cash flow

DF = (1 + @Yld/@Frequency)

N = Number of coupon payments from settlement to maturity

Syntax

SELECT [westclintech].[wct].[DURATION] (
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@Rate, float,>
 ,<@Yld, 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.

@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.

@Yld

the security's annual yield. @Yld 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 bi-monthly @Frequency = 6; for monthly @Frequency =12. @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 @Frequency is any number other than 1, 2, 4, 6 or 12 DURATION returns an error.

If @Basis is invalid (see above list), DURATION returns an error.

Examples

This bond has a coupon rate of 3.0%, pays interest semi-annually on the 30 ^th of November and the 31^st of May and matures on 2033-11-30. The settlement date for the transaction is 2014-10-10 and the yield is 3.15%. The bond is quoted using the Actual/Actual day-count convention.

SELECT wct.DURATION(   '2014-10-10', --@Settlement
                       '2033-11-30', --@Maturity
                       0.03,         --@Rate
                       0.0315,       --@Yld
                       2,            --@Frequency
                       1             --@Basis
                   ) AS DURATION;

This produces the following result.

DURATION
14.4816608104738

This bond has a 2.80% coupon rate, pays interest semi-annually on the 30^th of September and the 30^th of March and matures on 2044-09-30. The price of the bond is 99.375 and the date of the transaction is 2014-10-10. The bond is quoted using the US 30/360 day-count convention.

SELECT wct.DURATION(   '2014-10-10', --@Settlement
                       '2044-09-30', --@Maturity
                       0.028,        --@Coupon
                       wct.YIELD(   '2014-10-10', --@Settlement
                                    '2044-09-30', --@Maturity
                                    0.028,        --@Coupon
                                    99.375,       --@Price
                                    100,          --@Redemption
                                    2,            --@Frequency
                                    1             --@Basis
                                ),   --@Yield
                       2,            --@Frequency
                       10            --@Basis
                   ) AS DURATION;