1. Understanding Yield Spreads by Frank J. Fabozzi
PowerPoint Slides by
David S. Krause, Ph.D., Marquette University
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2. Chapter 4 Understanding Yield Spreads
Major learning outcomes:
The different yields offered by bonds in different sectors of the bond market
Assessing the relative value of individual securities
Ranking individual securities with respect to expected return potential
The relationship between interest rates offered on different bond issues at a point in time
The relationship of interest rates in different sectors of the economy at a given point in time

3. Key Learning Outcomes
Identify the interest rate policy tools used by the U.S. Federal Reserve Board.
Explain the Treasury yield curve and describe the various shapes of the yield curve.
Describe the term structure of interest rates.
Describe the three theories of the term structure of interest rates: pure expectations theory, liquidity preference theory, and market segmentation theory.
For each theory of the term structure of interest rates, explain the implication that the shape of the yield curve suggests regarding the market’s expectation about future interest rates.
Define a Treasury spot rate.
Define a spread product and a spread sector.

4. Key Learning Outcomes
Explain the different types of yield spread measures (absolute yield spread, relative yield spread, and yield ratio) and how to calculate yield spread measures given the yields for two securities.
Distinguish between intermarket and intramarket sector spreads.
Describe an issuer’s on-the-run yield curve.
Describe a credit spread and the suggested relationship between credit spreads and the well being of the economy.
Identify the relationship between embedded options and yield spreads.
Define a nominal spread.
Explain an option-adjusted spread.
Explain how the liquidity of an issue affects its yield spread

5. Key Learning Outcomes
Explain the relationship between the yield on Treasury securities and the yield on tax-exempt municipal securities.
Calculate the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security.
Define LIBOR and why it is an important measure to funded investors who borrow short term.
Describe an interest rate swap, the swap rate, the swap spread, and the swap spread curve.
Explain how an interest rate swap can be used to create synthetic fixed-rate assets or floating-rate assets.
Describe the factors that determine the swap spread.
Discuss the observed relationship between swap spreads and credit spreads.

6. Interest Rate Determination
The interest rate offered on a particular bond issue depends on the interest rate that can be earned on risk-free instruments and the perceived risks associated with the issue.

7. Federal Reserve Board
The U.S. Federal Reserve Board is the policy making body whose interest rate policy tools directly influence short-term interest rates and indirectly influence long-term interest rates in the United States.
The Fed’s most frequently employed interest rate policy tools are open market operations and changing the discount rate; less frequently used tools are changing bank reserve requirements and verbal persuasion to influence how bankers supply credit to businesses and consumers.

8. Interest Rate Determination
The actions of the Federal Reserve (Fed) influence the level of interest rates as well as the state of the U.S. economy
The Fed is the policy making body whose interest rate policy tools directly influence short-term interest rates and indirectly influence the long-term rates
Once the Fed makes a policy decision it immediately announces the policy in a statement issued at the close of the meeting
The Fed also communicates its future intentions via the publishing of its meeting minutes, speeches, and testimony before Congress
Bond managers pursuing an active portfolio management strategy closely watch the economy to anticipate a change in Federal Reserve policy.

9. Interest Rate Determination
Bond managers closely follow:
Non-farm payrolls
Industrial production
Housing starts
Motor vehicle sales
Durable goods orders
National Association of Purchasing Management supplier deliveries
Commodity prices
Hurricanes, wars, and other international events

10. Interest Rate Determination
In implementing monetary policy, the Fed uses the following tools:
Open market operations (most commonly used tool)
Discount rate
Bank reserve requirements
Verbal persuasion to influence how bankers supply credit to business and customers

11. U.S. Treasury Rates
U.S. Treasuries are generally considered to be “default risk free”
The secondary market for Treasuries is an over-the-counter market where a group of U.S. government securities dealers maintain continuous bids and offers on outstanding issues
The Treasury market is the most liquid financial market in the world

12. U.S. Treasuries
Because Treasury securities have no credit risk, market participants look at the interest rate or yield offered on an on-the-run Treasury security as the minimum interest rate required on a non-Treasury security with the same maturity.
The Treasury yield curve shows the relationship between yield and maturity of on-the-run Treasury issues.

