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Ch a p ter 6 PREVIEW The Risk and Term Structure of Interest Rates In our supply and demand analysis of interest-rate behavior in Chapter 5, we examined the determination of just one interest rate. Yet we saw earlier that there are enormous numbers of bonds on which the interest rates can and do differ. In this chapter, we complete the interest-rate picture by examining the relationship of the various interest rates to one another. Understanding why they differ from bond to bond can help businesses, banks, insurance companies, and private investors decide which bonds to purchase as investments and which ones to sell. We first look at why bonds with the same term to maturity have different interest rates. The relationship among these interest rates is called the risk structure of interest rates, although risk, liquidity, and income tax rules all play a role in determining the risk structure. A bond’s term to maturity also affects its interest rate, and the relationship among interest rates on bonds with different terms to maturity is called the term structure of interest rates. In this chapter, we examine the sources and causes of fluctuations in interest rates relative to one another and look at a number of theories that explain these fluctuations. Risk Structure of Interest Rates Figure 1 shows the yields to maturity for several categories of long-term bonds from 1919 to 2002. It shows us two important features of interest-rate behavior for bonds of the same maturity: Interest rates on different categories of bonds differ from one another in any given year, and the spread (or difference) between the interest rates varies over time. The interest rates on municipal bonds, for example, are above those on U.S. government (Treasury) bonds in the late 1930s but lower thereafter. In addition, the spread between the interest rates on Baa corporate bonds (riskier than Aaa corporate bonds) and U.S. government bonds is very large during the Great Depression years 1930–1933, is smaller during the 1940s–1960s, and then widens again afterwards. What factors are responsible for these phenomena? Default Risk 120 One attribute of a bond that influences its interest rate is its risk of default, which occurs when the issuer of the bond is unable or unwilling to make interest payments when promised or pay off the face value when the bond matures. A corporation suffering big losses, such as Chrysler Corporation did in the 1970s, might be more likely CHAPTER 6 The Risk and Term Structure of Interest Rates 121 Annual Yield (%) 16 14 12 Corporate Aaa Bonds 10 8 Corporate Baa Bonds 6 U.S. Government Long-Term Bonds 4 2 0 1920 State and Local Government (Municipal) 1930 1940 1950 1960 1970 1980 1990 2000 F I G U R E 1 Long-Term Bond Yields, 1919–2002 Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15/data/. www.federalreserve.gov /Releases/h15/update/ The Federal Reserve reports the returns on different quality bonds. Look at the bottom of the listing of interest rates for AAA and BBB rated bonds. to suspend interest payments on its bonds.1 The default risk on its bonds would therefore be quite high. By contrast, U.S. Treasury bonds have usually been considered to have no default risk because the federal government can always increase taxes to pay off its obligations. Bonds like these with no default risk are called default-free bonds. (However, during the budget negotiations in Congress in 1995 and 1996, the Republicans threatened to let Treasury bonds default, and this had an impact on the bond market, as one application following this section indicates.) The spread between the interest rates on bonds with default risk and default-free bonds, called the risk premium, indicates how much additional interest people must earn in order to be willing to hold that risky bond. Our supply and demand analysis of the bond market in Chapter 5 can be used to explain why a bond with default risk always has a positive risk premium and why the higher the default risk is, the larger the risk premium will be. To examine the effect of default risk on interest rates, let us look at the supply and demand diagrams for the default-free (U.S. Treasury) and corporate long-term bond markets in Figure 2. To make the diagrams somewhat easier to read, let’s assume that initially corporate bonds have the same default risk as U.S. Treasury bonds. In this case, these two bonds have the same attributes (identical risk and maturity); their equilibrium prices and interest rates will initially be equal (P c1  P T1 and i c1  i T1 ), and the risk premium on corporate bonds (i c1  i T1 ) will be zero. 1 Chrysler did not default on its loans in this period, but it would have were it not for a government bailout plan intended to preserve jobs, which in effect provided Chrysler with funds that were used to pay off creditors. PART II Financial Markets Price of Bonds, P (P increases ↑ ) Interest Rate, i (i increases ) Price of Bonds, P (P increases ↑ ) Interest Rate, i (i increases ) ↑ 122 ↑ ST Sc P c1 i T2 i 1c P c2 Risk Premium P T2 i T2 P T1 i T1 i 2c D c2 D c1 Quantity of Corporate Bonds (a) Corporate bond market D T1 DT2 Quantity of Treasury Bonds (b) Default-free (U.S. Treasury) bond market F I G U R E 2 Response to an Increase in Default Risk on Corporate Bonds An increase in default risk on corporate bonds shifts the demand curve from D c1 to D c2. Simultaneously, it shifts the demand curve for Treasury bonds from D T1 to D T2. The equilibrium price for corporate bonds (left axis) falls from P c1 to P c2 , and the equilibrium interest rate on corporate bonds (right axis) rises from i c1 to i c2. In the Treasury market, the equilibrium bond price rises from P T1 to P T2, and the equilibrium interest rate falls from i T1 to i T2. The brace indicates the difference between i c2 and i T2, the risk premium on corporate bonds. (Note: P and i increase in opposite directions. P on the left vertical axis increases as we go up the axis, while i on the right vertical axis increases as we go down the axis.) Study Guide Two exercises will help you gain a better understanding of the risk structure: 1. Put yourself in the shoes of an investor—see how your purchase decision would be affected by changes in risk and liquidity. 2. Practice drawing the appropriate shifts in the supply and demand curves when risk and liquidity change. For example, see if you can draw the appropriate shifts in the supply and demand curves when, in contrast to the examples in the text, a corporate bond has a decline in default risk or an improvement in its liquidity. If the possibility of a default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease. In addition, the corporate bond’s return will be more uncertain as well. The theory of asset demand predicts that because the expected return on the corporate bond falls relative to the expected return on the default-free Treasury bond while its relative riskiness rises, the corporate bond is less desirable (holding everything else equal), and demand for it will fall. The demand curve for corporate bonds in panel (a) of Figure 2 then shifts to the left, from D c1 to D c2. At the same time, the expected return on default-free Treasury bonds increases relative to the expected return on corporate bonds, while their relative riskiness CHAPTER 6 The Risk and Term Structure of Interest Rates 123 declines. The Treasury bonds thus become more desirable, and demand rises, as shown in panel (b) by the rightward shift in the demand curve for these bonds from D T1 to D T2. As we can see in Figure 2, the equilibrium price for corporate bonds (left axis) falls from P c1 to P c2, and since the bond price is negatively related to the interest rate, the equilibrium interest rate on corporate bonds (right axis) rises from i c1 to i c2. At the same time, however, the equilibrium price for the Treasury bonds rises from P T1 to P T2, and the equilibrium interest rate falls from i T1 to i T2. The spread between the interest rates on corporate and default-free bonds—that is, the risk premium on corporate bonds—has risen from zero to i c2  i T2. We can now conclude that a bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium. Because default risk is so important to the size of the risk premium, purchasers of bonds need to know whether a corporation is likely to default on its bonds. Two major investment advisory firms, Moody’s Investors Service and Standard and Poor’s Corporation, provide default risk information by rating the quality of corporate and municipal bonds in terms of the probability of default. The ratings and their description are contained in Table 1. Bonds with relatively low risk of default are called investment-grade securities and have a rating of Baa (or BBB) and above. Bonds with Table 1 Bond Ratings by Moody’s and Standard and Poor’s Rating Moody’s Standard and Poor’s Aaa AAA Highest quality (lowest default risk) Aa AA High quality A A Upper medium grade Baa BBB Medium grade Ba B BB B Lower medium grade Speculative Caa Ca C CCC, CC C D Poor (high default risk) Highly speculative Lowest grade Descriptions Examples of Corporations with Bonds Outstanding in 2003 General Electric, Pfizer Inc., North Carolina State, Mobil Oil Wal-Mart, McDonald’s, Credit Suisse First Boston Hewlett-Packard, Anheuser-Busch, Ford, Household Finance Motorola, Albertson’s, Pennzoil, Weyerhaeuser Co., Tommy Hilfiger Royal Caribbean, Levi Strauss Rite Aid, Northwest Airlines Inc., Six Flags Revlon, United Airlines US Airways, Polaroid Enron, Oakwood Homes 124 PART II Financial Markets ratings below Baa (or BBB) have higher default risk and have been aptly dubbed speculative-grade or junk bonds. Because these bonds always have higher interest rates than investment-grade securities, they are also referred to as high-yield bonds. Next let’s look back at Figure 1 and see if we can explain the relationship between interest rates on corporate and U.S. Treasury bonds. Corporate bonds always have higher interest rates than U.S. Treasury bonds because they always have some risk