UNDERSTANDING YIELD SPREADS
III. U.S. TREASURY RATES
The securities issued by the U.S. Department of the Treasury are backed by the full faith and credit of the U.S. government. Consequently, market participants throughout the world view these securities as being ‘‘default risk-free’’ securities. However, there are risks associated with owning U.S. Treasury securities.
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.
Although Treasury bonds have traditionally been issued with maturities up to 30 years, the Treasury suspended issuance of the 30-year bond in October 2001.
Inflation-protection securities: Coupon securities whose principal’s reference rate is the Consumer Price Index.
The on-the-run issue or current issue is the most recently auctioned issue of Treasury notes and bonds of each maturity. The off-the-run issues are securities that were previously issued and are replaced by the on-the-run issue. Issues that have been replaced by several more recent issues are said to be ‘‘well off-the-run issues.’’
The secondary market for Treasury securities is an over-the-counter market where a group of U.S. government securities dealers provides continuous bids and offers on specific
outstanding Treasuries. This secondary market is the most liquid financial market in the world. Off-the-run issues are less liquid than on-the-run issues.
A. Risks of Treasury Securities
With this brief review of Treasury securities, let’s look at their risks. We listed the general risks in Chapter 2 and repeat them here: (1) interest rate risk, (2) call and prepayment risk, (3) yield curve risk, (4) reinvestment risk, (5) credit risk, (6) liquidity risk, (7) exchange-rate risk, (8) volatility risk, (9) inflation or purchasing power risk, and (10) event risk.
All fixed income securities, including Treasury securities, expose investors to interest rate risk.1However, the degree of interest rate risk is not the same for all securities. The reason is that maturity and coupon rate affect how much the price changes when interest rates change.
One measure of a security’s interest rate risk is itsduration.2 Since Treasury securities, like other fixed income securities, have different durations, they have different exposures to interest rate risk as measured by duration.
Technically, yield curve risk and volatility risk are risks associated with Treasury securities.
However, at this early stage of our understanding of fixed income analysis, we will not attempt to explain these risks. It is not necessary to understand these risks at this point in order to appreciate the material that follows in this section.
Because Treasury securities are noncallable, there is no reinvestment risk due to an issue being called.3 Treasury coupon securities carry reinvestment risk because in order to realize the yield offered on the security, the investor must reinvest the coupon payments received at an interest rate equal to the computed yield. So, all Treasury coupon securities are exposed to reinvestment risk. Treasury bills are not exposed to reinvestment risk because they are zero-coupon instruments.
As for credit risk, the perception in the global financial community is that Treasury securities have no credit risk. In fact, when market participants and the popular press state that Treasury securities are ‘‘risk free,’’ they are referring to credit risk.
Treasury securities are highly liquid. However, on-the-run and off-the-run Treasury securities trade with different degrees of liquidity. Consequently, the yields offered by on-the-run and off-the-run issues reflect different degrees of liquidity.
Since U.S. Treasury securities are dollar denominated, there is no exchange-rate risk for an investor whose domestic currency is the U.S. dollar. However, non-U.S. investors whose domestic currency is not the U.S. dollar are exposed to exchange-rate risk.
Fixed-rate Treasury securities are exposed to inflation risk. Treasury inflation protection securities (TIPS) have a coupon rate that is effectively adjusted for the rate of inflation and therefore have protection against inflation risk.
1Interest rate risk is the risk of an adverse movement in the price of a bond due to changes in interest rates.
2Duration is a measure of a bond’s price sensitivity to a change in interest rates.
3The Treasury no longer issues callable bonds. The Treasury issued callable bonds in the early 1980s and all of these issues will mature no later than November 2014 (assuming that they are not called before then). Moreover, as of 2004, the longest maturity of these issues is 10 years. Consequently, while outstanding callable issues of the Treasury are referred to as ‘‘bonds,’’ based on their current maturity these issues would not be compared to long-term bonds in any type of relative value analysis. Therefore, because the Treasury no longer issues callable bonds and the outstanding issues do not have the maturity characteristics of a long-term bond, we will ignore these callable issues and simply treat Treasury bonds as noncallable.