13. U.S. Treasuries The Treasury issues the following securities:
Treasury bills: Zero-coupon securities with a maturity at issuance of one year or less. The Treasury currently issues 1-month, 3-month, and 6-month bills.
Treasury notes: Coupon securities with maturity at issuance greater than 1 year but not greater than 10 years. The Treasury currently issues 2-year, 5-year, and 10-year notes.
Treasury bonds: Coupon securities with maturity at issuance greater than 10 years. The Treasury currently issues bonds with maturities up to 30 years.
Inflation-protection securities: Coupon securities whose principal’s reference rate is the Consumer Price Index.

14. U.S. Treasury Risks
Although Treasuries do not have credit, foreign exchange, or reinvestment risk (because they are non-callable), they are exposed to all of the other credit-related risks (i.e. interest rate, call, yield curve, liquidity, volatility, inflation, and event).
The actions of the U.S. Federal Reserve and the other central banks can have an adverse or favorable impact on rates.

15. The Treasury Yield Curve
The yield offered on an on-the-run Treasury security is the minimum interest rate required on a non-Treasury security with the same maturity
The relationship between the yield and the maturity of on-the-run Treasury securities is know as the Treasury yield curve

16. Treasury Yield Curve
The Treasury yield curve shows the relationship between yield and maturity of on-the-run Treasury issues.
The typical shape for the Treasury yield curve is upward sloping—yield increases with maturity—which is referred to as a normal yield curve.
Inverted yield curves (yield decreasing with maturity) and flat yield curves (yield roughly the same regardless of maturity) have been observed for the yield curve.

17. Yield Curve Web Sites Yield Curves, Fixed Income Pricing and Indices
Daily Treasury Yield Curve Rates
Bloomberg

18. Treasury Yield Curve
Two factors complicate the relationship between maturity and yield as indicated by the Treasury yield curve:
(1) the yield for on-the-run issues is distorted since these securities can be financed at cheaper rates and, as a result, offer a lower yield than in the absence of this financing advantage and
(2) on-the-run Treasury issues and off-the-run issues have different interest rate reinvestment risks.
The yields on Treasury strips of different maturities provide a superior relationship between yield and maturity compared to the on-the-run Treasury yield curve.
The yield on a zero-coupon or stripped Treasury security is called the Treasury spot rate.

19. Treasury Yield Curve
There are some potential issues with using on-the-run Treasuries to construct a yield curve:
Because these are often used as repurchase agreements, the investors (hedge funds) will accept a slightly lower rate because of the cheaper source of financing used to fund the purchase
The level of reinvestment risk can be different for on-the-run and off-the-run Treasuries because of slightly different coupon rates and maturities
Because of these potential issues, market watchers look at the relationship between yield and maturity for zero-coupon Treasuries

20. Term Structure of Interest Rates
The term structure of interest rates is the relationship between maturity and Treasury spot rates.
Three theories have been offered to explain the shape of the yield curve:
pure expectations theory,
liquidity preference theory, and
market segmentation theory.

21. Pure Expectations Theory
The pure expectations theory asserts that the market sets yields based solely on expectations for future interest rates.
According to the pure expectations theory:
(1) a rising term structure reflects an expectation that future short-term rates will rise,
(2) a flat term structure reflects an expectation that future short-term rates will be mostly constant, and
(3) a falling term structure reflects an expectation that future short-term rates will decline.

22. Pure Expectations Theory
This is the simplest and most direct link between the yield curve and investors’ expectations about future interest rates because long-term interest rates are linked to expectations about future inflation.
The pure expectations theory explains the term structure in terms of expected future short-term interest rates.
Under the pure expectations theory, the market will set the yields on a two-year bond so that the returns on the bond are equal to the return on a one-year bond plus the expected return on a one-year bond purchased one year from today, etc…..

