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:
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