In this article we will look at calculating bond yields.
First lets look at our ISMA pricing formula for a regular corporate or government bond.
P = dirty price (clean price plus accrued interest) of the bond
r1 = number of days from the settlement date to the next nominal coupon payment date (based on the appropriate accrual convention).
r2 = number of days from the date of the last 'normal' coupon payment to the maturity date
(based on the appropriate accrual convention). This is equal to zero if the bond does not have an odd final period.
s = number of days in the relevant coupon payment period (based on the appropriate accrual convention).
d1 = the first/next coupon payment. For an odd first period, this amount may differ from the standard coupon payment. It may also equal zero if the bond is trading ex-dividend.
d2 = the coupon payment due on the next nominal payment date. For bonds with an odd first period, this amount may differ from the standard coupon payment.
c = annual coupon payment per 100 units of face value.
c* = the final coupon amount for a bond with an odd final period. This is zero for all other bonds.
h = number of coupon periods in a year
n = number of full coupon periods remaining until redemption. The number of remaining coupon payments is therefore equal to .
v = the discount factor for one period,
y = the required annual nominal redemption yield, expressed as a decimal.
As a basis for deriving some of the , it is also useful to give an expression for bond price when there are only 1 (n = 0) or 2 (n = 1) outstanding coupon payments. In these cases the ISMA formula simplifies to:
Because we cannot solve for Y in above equations we use a Newton Paphson Iteration procedure.
Bonds are often quoted by different types of yields, and its often useful to calculate multiple types of yields so different types of bonds can be compared. Most often bonds will be quoted with a yield that reflects their daycount and their compounding frequency (Annual, Semi-annual etc).
True Yield - True yields are computed based on a cash flow stream that has been adjusted for the actual payment dates. That is, each scheduled coupon payment is discounted back from the actual payment date based on the selected business day convention and the relevant holiday schedule provided by the user.
US Street Yield - The convention used by market participants in the U.S. to value treasuries. Based on an accrual basis of Actual/Actual and assumes that yields are compounded semi-annually, even in fractional first periods (compare with the ). If the bond is in its final coupon period, then the US Street yield is computed using the US market final period pricing convention (see ).
US Treasury Yield - The convention used by the U.S. Treasury to value bonds. Based on an accrual basis of Act/Act and assumes that yields are compounded semi-annually in all but the fractional first period. If the bond is in its final coupon period, then the US Street yield is computed using the US market final period pricing convention (see ).
JGB Yield - The yield convention used by Japanese Government Bonds
Yield is based on the following simple interest formula:
where T is the number of days from settle to maturity divided by 365. If there is more than one year to maturity, the numerator must be reduced for every leap day that falls within the period. PPH is clean price.
Money Market Yield - The yield to maturity based on the .
For more information see our pricing plans.