23. Pure Expectations Theory
Under this theory, when the term structure is upward sloping, the implication is that future short-term rates are expected to rise.
When the term structure is downward sloping, future short-term rates are expected to decline.
When rates are flat, rates are not expected to change.

24. Pure Expectations Theory
Irving Fisher is the author of the theory, which is popularly accepted.
The notion is that interest rates reflect the sum of a relatively stable real rate of interest plus a premium for expected inflation.
The shortcoming of this theory is that it assumes investors are indifferent to interest rate risk and any other factors associated with investing in bonds with different maturities.

25. Liquidity Preference Theory
This theory asserts that market participants want to be compensated for the interest rate risk associated with holding longer-term bonds.
The longer the maturity, the greater the price volatility.
Accordingly, this theory uses the pure expectations theory and adds a yield premium for interest rate risk.
This is the reason given to the question of why yield curves are traditionally upward sloping.

26. Liquidity Preference Theory
Under this theory, when the term structure is upward sloping, the implication is that rates are expected to rise or will be unchanged (or even fall), but with a yield premium for interest rate risk.
When the term structure is downward sloping or flat, future short-term rates are expected to decline.
This is also called the biased expectations theory.

27. Market Segmentation Theory
The market segmentation theory asserts that there are different maturity sectors of the yield curve and that each maturity sector is independent or segmented from the other maturity sectors.
Within each maturity sector, the interest rate is determined by the supply and demand for funds.
According to the market segmentation theory, any shape is possible for the yield curve.

28. Market Segmentation Theory
Under this theory, it is argued that the different maturity sectors of the yield curve are influenced heavily by the forces of supply and demand.
In other words, each maturity sector or segmented market is independent.
It is thought that there are two groups:
Bond investors who manage funds versus a broad-based bond market index.
Bond managers who concern themselves with matching the maturities of the liabilities (This follows the basic principle of asset-liability management).
This theory has strong support since regulations force many market participations to hold bonds of a fixed maturity and risk (i.e. investment grade). Also, certain foreign investors favor certain maturities (i.e. 10 year Treasuries).
This supports a term structure of any shape and is not contradictory of the other theories because within each sector the bond managers may act rationally. It explains how term structures can be ‘humped.’

29. Treasury Strips
Even though the Department of the Treasury does not issue zero-coupon bonds with maturities greater than one year, government dealers synthetically create zero-coupon securities by separating the coupon and principal payments.
These zero-coupon bonds have no reinvestment risk.
Therefore, these become purer measures of yield and maturity and are used to measure the Treasury yield curve.
The yield on a Treasury zero-coupon is known as the spot rate.
The relationship between maturity and Treasury spot rates is known as the term structure of interest rates.

30. Non-Treasury Securities
Even though the use of the non-spot rate Treasury yields has some slight imperfections, they are often used to compute the yield spread versus non-Treasury securities.
Because non-Treasury sectors of the bond market offer a higher yield than Treasuries, these are referred to as spread sectors.
The non-Treasury debt offering are referred to as spread products.

31. Yield Spreads
Despite the imperfections of the Treasury yield curve as a benchmark for the minimum interest rate that an investor requires for investing in a non-Treasury security, it is common to refer to a non-Treasury security’s additional yield over the nearest maturity on-the-run Treasury issue as the ‘‘yield spread.’’
The yield spread can be computed in three ways:
(1) the difference between the yield on two bonds or bond sectors (called the absolute yield spread),
(2) the difference in yields as a percentage of the benchmark yield (called the relative yield spread), and
(3) the ratio of the yield relative to the benchmark yield (called the yield ratio).