of default, whereas U.S. Treasury bonds do not. Because Baa-rated corporate bonds have a greater default risk than the higher-rated Aaa bonds, their risk premium is greater, and the Baa rate therefore always exceeds the Aaa rate. We can use the same analysis to explain the huge jump in the risk premium on Baa corporate bond rates during the Great Depression years 1930–1933 and the rise in the risk premium after 1970 (see Figure 1). The depression period saw a very high rate of business failures and defaults. As we would expect, these factors led to a substantial increase in default risk for bonds issued by vulnerable corporations, and the risk premium for Baa bonds reached unprecedentedly high levels. Since 1970, we have again seen higher levels of business failures and defaults, although they were still well below Great Depression levels. Again, as expected, default risks and risk premiums for corporate bonds rose, widening the spread between interest rates on corporate bonds and Treasury bonds. Application The Enron Bankruptcy and the Baa-Aaa Spread In December 2001, the Enron Corporation, a firm specializing in trading in the energy market, and once the seventh-largest corporation in the United States, was forced to declare bankruptcy after it became clear that it had used shady accounting to hide its financial problems. (The Enron bankruptcy, the largest ever in the United States, will be discussed further in Chapter 8.) Because of the scale of the bankruptcy and the questions it raised about the quality of the information in accounting statements, the Enron collapse had a major impact on the corporate bond market. Let’s see how our supply and demand analysis explains the behavior of the spread between interest rates on lower quality (Baa-rated) and highest quality (Aaa-rated) corporate bonds in the aftermath of the Enron failure. As a consequence of the Enron bankruptcy, many investors began to doubt the financial health of corporations with lower credit ratings such as Baa. The increase in default risk for Baa bonds made them less desirable at any given interest rate, decreased the quantity demanded, and shifted the demand curve for Baa bonds to the left. As shown in panel (a) of Figure 2, the interest rate on Baa bonds should have risen, which is indeed what happened. Interest rates on Baa bonds rose by 24 basis points (0.24 percentage points) from 7.81% in November 2001 to 8.05% in December 2001. But the increase in the perceived default risk for Baa bonds after the Enron bankruptcy made the highest quality (Aaa) bonds relatively more attractive and shifted the demand curve for these securities to the right—an outcome described by some analysts as a “flight to quality.” Just as our analysis predicts in Figure 2, interest rates on Aaa bonds fell by 20 basis points, from 6.97% in November to 6.77% in December. The overall outcome was that the spread between interest rates on Baa and Aaa bonds rose by 44 basis points from 0.84% before the bankruptcy to 1.28% afterward. CHAPTER 6 The Risk and Term Structure of Interest Rates 125 Liquidity Another attribute of a bond that influences its interest rate is its liquidity. As we learned in Chapter 4, a liquid asset is one that can be quickly and cheaply converted into cash if the need arises. The more liquid an asset is, the more desirable it is (holding everything else constant). U.S. Treasury bonds are the most liquid of all long-term bonds, because they are so widely traded that they are the easiest to sell quickly and the cost of selling them is low. Corporate bonds are not as liquid, because fewer bonds for any one corporation are traded; thus it can be costly to sell these bonds in an emergency, because it might be hard to find buyers quickly. How does the reduced liquidity of the corporate bonds affect their interest rates relative to the interest rate on Treasury bonds? We can use supply and demand analysis with the same figure that was used to analyze the effect of default risk, Figure 2, to show that the lower liquidity of corporate bonds relative to Treasury bonds increases the spread between the interest rates on these two bonds. Let us start the analysis by assuming that initially corporate and Treasury bonds are equally liquid and all their other attributes are the same. As shown in Figure 2, their equilibrium prices and interest rates will initially be equal: P c1  P T1 and i c1  i T1. If the corporate bond becomes less liquid than the Treasury bond because it is less widely traded, then (as the theory of asset demand indicates) its demand will fall, shifting its demand curve from D c1 to D c2 as in panel (a). The Treasury bond now becomes relatively more liquid in comparison with the corporate bond, so its demand curve shifts rightward from D T1 to D T2 as in panel (b). The shifts in the curves in Figure 2 show that the price of the less liquid corporate bond falls and its interest rate rises, while the price of the more liquid Treasury bond rises and its interest rate falls. The result is that the spread between the