Bond Yield

What Is Bond Yield?

Bond yield is the return an investor realizes on a bond and can be derived in different ways.

The coupon rate is the annual interest rate established when the bond is issued. The current yield depends on the bond's price and its coupon, or interest payment.

Additional calculations of a bond's yield include yield to maturity (YTM), bond equivalent yield (BEY), and effective annual yield (EAY).

Key Takeaways

  • Bond yield is the return an investor realizes on an investment in a bond.  
  • A bond can be purchased for more than its face value, at a premium, or less than its face value, at a discount.
  • The current yield is the bond's coupon rate divided by its market price.
  • Price and yield are inversely related and as the price of a bond goes up, its yield goes down.
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Bond Yields: Current Yield And YTM

Understanding Bond Yield

Bonds are essentially a loan to bond issuers. Investors earn interest on a bond throughout the life of the bond and receive the face value of the bond upon maturity.

A bond can be purchased for more than its face value, at a premium, or less than its face value, at a discount, which will change the yield an investor earns on the bond.

Bonds are rated by services approved by the U.S. Securities and Exchange Commission 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 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.

Coupon Rate = Annual Coupon Payment Bond Face Value \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% ($100 / $1,000 = 10%).

Bond Yield vs. Price

Price and yield are inversely related. As the price of a bond goes up, its yield goes down and as 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. However, 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.

Current Yield = Annual Coupon Payment Bond Price \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.

Yield to Maturity

A bond's yield to maturity (YTM) is equal to the interest rate that 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:

Price = t 1 T Cash Flows t ( 1 + YTM ) t where: YTM =  Yield to maturity \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=t1T(1+YTM)tCash Flowstwhere: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 (BEY), 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 (EAY) would be calculated as follows:

EAY = ( 1 + YTM 2 ) 2 1 where: EAY = Effective annual yield \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)21where: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 Rating

A bond rating is a grade given to a bond and indicates its credit quality. The rating takes into consideration a bond issuer's financial strength or its ability to pay a bond's principal and interest in a timely fashion. There are three bond rating agencies in the United States that account for approximately 95% of all bond ratings and include Fitch Ratings, Standard & Poor’s Global Ratings, and Moody’s Investors Service.

Calculating a Bond's Yield

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 the "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.

What Does a Bond's Yield Tell Investors?

A bond's yield is the return to an investor from the bond's interest, or coupon, payments. It can be calculated as a simple coupon yield or using a more complex method like yield to maturity. Higher yields mean that bond investors are owed larger interest payments, but may also be a sign of greater risk. The riskier a borrower is, the more yield investors demand. Higher yields are often common with a longer maturity bond.

Are High-Yield Bonds Better Investments Than Low-Yield Bonds?

Bond investment depends on an investor's circumstances, goals, and risk tolerance. Low-yield bonds may be better for investors who want a virtually risk-free asset, or one who is hedging a mixed portfolio by keeping a portion of it in a low-risk asset. High-yield bonds may be better suited for investors who are willing to accept a degree of risk in return for a higher return.

How Do Investors Utilize Bond Yields?

In addition to evaluating the expected cash flows from individual bonds, yields are used for more sophisticated analyses. Traders may buy and sell bonds of different maturities to take advantage of the yield curve, which plots the interest rates of bonds having equal credit quality but differing maturity dates. The slope of the yield curve gives an idea of future interest rate changes and economic activity. They may also look to the difference in interest rates between different categories of bonds, holding some characteristics constant.

A yield spread is a difference between yields on differing debt instruments of varying maturities, credit ratings, issuer, or risk level, calculated by deducting the yield of one instrument from the other such as the spread between AAA corporate bonds and U.S. Treasuries. This difference is most often expressed in basis points (bps) or percentage points.

The Bottom Line

Bond yield is the amount of return an investor will realize on a bond. The coupon rate and Coupon 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.

Article Sources
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  1. Forbes. "What Are Bond Rating Agencies?"

  2. U.S. Securities and Exchange Commission. "Bonds."

  3. U.S. Securities and Exchange Commission. "Investor Bulletin: Fixed Income Investments - When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall."

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