32. Yield Spreads
Yield spread (measured in basis points) is the difference between any two bond issues and is computed as follows:
Yield spread = yield on Bond 1 – yield on Bond 2
When the second bond is a benchmark (i.e. Treasury), the yield spread is referred to as the absolute yield spread – it is measured in basis points (bps).
To measure yield of a bond versus the reference bond, the relative yield spread is computed:
Relative yield spread = Yield spread / Yield on Bond 2
Another measure of relative yield spread is to compute the yield ratio:
Yield ratio = Yield on Bond 1 / Yield on Bond 2

33. Yield Spreads
It is useful to compute relative yield spreads because the magnitude of the spread is affected by the level of interest rates:
View examples of differences in yield spreads across time
Yield spreads are key to active bond management
Bond management strategies focus on understanding the differences in yield spreads and assessing the factors that cause the yield spread to widen or narrow
Bond managers forecast how yield spreads will change across sectors, economic changes, across the investment horizon (maturities), etc.

34. Intermarket Yield Spreads
An intermarket yield spread is the yield spread between two securities with the same maturity in two different sectors of the bond market.
The most common intermarket sector spread calculated is the yield spread between the yield on a security in a non-Treasury market sector and a Treasury security with the same maturity.

35. Intramarket Yield Spreads
An intramarket sector spread is the yield spread between two issues within the same market sector.

36. Yield Spreads Within and Across Sectors and Markets
The bond market is arranged into sectors based on the type of issuer, for example:
Government
U.S. Treasury
Agencies
Municipality
State
City
School District
Other
Corporate
Asset- and Mortgage-backed
Foreign

37. Yield Spreads Within and Across Sectors and Markets
Different sectors have different risk and return characteristics
Market sectors can be further divided to reflect common economic characteristics:
Industrial
Utility
Finance
Banks
Asset- and mortgage-backed securities also have their unique sub-sector classifications

38. Yield Spreads Within and Across Sectors and Markets
The yield spreads between yields offered in two different sectors is called the intermarket sector spread
This is also always measured versus the Treasury yield
The yield spread differential within a market sector is the intramarket sector spread
This spread typically increases with maturity
Yield curves are computed for a given sector, much like the Treasury yield curve

39. Issuer Specific Yield Spreads
An issuer specific yield curve can be computed given the yield spread, by maturity, for an issuer and the yield for on-the-run Treasury securities.
The factors other than maturity that affect the intermarket and intramarket yield spreads are
(1) the relative credit risk of the two issues;
(2) the presence of embedded options;
(3) the relative liquidity of the two issues; and,
(4) the taxability of the interest.

40. Credit Spreads
The yield spread between Treasury and non-Treasury bonds that are identical in all respects except credit rating is referred to as the credit or quality spread.

41. Credit Spreads
A credit spread or quality spread is the yield spread between a non-Treasury security and a Treasury security that are ‘‘identical in all respects except for credit rating.’’
Some market participants argue that credit spreads between corporates and Treasuries change systematically because of changes in economic prospects—widening in a declining economy (‘‘flight to quality’’) and narrowing in an expanding economy.

42. Credit Spreads
Credit spreads between Treasury and corporate bonds change systematically with changes in the overall economy.
Credit spreads widen (narrow) in a declining (expanding) economy.
Historical examples
Exhibit 4 shows the changes in credit spreads since 1919
The spread is measured as the difference between the Baa and Aaa rated corporate debt
The relationship between macro-economic conditions and yield spread is clearly shown in the exhibit

43. Credit Spreads

44. Embedded Options
Generally investors require a larger spread to a comparable Treasury security for issues with an embedded option favorable to the issuer, and a smaller spread for an issue with an embedded option favorable to the investor.
For mortgage-backed securities, one reason for the increased yield spread relative to a comparable Treasury security is exposure to prepayment risk.
The option-adjusted spread of a security seeks to measure the yield spread after adjusting for embedded options.

45. Embedded Options
Embedded options (such as the call provision) effect the yield of a bond and effects the yield spread
Mortgage-backed securities have prepayment risk effecting the yield spread
Reported yield spreads do not adjust for embedded options (these are raw or nominal yield spreads).
The adjusted yield spread is called the option-adjusted spread (OAS).

