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XLeratorDB/financial Documentation

SQL Server YIELD function


YIELD

Updated: 10 Oct 2014


Use YIELD to calculate the yield, given the price, for a security that pays periodic interest and has a par value of 100. There is no closed-form solution for calculating the yield when there is more than one coupon period to redemption; the solution is found by iteration. 
When the settlement date is in the final coupon period the formula for yield is:

XLeratorDB formula for YIELD function for SQL Server
Where
                C = 100 * coupon rate / frequency
                P = price
                RV = redemption value
                DSR = number of days from settlement to redemption
                E = the number of days in the current coupon period
                F = Frequency
                A = C * accrued days / E
Syntax
SELECT [wctFinancial].[wct].[YIELD](
  <@Settlement, datetime,>
 ,<@Maturity, 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. 
@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 clean price of the security. @Yld 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 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 @Settlement is NULL then @Settlement = GETDATE().
·         If @Maturity is NULL then @Maturity = GETDATE().
·         If @Rate is NULL then @Rate = 0.
·         If @Price is NULL then @Price = 100.
·         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 YIELD returns an error.
·         If @Basis is invalid (see above list), YIELD returns an error.
Examples
In this example we calculate the yield given a price of 96.004 for a bond maturing on 2034-06-15. The settlement date is 2014-05-01, 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.YIELD(
   '2014-05-01', --@Settlement
   '2034-06-15', --@Maturity
   0.025,         --@Rate
   96.004,        --@Price
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as YIELD
This produces the following result
                 YIELD
----------------------
    0.0276002534029673


In this example, we calculate the yield of a zero-coupon bond.
SELECT wct.YIELD(
   '2014-05-01', --@Settlement
   '2044-06-15', --@Maturity
   0.00,          --@Rate
   40.6584,       --@Price
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as YIELD
This produces the following result.
                 YIELD
----------------------
    0.0300999648699087


In this example we calculate the yield of a bond settling in the final coupon period.
SELECT wct.YIELD(
   '2014-05-01',  --@Settlement
   '2014-07-15',  --@Maturity
   0.0190,        --@Rate
   100.3802,      --@Price
   100,           --@Redemption
   2,             --@Frequency
   0              --@Basis
   ) as YIELD
This produces the following result.
                 YIELD
----------------------
 0.000499094074045242


Here we calculate the yield of a bond maturing on the 30th of September 2034, with semi-annual coupons payable on March 30th and September 30th.
SELECT wct.YIELD(
   '2014-05-01',  --@Settlement
   '2034-09-30',  --@Maturity
   0.0257,        --@Rate
   98.1233,       --@Price
   100,           --@Redemption
   2,             --@Frequency
   11             --@Basis
   ) as YIELD
This produces the following result.
                 YIELD
----------------------
    0.0268999940423681


Here's an example of a bond with a negative yield.
SELECT wct.YIELD(
   '2014-05-01',  --@Settlement
   '2014-09-30',  --@Maturity
   0.0257,        --@Rate
   101,           --@Price
   98,            --@Redemption
   2,             --@Frequency
   0              --@Basis
   ) as YIELD
This produces the following result.
                 YIELD
----------------------
   -0.0462187493233163
 


This is an example of a bond paying interest every 26 weeks.
SELECT wct.YIELD(
      '2014-10-01',     --@Settlement
      '2023-03-13',     --@Maturity
      0.1250,           --@Rate
      108.126105929164, --@Price
      100,              --@Redemption
      182,              --@Frequency
      9                 --@Basis
      ) as YIELD
This produces the following result.
                 YIELD
----------------------
     0.109999999999346

 

See Also

 



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