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Coupons are normally described in terms of the "coupon rate", which is calculated by adding the sum of coupons paid per year and dividing it by the bond's face value. [2] For example, if a bond has a face value of $1,000 and a coupon rate of 5%, then it pays total coupons of $50 per year.
Analytic Example: Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
The coupon rate (nominal rate, or nominal yield) of a fixed income security is the interest rate that the issuer agrees to pay to the security holder each year, expressed as a percentage of the security's principal amount or par value. [1] The coupon rate is typically stated in the name of the bond, such as "US Treasury Bond 6.25%".
Price example: XYZ Ltd. issues a bond with a $1000 face value and a $980 published price, with a coupon rate of 5% paid semi-annually and a maturity date of five years. The annual coupon payment is 5% of $1000, or $50. The investor receives a $25 coupon payment every six months until the maturity date.
The forward rate is the future yield on a bond. It is calculated using the yield curve . For example, the yield on a three-month Treasury bill six months from now is a forward rate .
For example, you might pay $5,000 for a zero-coupon bond with a face value of $10,000 and receive the full price, $10,000, upon maturity in 20 or 30 years. Zero-coupon CDs work the same way.
Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates. Investment banks or dealers may separate coupons from the principal of coupon bonds, which is known as the residue, so that different investors may receive the principal and each of the coupon payments.
In the case where the only discount rate one has is not a zero-rate (neither taken from a zero-coupon bond nor converted from a swap rate to a zero-rate through bootstrapping) but an annually-compounded rate (for example if the benchmark is a US Treasury bond with annual coupons) and one only has its yield to maturity, one would use an annually ...