46. Liquidity and Taxability
The amount of liquidity (breadth and depth of the market) can affect the yield spread.
Differences between the yields of off- and on-the-run Treasuries is an example.
Because on-the-run is in greater demand, the price is slightly higher and yield lower than off-the-run.
The size of the issue affects liquidity, with larger issues having greater liquidity
In the U.S., income tax is collected on the interest income – except for qualified municipal bonds

47. Liquidity
A yield spread exists due to the difference in the perceived liquidity of two issues.
One factor that affects liquidity (and therefore the yield spread) is the size of an issue—the larger the issue, the greater the liquidity relative to a smaller issue, and the greater the liquidity, the lower the yield spread.

48. Taxability
Because of the tax-exempt features of municipal bonds, the yield is less than similar maturities of other bonds
The yield ratio is used to compare the yields of tax-exempt and similar maturity Treasuries (Exhibit 6)
The yield ratio for municipal bonds will change depending upon changes in the individual income tax rate
The higher the tax rate, the more attractive the tax exempt bond and the lower the yield ratio

49. Taxability
Because of the tax-exempt feature of municipal bonds, the yield on municipal bonds is less than that on Treasuries with the same maturity.
The difference in yield between tax-exempt securities and Treasury securities is typically measured in terms of a yield ratio—the yield on a tax-exempt security as a percentage of the yield on a comparable Treasury security.
The after-tax yield is computed by multiplying the pre-tax yield by one minus the marginal tax rate.
In the tax-exempt bond market, the benchmark for calculating yield spreads is a generic AAA general obligation bond with a specified maturity.

50. Municipal Bond Yields
The U.S. Municipal bond market is dividend into two sectors:
General Obligation bonds
Revenue bonds
The benchmark for municipal bonds is not the on-the-run Treasury rate, but the generic AAA general obligation bond.
The yield curve is constructed by dealer firms active in the market

51. Municipal Bond Yields
The after-tax yield is computed as the pre-tax yield times (1 minus the marginal tax rate).
Not all municipal bonds are tax-free.
Another way to put taxable and tax exempt bonds on a comparable basis is to compute the tax-equivalent rate, which is the tax exempt yield divided by (1 minus the marginal tax rate).
Some states tax municipal bond income (issued in other states) that are exempt from federal income taxes

52. Supply and Demand Factors Influence on Bond Yields
At times, the typical yield spread / yield curve will be impacted by temporary imbalances between supply and demand (market segmentation theory)
Over and under supply of the bonds of certain issuers in certain sectors will result in yields above or below comparable securities
Some bond managers study the forward calendar of planed offerings to understand potential supply and demand imbalances – and the impact on the yield curve

53. Non U.S. Interest Rate
The U.K., German, and Japanese bond markets are important benchmarks for comparison purposes
For example, the German bund is the primary long-term benchmark yield for European securities
The London interbank offered rate (LIBOR) is the short-term worldwide benchmark interest rate
The yield spreads and yield curves in foreign countries respond to similar supply and demand patterns observed in the U.S. market

54. Non U.S. Government Bond Markets
Technical factors having to do with temporary imbalances between the supply of and demand for new issues affect yield spreads.
The same factors that affect yield spreads in the United States affect yield spreads in other countries and between countries.
Major non-U.S. bond markets have government benchmark yield curves similar to the U.S. Treasury yield curve.
Because of the important role of the German bond market, nominal spreads in the European bond market are typically computed relative to German government bonds.

55. LIBOR
Funded investors who borrow short term typically measure the relative value of a security using borrowing rates rather than the Treasury rate.
The most popular borrowing cost reference rate is the London interbank offered rate (LIBOR), which is the interest rate banks pay to borrow funds from other banks in the London interbank market.
Funded investors typically pay a spread over LIBOR and seek to earn a spread over that funding cost when they invest the borrowed funds.

56. Interest Rate Swaps
In an interest rate swap, two parties agree to exchange periodic interest payments with the dollar amount of the interest payments exchanged based on a notional principal (also called a notional amount).
In a typical interest rate swap, one party (the fixed-rate payer) agrees to pay to the counterparty fixed interest payments at designated dates for the life of the contract and the counterparty (the fixed-rate receiver) agrees to make interest rate payments that float with some reference rate.

