The U.S. bond market is like the sport of baseball - you have to understand and appreciate the rules and strategies, or else it seems boring. It's also like baseball in that its rules and pricing conventions have evolved over time, and they sometimes seem as esoteric as the balk rule in baseball. 

In the baseball Official Major League Rule Book, it takes more than 3,600 words to cover the rules of what the pitcher can and cannot do. In this article, we're going cover bond market pricing conventions in less than 2,000 words. Bond market classifications are briefly discussed, followed by yield calculations, pricing benchmarks and pricing spreads.

A basic knowledge of these pricing conventions will make the bond market seem as exciting as the best World Series baseball game. (For related reading, check out the Bond Basics and Advanced Bond Concepts tutorials.)

Bond Market Classifications
The bond market consists of a great number of issuers and types of securities. To talk about each specific type might fill an entire textbook; therefore, for the purposes of discussing how various bond market pricing conventions work, we make the following major bond classifications: 
  • U.S. Treasuries: Bonds issued by the United States Department of the Treasury. 
  • Corporate Bonds: Bonds issued by corporations that carry an investment grade rating.
  • High-Yield Bonds: Also known as non-investment grade, or junk, bonds, these are bonds with a below investment grade rating.
  • Mortgage-Backed Securities (MBS): A bond collateralized by the cash flows of principal and interest payments from an underlying pool of single family residential mortgages.
  • Asset-Backed Securities (ABS): A bond collateralized by the cash flows of an underlying pool of assets such as auto loans, credit card receivables, home equity loans, aircraft leases, etc. The list of assets that has been securitized into ABSs is almost endless.
  • Agency Bonds: Debt issued by the government-sponsored enterprises (GSEs), including Fannie Mae, Freddie Mac and the Federal Home Loan Banks.
  • Municipal Bonds (Munis): A bond issued by a state, city or local government or its agencies.
  • Collateralized Debt Obligations (CDOs): A type of asset-backed security backed by any one or several other ABS, MBS, bonds or loans. 
To read articles on various types of bonds, check out the Bonds Articles Archive.

A Bond's Expected Return
Yield is the measure used most frequently to estimate or determine a bond's expected return.  Yield is also used as a relative value measure between bonds. There are two primary yield measures that must be understood to understand how different bond market pricing conventions work: yield to maturity and spot rates.

A yield-to-maturity calculation is made by determining the interest rate (discount rate) that will make the sum of a bond's cash flows, plus accrued interest, equal to the current price of the bond. This calculation has a couple important assumptions: First, that the bond will be held until maturity, and second that the bond's cash flows can be re-invested at the yield to maturity. 

A spot rate calculation is made by determining the interest rate (discount rate) that makes the present value of a zero-coupon bond equal to its price. A series of spot rates must be calculated to price a coupon paying bond  - each cash flow must be discounted using the appropriate spot rate such that the sum of the present values of each cash flow equals the price. As we discuss later, spot rates are most often used as a building block in relative value comparisons for certain types of bonds.

Benchmarks
Most bonds are priced relative to a benchmark. This is where bond market pricing gets a little tricky. Different bond classifications, as we have defined them above, use different pricing benchmarks.

Some of the most common pricing benchmarks are on-the-run U.S. Treasuries (the most current series). Many bonds are priced relative to a specific Treasury bond. For example, the on-the-run 10-year Treasury might be used as the pricing benchmark for a 10-year corporate bond issue.

When the maturity of a bond cannot be known with exactness because of call or put features, the bond is frequently priced to a benchmark curve. This is because the estimated maturity of the callable or put-able bond most likely does not coincide exactly with the maturity of a specific Treasury. 

Benchmark pricing curves are constructed using the yields of underlying securities with maturities from three months to 30 years. Several different benchmark interest rates or securities are used to construct different benchmark pricing curves. Because there are gaps in the maturities of securities used to construct a curve, yields must be interpolated between the observable yields. 

For example, one of the most commonly used benchmarks curves is the on-the-run U.S. Treasury curve, which is constructed using the most recently issued U.S. Treasury bonds, notes, and bills. Because securities are only issued by the U.S. Treasury with three month, six month, two year, three year, five year, 10 year and 30 year maturities, the yields of theoretical bonds with maturities that lay between those maturities must be interpolated. This Treasury curve is known as the interpolated yield curve (or I-curve) by bond market participants. (To learn more about the Treasury curve, read The Impact Of An Inverted Yield Curve.)