Chapter 4 Understanding Yield Spreads 77
EXHIBIT 1 Relationship Between Yield and Maturity for On-the-Run Treasury Issues on February 8, 2002
Issue (maturity) Yield (%)
1 month 1.68
3 months 1.71
6 months 1.81
1 year1 2.09
2 years 2.91
5 years 4.18
10 years 4.88
30 years2 5.38
1The 1-year issue is based on the 2-year issue closest to maturing in one year.
2The 30-year issue shown is based on the last 30-year issue before the Treasury suspended issuance of Treasury bonds in October 2001.
Source:Global Relative Value, Lehman Brothers, Fixed Income Research, February 11, 2002, p. 128.
Finally, the yield on Treasury securities is impacted by a myriad of events that can be classified as political risk, a form of event risk. The actions of monetary and fiscal policy in the United States, as well as the actions of other central banks and governments, can have an adverse or favorable impact on U.S. Treasury yields.
B. The Treasury Yield Curve
Given that Treasury securities do not expose investors to credit risk, market participants look at the 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 relationship between yield and maturity of on-the-run Treasury securities on February 8, 2002 is displayed in Exhibit 1 in tabular form. The relationship shown in Exhibit 1 is called theTreasury yield curve—even though the ‘‘curve’’ shown in the exhibit is presented in tabular form.
The information presented in Exhibit 1 indicates that the longer the maturity the higher the yield and is referred to as anupward sloping yield curve. Since this is the most typical shape for the Treasury yield curve, it is also referred to as a normal yield curve. Other relationships have been observed. An inverted yield curve indicates that the longer the maturity, the lower the yield. For a flat yield curve the yield is approximately the same regardless of maturity.
Exhibit 2 provides a graphic example of the variants of these shapes and also shows how a yield curve can change over time. In the exhibit, the yield curve at the beginning of 2001 was inverted up to the 5-year maturity but was upward sloping beyond the 5-year maturity.
By December 2001, all interest rates had declined. As seen in the exhibit, interest rates less than the 10-year maturity dropped substantially more than longer-term rates resulting in an upward sloping yield curve.
The number of on-the-run securities available in constructing the yield curve has decreased over the last two decades. While the 1-year and 30-year yields are shown in the February 8, 2002 yield curve, as of this writing there is no 1-year Treasury bill and the maturity of the 30-year Treasury bond (the last one issued before suspension of the issuance of 30-year
EXHIBIT 2 U.S. Treasury Yield Curve: December 2000 and December 2001
Yield (%) 5.60 5.40 5.20 5.00 4.80 4.60 4.40 4.20 4.00 3.80 3.60 3.40 3.20 3.00 2.80
Yield (%) 5.60 5.40 5.20 5.00 4.80 4.60 4.40 4.20 4.00 3.80 3.60 3.40 3.20 3.00 2.80
5.11 4.99
5.12
5.51 5.48
5.04
4.34
3.05 12/31/01 12/31/00
2 yr 5 yr 10 yr 30 yr
Source: Lehman Brothers Fixed Income Research, Global Fixed Income Strategy ‘‘Playbook,’’ January 2002.
Treasury bonds) will decline over time. To get a yield for maturities where no on-the-run Treasury issue exists, it is necessary to interpolate from the yield of two on-the-run issues.
Several methodologies are used in practice. (The simplest is just a linear interpolation.) Thus, when market participants talk about a yield on the Treasury yield curve that is not one of the available on-the-run maturities—for example, the 8-year yield—it is only an approximation.
It is critical to understand that any non-Treasury issue must offer a premium above the yield offered for the same maturity on-the-run Treasury issue. For example, if a corporation wanted to offer a 10-year noncallable issue on February 8, 2002, the issuer must offer a yield greater than 4.88% (the yield for the 10-year on-the-run Treasury issue). How much greater depends on the additional risks associated with investing in the 10-year corporate issue compared to investors in the 10-year on-the-run Treasury issue. Even off-the-run Treasury issues must offer a premium to reflect differences in liquidity.
