The document discusses various topics related to bond yields and interest rates: 1) Bond yields are determined by risk-free rates plus credit risk premiums. The Fed uses tools like open market operations and reserve requirements to implement monetary policy. 2) Treasury securities include bills, notes, bonds, and inflation-protected bonds. Treasuries have little credit risk but are still exposed to interest rate and other risks. 3) The Treasury yield curve shows the relationship between Treasury yields and maturities. Factors like on-the-run status, liquidity, and reinvestment risk complicate this relationship. 4) Yield spreads measure differences in bond yields and are used to assess credit risk, liquidity

1. Understanding Yield
Spreads

2. 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.

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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).

14. 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

15. 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 or different issues within the same 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.

16. 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.

17. 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.

18. 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).

19. 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

20. 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

21. 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

22. 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.

23. 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.

24. 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.

25. 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.

26. Interest Rate Swaps and Spreads

27. Interest Rate Swaps and Spreads

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