Other Popular Benchmark Pricing Curves
  • Spot Rate Treasury Curve: A curve constructed using the theoretical spot rates of U.S. Treasuries.
  • Swap Curve: A curve constructed using the fixed interest rate side of interest rate swaps.
  • Eurodollars Curve: A curve constructed using interest rates derived from eurodollar futures pricing.
  • Agency Curve: A curve constructed using the yields of non-callable, fixed-rate agency debt.
Yield Spreads
A bond's yield relative to the yield of its benchmark is called a spread. The spread is used both as a pricing mechanism and as a relative value comparison between bonds. For example, a trader might say that a certain corporate bond is trading at a spread of 75 basis points above the 10-year Treasury. This means that the yield to maturity of that bond is 0.75% greater than the yield to maturity of the on-/the-run 10-year Treasury. If a different corporate bond with the same credit rating, outlook and duration was trading at a spread of 90 basis points on a relative value basis, the second bond would be a better buy. 

There are different types of spread calculations used for the different pricing benchmarks. The four primary yield spread calculations are:
  • Nominal Yield Spread: The difference in the yield to maturity of a bond and the yield to maturity of its benchmark.
  • Zero-Volatility Spread (Z-spread): The constant spread that, when added to the yield at each point on the spot rate Treasury curve where a bond's cash flow is received, will make the price of a security equal to the present value of its cash flows.
  • Option-Adjusted Spread (OAS): An OAS is used to evaluate bonds with embedded options (such as a callable bond or put-able bond). It is the constant spread that, when added to the yield at each point on a spot rate curve (usually the U.S. Treasury spot rate curve) where a bond's cash flow is received, will make the price of the bond equal to the present value of its cash flows. However, to calculate the OAS, the spot rate curve is given multiple interest rate paths. In other words, many different spot rate curves are calculated and the different interest rate paths are averaged  An OAS accounts for interest rate volatility and the probability of the prepayment of principal of the bond. 
  • Discount Margin (DM): Bonds with variable interest rates are usually priced close to their par value. This is because the interest rate (coupon) on a variable rate bond adjusts to current interest rates based on changes in the bond's reference rate. The DM is the spread that, when added to the bond's current reference rate, will equate the bond's cash flows to its current price. 
Types of Bonds and Their Benchmark and Spread Calculation
  • High-Yield Bonds: High-yield bonds are usually priced at a nominal yield spread to a specific on-the-run U.S. Treasury bond. However, sometimes when the credit rating and outlook of a high-yield bond deteriorates, the bond will start to trade at an actual dollar price. For example, such a bond trades at $75.875 as opposed to 500 basis points over the 10-year Treasury. (To learn more, read Junk Bonds: Everything You Need To Know and High Yield, Or Just High Risk?)
  • Corporate Bonds: A corporate bond is usually priced at a nominal yield spread to a specific on-the-run U.S. Treasury bond that matches its maturity. For example, 10-year corporate bonds are priced to the 10-year Treasury. (For more on this bond type, see Corporate Bonds: An Introduction To Credit Risk.)

  • Mortgage-Backed Securities: There are many different types of MBS. Many of them trade at a nominal yield spread at their weighted average life to the U.S. Treasury I-curve. Some adjustable-rate MBS trade at a DM, others trade at a Z-spread. Some CMOs trade at a nominal yield spread to a specific Treasury. For example, a 10-year planned amortization class bond might trade at a nominal yield spread to the on-the-run 10-year Treasury, or Z-bond might trade at a nominal yield spread to the on-the-run 30-year Treasury. Because MBS have embedded call options (borrowers have the free option of prepaying their mortgages), they are frequently evaluated using an OAS. (For related reading, check out Profit From Mortgage Debt With MBS.)
  • Asset-Backed Securities: ABS frequently trade at a nominal yield spread at their weighted average life to the swap curve.
  • Agencies: Agencies frequently trade at a nominal yield spread to a specific Treasury, such as the on-the-run 10-year Treasury. Callable agencies are sometime evaluated based on an OAS where the spot rate curve(s) are derived from the yields on non-callable agencies. (Want to learn more? See Agency Bonds: Limited Risk And Higher Return.)
  • Municipal Bonds: Because of the tax advantages of municipal bonds (usually not taxable), their yields are not as highly correlated with U.S. Treasury yields as other bonds. Therefore, munis frequently trade on an outright yield to maturity or even a dollar price. However, a muni's yield as a ratio to a benchmark Treasury yield is sometimes used as a relative value measure.

  • Collateralized Debt Obligations: Like the MBS and ABS that frequently back CDOs, there are many different pricing benchmarks and yield measures used to price CDOs. The eurodollar curve is sometimes used as a benchmark. Discount margins are used on floating rate tranches. OAS calculations are made for relative value analysis. 
Conclusion
Bond market pricing conventions are a little bit tricky, but like baseball rules, understanding the basics takes the mystery out of them. Bond pricing is really just a matter of identifying a pricing benchmark, determining a spread and understanding the difference between two basic yield calculations: yield to maturity and spot rates. With that knowledge, understanding how various types of bonds are priced shouldn't be intimidating. 

For more on the bond market, see The Bond Market: A Look Back.