What Is a Bond Yield?

A bond yield is the return an investor realizes on a bond. Put simply, a bond yield is the return on the capital invested by an investor. Bond yields are different from bond prices—both of which share an inverse relationship. The yield matches the bond's coupon rate when the bond is issued. Bond yields can be derived in different ways, including the coupon yield and current yield. Additional calculations of a bond's yield include yield to maturity (YTM) among others.

Formula and Calculation of a Bond Yield

The simplest way to calculate a bond yield is to divide its coupon payment by the face value of the bond. This is called the coupon rate.

$\text{Coupon Rate}=\frac{\text{Annual Coupon Payment}}{\text{Bond Face Value}}$Coupon Rate=Bond Face ValueAnnual Coupon Payment​

If a bond has a face value of $1,000 and made interest or coupon payments of $100 per year, then its coupon rate is 10% or $100 ÷ $1,000.

Understanding Bond Yields

Bonds are essentially a loan to bond issuers. They are considered safe investments. That's because bond values don't change the same way stock prices do. They offer investors a reliable stream of income and provide bondholders with a fixed form of income.

Investors earn interest on a bond throughout the life of the asset and receive the face value of the bond upon maturity. Investors can purchase bonds for more than their face value at a premium or less than the face value at a discount. Whichever they buy will change the yield they earn on the bond.

Bonds are rated by services approved by the Securities and Exchange Commission (SEC) and ratings range from "AAA" as investment grade with the lowest risk to "D," which are bonds in default, or junk bonds, with the highest risk.

The return realized by a bond investor is called the yield. There are a couple of different yield-related concepts. These include the:

• Coupon Yield: This is the annual interest rate established when the bond is issued. This figure remains the same for the lifetime of the bond.
• Current Yield: This figure depends on the bond's price and its coupon (or its interest payment). So if the price of the bond changes, the bond's yield also changes.
  

Bond Yield vs. Bond Price

Price and yield are inversely related. This means that as the price of a bond goes up, its yield goes down. Conversely, as the yield goes up, the price of the bond goes down.

If an investor purchases a bond with a face value of $1000 that matures in five years with a 10% annual coupon rate, the bond pays 10%, or $100, in interest annually. If interest rates rise above 10%, the bond's price will fall if the investor decides to sell it.

If the interest rate for similar investments rises to 12%, the original bond will still earn a coupon payment of $100, which would be unattractive to investors who can buy bonds that pay $120 as interest rates have risen. To sell the original $1000 bond, the price can be lowered so that the coupon payments and maturity value equal a yield of 12%.

If interest rates fall, the bond's price would rise because its coupon payment is more attractive. The further rates fall, the higher the bond's price will rise. In either scenario, the coupon rate no longer has any meaning for a new investor. But if the annual coupon payment is divided by the bond's price, the investor can calculate the current yield and get an estimate of the bond's true yield.

$\text{Current Yield}=\frac{\text{Annual Coupon Payment}}{\text{Bond Price}}$Current Yield=Bond PriceAnnual Coupon Payment​

The current yield and the coupon rate are incomplete calculations for a bond's yield because they do not account for the time value of money, maturity value, or payment frequency, and more complex calculations are required.

Additional Bond Yield Calculations

As noted above, there are additional calculations of a bond's yield. These include the YTM, bond equivalent yield (BEY), and effective annual yield (EAY).

Yield to Maturity (YTM)

A bond's yield to maturity is equal to the interest rate which makes the present value of all a bond's future cash flows equal to its current price. These cash flows include all the coupon payments and maturity value. Solving for YTM is a trial and error process that can be done on a financial calculator, but the formula is as follows:

$\begin{aligned} &\text{Price}=\sum^T_{t-1}\frac{\text{Cash Flows}_t}{(1+\text{YTM})^t}\\ &\textbf{where:}\\ &\text{YTM}=\text{ Yield to maturity} \end{aligned}$​Price=t−1∑T​(1+YTM)tCash Flowst​​where:YTM= Yield to maturity​

In the previous example, a bond with a $1,000 face value, five years to maturity, and $100 annual coupon payments is worth $927.90 to match a new YTM of 12%. The five coupon payments plus the $1,000 maturity value are the bond's six cash flows.

Finding the present value of each of those six cash flows with an interest rate of 12% will determine what the bond's current price should be.

Bond Equivalent Yield (BEY)

Bond yields are quoted as a bond equivalent yield, which adjusts for the bond coupon paid in two semi-annual payments. In the previous example, the bonds' cash flows were annual, so the YTM is equal to the BEY. However, if the coupon payments were made every six months, the semi-annual YTM would be 5.979%. The BEY is a simple annualized version of the semi-annual YTM and is calculated by multiplying the YTM by two. In this example, the BEY of a bond that pays semi-annual coupon payments of $50 would be 11.958% (5.979% X 2 = 11.958%). The BEY does not account for the time value of money for the adjustment from a semi-annual YTM to an annual rate.

Effective Annual Yield (EAY)

Investors can define a more precise annual yield given the BEY for a bond when considering the time value of money in the calculation. In the case of a semi-annual coupon payment, the effective annual yield would be calculated as follows:

$\begin{aligned} &\text{EAY} = \left ( 1 + \frac { \text{YTM} }{ 2 } \right ) ^ 2 - 1 \\ &\textbf{where:}\\ &\text{EAY} = \text{Effective annual yield} \\ \end{aligned}$​EAY=(1+2YTM​)2−1where:EAY=Effective annual yield​

If an investor knows that the semi-annual YTM was 5.979%, they could use the previous formula to find the EAY of 12.32%. Because the extra compounding period is included, the EAY will be higher than the BEY.

Bond Yield Calculation Issues

Some factors skew the calculations in determining a bond's yield. In the previous examples, it was assumed that the bond had exactly five years left to maturity when it was sold, which is rare. The fractional periods can be defined but the accrued interest is more difficult to calculate.

Assume a bond has four years and eight months to maturity. The exponent in the yield calculations can be turned into a decimal to adjust for the partial year.

However, this means that four months in the current coupon period have elapsed with two remaining, which requires an adjustment for accrued interest. A new bond buyer will be paid the full coupon, so the bond's price will be inflated slightly to compensate the seller for the four months in the current coupon period that have elapsed.

Bonds can be quoted with a clean price that excludes the accrued interest or a dirty price that includes the amount owed to reconcile the accrued interest. When bonds are quoted in a system like a Bloomberg or Reuters terminal, the clean price is used.

The Bottom Line

Bond yield is the amount of return an investor will realize on a bond. The coupon rate and current yield are basic yield concepts and calculations. A bond rating is a grade given to a bond and indicates its credit quality and often the level of risk to the investor in purchasing the bond.