57. Interest Rate Swaps
In an interest rate swap, the fixed rate paid by the fixed-rate payer is called the swap rate.
The most common reference rate used in a swap is LIBOR.
The swap spread is the spread that the fixed-rate payer agrees to pay above the Treasury yield with the same term to maturity as the swap.
The swap rate is the sum of the yield of a Treasury with the same maturity as the swap plus the swap spread.
Institutional investors can use an interest rate swap to convert a fixed-rate asset (or liability) into a floating-rate asset (or liability) and vice versa.

58. Interest Rate Swaps
The swap spread is viewed by market participants throughout the world as the appropriate spread measure for valuation and relative value analysis.
The swap spread is the spread of the global cost of short-term borrowing over the Treasury rate.
There is a high correlation between swap spreads and credit spreads in various sectors of the bond market.
A swap spread curve shows the relationship between the swap rate and swap maturity for a given country.

59. Interest Rate Swaps
In the interest rate swap, one party exchanges a stream of interest for another party's stream.
Interest rate swaps are normally 'fixed against floating', but can also be 'fixed against fixed' or 'floating against floating' rate swaps.
Interest rate swaps are often used by companies to alter their exposure to interest-rate fluctuations, by swapping fixed-rate obligations for floating rate obligations, or swapping floating rate obligations to fixed-rate obligations.
By swapping interest rates, a company is able to synthetically alter their interest rate exposures and bring them in line with management's appetite for interest rate risk.

60. Interest Rate Swaps and Spreads
In an interest rate swap, two parties agree to exchange periodic interest payment
The amount of the interest payments exchanged is based on a predetermined principal, called the notional principal.
The amount each counterparty agrees to pay the other is the agreed-upon periodic interest rate times the notational principal
The only monies exchanged between the parties are the interest payments.
In most swaps, one party pays the other based on a fixed interest rate and the other pays based on a variable interest rate.

61. Interest Rate Swaps and Spreads
One party is called the fixed-rate payer, while the other is the fixed-rate receiver (or variable-rate party).
The fixed rate that the fixed-rate payer pays is called the swap rate.
The reference rate used for the floating rate in a swap is a short-term money market rate, such as the prime rate, T-bill rate, or LIBOR

62. Interest Rate Swaps and Spreads
Current convention has evolved that the dealer quoting a swap rate sets the floating (variable) rate equal to the reference rate and then quotes the fixed-rate that will apply.
The fixed-rate has a specified “spread” above the yield for a Treasury with the same maturity (with the same term to maturity as the swap)
This is called the swap spread (see next two graphs)
The swap rate is the sum of the yield for a Treasury with the same term to maturity as the swap plus the swap spread.

63. Swap Example
Consider the following illustration in which Party A agrees to pay Party B periodic interest rate payments of LIBOR + 50bps in exchange for periodic interest rate payments of 3.00%.
Note that there is no exchange of the principal amounts and that the interest rates are on a "notional" principal amount.
Also note that the interest payments are settled in net (e.g. if LIBOR + 50bps is 1.20% then Party A receives 1.80% and pays B nothing). The fixed rate (3.00% in this example) is referred to as the swap rate.

64. Interest Rate Swaps and Spreads
Interest rate swaps have important applications in banking, corporate finance, and fixed income portfolio management. They are an important risk management tool.
Basically, investors can covert a fixed-rate asset into a floating-rate asset (and vice versa) with an interest rate swap.
Fannie Mae uses interest rate swaps to “hedge” its cash flows.

65. Interest Rate Swaps and Spreads
The swap spread reflects the current amount of perceived risk in the corporate bond market.
The correlation has been high between swap spreads and credit spreads in the various sectors of the bond market.
Exhibits 8 and 9 show a strong relationship between swap and credit spreads
A swap spread curve is shown in Exhibit 10
This is the relationship between the swap rate and the swap maturity. These are generally viewed by sector or country
The swap spreads tend to move together.

66. Interest Rate Swaps and Spreads

67. Interest Rate Swaps and Spreads