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 closedform 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:
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 securityâ€™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 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 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
float
Remarks
Â· If @Settlement is NULL then @Settlement = GETDATE().
Â· If @Maturity is NULL then @Maturity = GETDATE().
Â· If @Rate is NULL then @Rate = 0.
Â· If @Price is NULL then @Price = 100.
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 YIELD returns an error.
Â· 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 20340615. The settlement date is 20140501, the coupon rate is 2.50%, the redemption value is 100, the coupon is paid twiceyearly, and the bais code is 1.
SELECT wct.YIELD(
'20140501', @Settlement
'20340615', @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 zerocoupon bond.
SELECT wct.YIELD(
'20140501', @Settlement
'20440615', @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(
'20140501', @Settlement
'20140715', @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 30^{th} of September 2034, with semiannual coupons payable on March 30^{th} and September 30^{th}.
SELECT wct.YIELD(
'20140501', @Settlement
'20340930', @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(
'20140501', @Settlement
'20140930', @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(
'20141001', @Settlement
'20230313', @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