Two factors complicate the relationship between maturity and yield as portrayed by the yield curve. The first is that the yield for on-the-run issues may be distorted by the fact that purchase of these securities can be financed at lower rates and as a result these issues offer artificially low yields. To clarify, some investors purchase securities with borrowed funds and use the securities purchased as collateral for the loan. This type of collateralized borrowing is called a repurchase agreement. Since dealers want to obtain use of these securities for their own trading activities, they are willing to lend funds to investors at a lower interest rate than is otherwise available for borrowing in the market. Consequently, incorporated into the price of an on-the-run Treasury security is the cheaper financing available, resulting in a lower yield for an on-the-run issue than would prevail in the absence of this financing advantage.
Chapter 4 Understanding Yield Spreads 79
The second factor complicating the comparison of on-the-run and off-the-run Treasury issues (in addition to liquidity differences) is that they have different interest rate risks and different reinvestment risks. So, for example, if the coupon rate for the 5-year on-the-run Treasury issue in February 2002 is 4.18% and an off-the-run Treasury issue with just less than 5 years to maturity has a 5.25% coupon rate, the two bonds have different degrees of interest rate risk. Specifically, the on-the-run issue has greater interest rate risk (duration) because of the lower coupon rate. However, it has less reinvestment risk because the coupon rate is lower.
Because of this, when market participants talk about interest rates in the Treasury market and use these interest rates to value securities they look at another relationship in the Treasury market: the relationship between yield and maturity for zero-coupon Treasury securities. But wait, we said that the Treasury only issues three zero-coupon securities—1-month, 3-month, and 6-month Treasury bills. Where do we obtain the relationship between yield and maturity for zero-coupon Treasury securities? We discuss this next.
1. Theories of the Term Structure of Interest Rates What information does the yield curve reveal? How can we explain and interpret changes in the yield curve? These questions are of great interest to anyone concerned with such tasks as the valuation of multiperiod securities, economic forecasting, and risk management. Theories of the term structure of interest rates4 address these questions. Here we introduce the three main theories or explanations of the term structure. We shall present these theories intuitively.5
The three main term structure theories are:
• the pure expectations theory (unbiased expectations theory)
• the liquidity preference theory (or liquidity premium theory)
• the market segmentation theory Each theory is explained below.
a. Pure Expectations Theory The pure expectations theory makes the simplest and most direct link between the yield curve and investors’ expectations about future interest rates, and, because long-term interest rates are plausibly linked to investor expectations about future inflation, it also opens the door to some interesting economic interpretations.
Thepure expectations theoryexplains the term structure in terms of expected future short-term interest rates. According to the pure expectations theory, the market sets the yield on a two-year bond so that the return on the two-year bond is approximately equal to the return on a one-year bond plus the expected return on a one-year bond purchased one year from today.
Under this theory, a rising term structure indicates that the market expects short-term rates to rise in the future. For example, if the yield on the two-year bond is higher than the yield on the one-year bond, according to this theory, investors expect the one-year rate a year from now to be sufficiently higher than the one-year rate available now so that the two ways of investing for two years have the same expected return. Similarly, a flat term structure reflects
4Term structure means the same as maturity structure—a description of how a bond’s yield changes as the bond’s maturity changes. In other words, term structure asks the question: Why do long-term bonds have a different yield than short-term bonds?
5Later, we provide a more mathematical treatment of these theories in terms of forward rates that we will discuss in Chapter 6.
an expectation that future short-term rates will be unchanged from today’s short-term rates, while a falling term structure reflects an expectation that future short-term rates will decline.
This is summarized below:
Shape of term structure Implication according to pure expectations theory upward sloping (normal) rates expected to rise
downward sloping (inverted) rates expected to decline
flat rates not expected to change
The implications above are the broadest interpretation of the theory.
How does the pure expectations theory explain a humped yield curve? According to the theory, this can result when investors expect the returns on one-year securities to rise for a number of years, then fall for a number of years.
The relationships that the table above illustrates suggest that the shape of the yield curve contains information regarding investors’ expectations about future inflation. A pioneer of the theory of interest rates (the economist Irving Fisher) asserted that interest rates reflect the sum of a relatively stable real rate of interest plus a premium for expected inflation. Under this hypothesis, if short-term rates are expected to rise, investors expect inflation to rise as well.
An upward (downward) sloping term structure would mean that investors expected rising (declining) future inflation. Much economic discussion in the financial press and elsewhere is based on this interpretation of the yield curve.
