Yield is the rate of return on fixed-income securities. While yield measures for money market securities are annualized but not compounded, long-term bond yields must take into account the compounding and periodicity, the assumed number of periods in a year, which equals the frequency of coupon payments in most cases.

## Yield measures for fixed-rate bonds

Since the yield to maturity is expressed as an annual percentage rate (i.e. a nominal rate), the periodicity is important. A semiannual coupon bond has a periodicity of 2, a quarterly bond has a periodicity of 4, etc.

### Semiannual bond-equivalent yield

An annual rate with a periodicity of 2 is called semiannual bond basis yield or semiannual bond equivalent yield because most bonds have two coupons per year. A yield to maturity expressed in one periodicity can be converted to a yield quoted at different periodicity using the following equation:

$$\left(1+\frac{{APR}_m}{m}\right)^m=\left(1+\frac{{APR}_n}{n}\right)^n$$

### True yield and government-equivalent yield

Bonds yield is typically calculated based on scheduled dates regardless of weekends and holidays. Such a yield calculation is based on street convention. Sometimes true yield is quoted, which is calculated by taking into account the actual weekends and holidays and is never higher than the street convention yield. A government equivalent yield restates the corporate bond yield calculated on a 30/360 basis to one calculated on an actual/actual basis. It is useful in finding out the yield spread of corporate bonds.

### Current yield

Current yield (also called interest yield or income yield) is calculated by dividing annual coupon payments by bond price. It is a crude measure because it ignores accrued interest and frequency of coupon payments. It also does not adjust for any discount or premium on bond. Simple yield equals the sum of coupon payment plus straight-line amortized discount/premium divided by flat price.

### Yield for bonds with embedded options: yield to call and yield to worst

Different yield measures are used for bonds with embedded options. Yield to call is the internal rate of return of the bond cash flows till the call date. Many bonds have a call schedule specifying more than one call date. Yield to worst is the lowest yield to call of a bond. Even though yield to worst is a commonly quoted yield measure for callable bonds, a more precise approach is to value the call option using some option pricing model, determine the option-adjusted price of the bond and calculate the resultant option-adjusted yield.

## Yield measure for floating rate notes

A floating-rate note (FRN) is a bond whose coupon rate is the sum of a reference rate such as LIBOR and a fixed margin (called quoted margin). Unlike the fixed-rate bond which pays constant coupon payments, the coupon payment of FRN changes in response to a change in the reference rate resulting in lesser interest rate risk.

### Required margin

The required margin (also called discount margin) on an FRN is the spread which when added to the reference rate equates the bond’s future cash flows to its current price. If the bond is trading at par, the quoted margin is equal to the required margin but if there is a change in the credit quality of the bond, they deviate. If the required margin is greater than the quoted margin, the bond trades at a discount and vice versa.

While both fixed-rate and floating-rate bonds respond similarly to changes in credit risk, the fixed-rate bond is also sensitive to changes in the benchmark rate while the floating-rate note is not.

A floating-rate note is valued by discounting the future cash flows of the note at an interest rate which equals the benchmark rate plus a discount margin.

$$P=\frac{\left(\frac{r_B+QM}{m}\right)\times F}{\left(1+\frac{r_B+DM}{m}\right)^1}+\frac{\left(\frac{r_B+QM}{m}\right)\times F}{\left(1+\frac{r_B+DM}{m}\right)^2}+…+\frac{\left(\frac{r_B+QM}{m}\right)\times F+F}{\left(1+\frac{r_B+DM}{m}\right)^N}$$

Where rB is the benchmark interest rate , QM is the quoted margin, m is the number of coupon payments per year, DM is the discount margin, F is the face value and n is the total number of coupon payments.

For example, if an FRN pays semi-annual coupons at 1-year LIBOR, which is currently 2.5% plus 2% and the required margin is 2.2% and it has 1 year till maturity, its value is calculated as follows:

$$P=\frac{\left(\frac{2.5\%+2\%}{2}\right)\times100}{\left(1+\frac{2.5\%+2.2\%}{2}\right)^1}+\frac{\left(\frac{2.5\%+2\%}{2}\right)\times100+100}{\left(1+\frac{2.5\%+2.2\%}{2}\right)^2}=99.8068$$

The same approach can be used to work out a discount margin if we know the current price of the FRN. 