The U.S. bond market is like baseball – you have to understand and appreciate the rules and strategies, or else it will seem boring. It's also like baseball in that its rules and pricing conventions have evolved and can seem esoteric at times.

The Major League Baseball's official rule book has thousands of words just to cover the rules of what the pitcher can and cannot do. In this article, we're going to cover 澳洲幸运5官方开奖结果体彩网:bond market pricing conventions in less than 1,800 words. Bond market classifications are briefly discussed, followed by yield calculations, pricing 澳洲幸运5官方开奖结果体彩网:benchmarks, and pricing spreads.

Basic knowledge of these 澳洲幸运5官方开奖结果体彩网:bond pricing conventions will make the bond market seem a🎃s exciting as the best World Series baseball gam🔯e.

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 bonꦇd market pricing conventions work, we make the following major bond classifications:

• 澳洲幸运5官方开奖结果体彩网:U.S. Treasuries: bonds issued by the United States Department of the Treasury
• 澳洲幸运5官方开奖结果体彩网:Corporate Bonds: bonds issued by corporations that carry an 澳洲幸运5官方开奖结果体彩网:investment-grade rating
• 澳洲幸运5官方开奖结果体彩网:High-Yield Bonds: bonds with ratings below investment grade – also known as non-investment grade bonds or junk bonds
• 澳洲幸运5官方开奖结果体彩网:Mortgage-Backed Securities (MBS): a bond collateralized by the cash flows of principal and interest payments from an underlying pool of single-family residential 澳洲幸运5官方开奖结果体彩网:mortgages
• 澳洲幸运5官方开奖结果体彩网: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 have been securitized into ABSs is almost endless.
• Agency Bonds: debt issued by the 澳洲幸运5官方开奖结果体彩网:governm🌞ent-sponsored enterprises (GSES), including 澳洲幸运5官方开奖结果体彩网:Fannie Mae, Freddie Mac, and the Federal Home Loan Banks
• 澳洲幸运5官方开奖结果体彩网: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

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 澳洲幸运5官方开奖结果体彩网:relative value measure between bonds. There are two primary yield measures that must be understood to understand how different bond market pricing conventions work: 澳洲幸运5官方开奖结果体彩网:yield to maturity and 澳洲幸运5官方开奖结果体彩网:spot rates.

A yield-to-maturity calculation is made by determining the interest rate (澳洲幸运5官方开奖结果体彩网:discount rate) that will make the sum of a bond's cash flows, plus 澳洲幸运5官方开奖结果体彩网:accrued interest, equal to the 澳洲幸运5官方开奖结果体彩网:current price of the bond. This calculation has two important assumptions: first, that the bond will be held until maturity, and second, that the bond's cash flows can be reinvested 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 澳洲幸运5官方开奖结果体彩网:zero-coupon bond equal to its price. A series of spot rates must be calculated to price a coupon paying bond – each 澳洲幸运5官方开奖结果体彩网: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 below, spot rates are most often used as a building block in rela🏅tive value comparisons for certain types of bonds.

Benchmarks for Bonds

Most bonds are priced relative to a 澳洲幸运5官方开奖结果体彩网:benchmark. This is where 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:on-the-run U.S. Treasuries (the most current series). Many bonds are priced relative to a specific 澳洲幸运5官方开奖结果体彩网: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 spec꧒ific Treasury.

Benchmark pricing curves are constructed using the yields of 澳洲幸运5官方开奖结果体彩网:underlying securities with maturities from three months to 30 years. Several different benchma🅰rk interest rates or securities are used to construct 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 澳洲幸运5官方开奖结果体彩网:commonly used benchmark 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 澳洲幸运5官方开奖结果体彩网:interpolated yield curve (or I-curve) by bond market participants.

Other Popular Bond Benchmark Pricing Curves

• 澳洲幸运5官方开奖结果体彩网:Spot Rate Treasury Curve: a curve constructed using the theoretical spot rates of U.S. Treasuries
• Swap Curve: a curve constructed using the 澳洲幸运5官方开奖结果体彩网:fixed interest rate side of 澳洲幸运5官方开奖结果体彩网:interest rate swaps
• Eurodollars Curve: a curve constructed using interest rates derived from 澳洲幸运5官方开奖结果体彩网:eurodollar futures pricing.
• Agency Curve: a curve constructed using the yields of non-callable, fixed-rate agency debt

Yield Spreads for Bonds

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 澳洲幸运5官方开奖结果体彩网:basis points above ꦉthe 10-year Treasury. This means that the yield to maturity of that bond is ꦛ0.75% greater than the yield to maturity of the on-the-run 10-year Treasury.

Notably, if a different corporate bond with the same 澳洲幸运5官方开奖结果体彩网:credit rating, outওlook and duration were trading at a spread of 90 basis point🥀s 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 澳洲幸运5官方开奖结果体彩网:yield spread calculations are:

1. 澳洲幸运5官方开奖结果体彩网:Nominal Yield Spread: the difference in the yield to maturity of a bond and the yield to maturity of its benchmark
2. 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 澳洲幸运5官方开奖结果体彩网:present value of its cash flows
3. 澳洲幸运5官方开奖结果体彩网:Option-Adjusted Spread (OAS): An OAS is used to evaluate bonds with 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:prepayment of the principal of the bond.
4. 澳洲幸运5官方开奖结果体彩网:Discount Margin (DM): Bonds with 澳洲幸运5官方开奖结果体彩网:variable interest rates are usually priced close to their 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网: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 Bo🃏nds and Their Benchm🏅ark Spread Calculation

High-Yield Bonds

High-yield bonds are usually priced at a 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:dollar price. For example, such a bond trades at $75.875, as opposed to 500 basis points over the 10-year Treasury🎐.

Corporate Bonds

A corporate bond is us𓂃ually priced at a nominal yield spread to a specific on-the-run U.S. Treasury bond tha𝓰t matches its maturity. For example, 10-year corporate bonds are priced to the 10-year Treasury.

Mortgage-Backed Securities (MBS)

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 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:planned amortization class bond might trade at a nominal yield spread to the on-the-run 10-year Treasury, or a Z-bond might trade at a nominal yield spread to the on-the-run 30-year Treasury. Because MBS have embedded 澳洲幸运5官方开奖结果体彩网:call options (b🐼orrowers have the free option of prepaying their mortgages), they are frequౠently evaluated using an OAS.

Asset-Backed Securities (ABS)

ABS frequently trade at a nominal yield spread at their weighted average life to the 澳洲幸运5官方开奖结果体彩网:swap curve.

Agencies

Agencies frequently trade at a nominal yield spread to a spec🐻ific Treasury, such as the on-the-run 10-year Treasury. Callable agencies are sometimes evaluated based on an OAS where the spot rate curve(s) are derived from the yields𝔍 on non-callable agencies.

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 澳洲幸运5官方开奖结果体彩网:Treasury yield is sometimes used as a relative value measure.

Collateralized Debt Obligation (CDOs)

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 m꧃ade for relative value analysis.

The Bottom Line

Bond market pricing conventions are a little bit tricky, but like baseball rules, 澳洲幸运5官方开奖结果体彩网:understanding the basics removes some of the ambiguity and may even make it enjoyable. Bond pricing is really just a m🧔atter 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.