The shortcoming of the pure expectations theory is that it assumes investors are indifferent to interest rate risk and any other risk factors associated with investing in bonds with different maturities.
b. Liquidity Preference Theory The liquidity preference 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 when interest rates change and investors want to be compensated for this risk. According to the liquidity preference theory, the term structure of interest rates is determined by (1) expectations about future interest rates and (2) a yield premium for interest rate risk.6Because interest rate risk increases with maturity, the liquidity preference theory asserts that the yield premium increases with maturity.
Consequently, based on this theory, an upward-sloping yield curve may reflect expectations that future interest rates either (1) will rise, or (2) will be unchanged or even fall, but with a yield premium increasing with maturity fast enough to produce an upward sloping yield curve.
Thus, for an upward sloping yield curve (the most frequently observed type), the liquidity preference theory by itself has nothing to say about expected future short-term interest rates.
For flat or downward sloping yield curves, the liquidity preference theory is consistent with a forecast of declining future short-term interest rates, given the theory’s prediction that the yield premium for interest rate risk increases with maturity.
Because the liquidity preference theory argues that the term structure is determined by both expectations regarding future interest rates and a yield premium for interest rate risk, it is referred to asbiased expectations theory.
6In the liquidity preference theory, ‘‘liquidity’’ is measured in terms of interest rate risk. Specifically, the more interest rate risk, the less the liquidity.
Chapter 4 Understanding Yield Spreads 81
c. Market Segmentation Theory Proponents of themarket segmentation theoryargue that within the different maturity sectors of the yield curve the supply and demand for funds determine the interest rate for that sector. That is, each maturity sector is an independent or segmented market for purposes of determining the interest rate in that maturity sector.
Thus, positive sloping, inverted, and humped yield curves are all possible. In fact, the market segmentation theory can be used to explain any shape that one might observe for the yield curve.
Let’s understand why proponents of this theory view each maturity sector as independent or segmented. In the bond market, investors can be divided into two groups based on their return needs: investors that manage funds versus a broad-based bond market index and those that manage funds versus their liabilities. The easiest case is for those that manage funds against liabilities. Investors managing funds where liabilities represent the benchmark will restrict their activities to the maturity sector that provides the best match with the maturity of their liabilities.7This is the basic principle of asset-liability management. If these investors invest funds outside of the maturity sector that provides the best match against liabilities, they are exposing themselves to the risks associated with an asset-liability mismatch. For example, consider the manager of a defined benefit pension fund. Since the liabilities of a defined benefit pension fund are long-term, the manager will invest in the long-term maturity sector of the bond market. Similarly, commercial banks whose liabilities are typically short-term focus on short-term fixed-income investments. Even if the rate on long-term bonds were considerably more attractive than that on short-term investments, according to the market segmentation theory commercial banks will restrict their activities to investments at the short end of the yield curve. Reinforcing this notion of a segmented market are restrictions imposed on financial institutions that prevent them from mismatching the maturity of assets and liabilities.
A variant of the market segmentation theory is thepreferred habitat theory. This theory argues that investors prefer to invest in particular maturity sectors as dedicated by the nature of their liabilities. However, proponents of this theory do not assert that investors would be unwilling to shift out of their preferred maturity sector; instead, it is argued that if investors are given an inducement to do so in the form of a yield premium they will shift out of their preferred habitat. The implication of the preferred habitat theory for the shape of the yield curve is that any shape is possible.
C. Treasury Strips
Although the U.S. Department of the Treasury does not issue zero-coupon Treasury securities with maturity greater than one year, government dealers can synthetically create zero-coupon securities, which are effectively guaranteed by the full faith and credit of the U.S. government, with longer maturities. They create these securities by separating the coupon payments and the principal payment of a coupon-bearing Treasury security and selling them off separately.
The process, referred to asstripping a Treasury security, results in securities calledTreasury strips. The Treasury strips created from coupon payments are called Treasury coupon strips and those created from the principal payment are called Treasury principal strips. We explained the process of creating Treasury strips in Chapter 3.
7One of the principles of finance is the ‘‘matching principle:’’ short-term assets should be financed with (or matched with) short-term liabilities; long-term assets should be financed with (or matched with) long-term sources of financing.