interest rates on the two bond types has risen. Therefore, the differences between interest rates on corporate bonds and Treasury bonds (that is, the risk premiums) reflect not only the corporate bond’s default risk but its liquidity, too. This is why a risk premium is more accurately a “risk and liquidity premium,” but convention dictates that it is called a risk premium. Income Tax Considerations Returning to Figure 1, we are still left with one puzzle—the behavior of municipal bond rates. Municipal bonds are certainly not default-free: State and local governments have defaulted on the municipal bonds they have issued in the past, particularly during the Great Depression and even more recently in the case of Orange County, California, in 1994 (more on this in Chapter 13). Also, municipal bonds are not as liquid as U.S. Treasury bonds. Why is it, then, that these bonds have had lower interest rates than U.S. Treasury bonds for at least 40 years, as indicated in Figure 1? The explanation lies in the fact that interest payments on municipal bonds are exempt from federal income taxes, a factor that has the same effect on the demand for municipal bonds as an increase in their expected return. Let us imagine that you have a high enough income to put you in the 35% income tax bracket, where for every extra dollar of income you have to pay 35 cents to the government. If you own a $1,000-face-value U.S. Treasury bond that sells for $1,000 and has a coupon payment of $100, you get to keep only $65 of the payment after taxes. Although the bond has a 10% interest rate, you actually earn only 6.5% after taxes. Suppose, however, that you put your savings into a $1,000-face-value municipal bond that sells for $1,000 and pays only $80 in coupon payments. Its interest rate is only 8%, but because it is a tax-exempt security, you pay no taxes on the $80 coupon payment, so you earn 8% after taxes. Clearly, you earn more on the municipal bond 126 PART II Financial Markets after taxes, so you are willing to hold the riskier and less liquid municipal bond even though it has a lower interest rate than the U.S. Treasury bond. (This was not true before World War II, when the tax-exempt status of municipal bonds did not convey much of an advantage because income tax rates were extremely low.) Another way of understanding why municipal bonds have lower interest rates than Treasury bonds is to use the supply and demand analysis displayed in Figure 3. We assume that municipal and Treasury bonds have identical attributes and so have the same bond prices and interest rates as drawn in the figure: P m1  P T1 and i m1  i T1. Once the municipal bonds are given a tax advantage that raises their after-tax expected return relative to Treasury bonds and makes them more desirable, demand for them rises, and their demand curve shifts to the right, from D m1 to D m2. The result is that their equilibrium bond price rises from P m1 to P m2, and their equilibrium interest rate falls from i m1 to i m2. By contrast, Treasury bonds have now become less desirable relative to municipal bonds; demand for Treasury bonds decreases, and D T1 shifts to D T2. The Treasury bond price falls from P T1 to P T2, and the interest rate rises from i T1 to i T2. The resulting lower interest rates for municipal bonds and higher interest rates for Treasury bonds explains why municipal bonds can have interest rates below those of Treasury bonds.2 Interest Rate, i (i increases ) Price of Bonds, P (P increases ↑ ) Interest Rate, i (i increases ) ↑ Price of Bonds, P (P increases ↑ ) ↑ ST Sm P m2 i m2 P m1 i m1 D m1 P T1 i T1 P T2 i T2 D m2 DT2 DT1 Quantity of Municipal Bonds Quantity of Treasury Bonds (a) Market for municipal bonds ( b) Market for Treasury bonds F I G U R E 3 Interest Rates on Municipal and Treasury Bonds When the municipal bond is given tax-free status, demand for the municipal bond shifts rightward from D m1 to D m2 and demand for the Treasury bond shifts leftward from DT1 to DT2. The equilibrium price of the municipal bond (left axis) rises from P m1 to P m2, so its interest rate (right axis) falls from i m1 to i m2, while the equilibrium price of the Treasury bond falls from P T1 to P T2 and its interest rate rises from iT1 to iT2. The result is that municipal bonds end up with lower interest rates than those on Treasury bonds. (Note: P and i increase in opposite directions. P on the left vertical axis increases as we go up the axis, while i on the right vertical axis increases as we go down the axis.) 2 In contrast to corporate bonds, Treasury bonds are exempt from state and local income taxes. Using the analysis in the text, you should be able to show that this feature of Treasury bonds provides an additional reason why interest rates on corporate bonds are higher than those on Treasury bonds. CHAPTER 6 Summary Application The Risk and Term Structure of Interest Rates 127 The risk structure of interest rates (the relationship among interest rates on bonds with the same maturity) is explained by three factors: default risk, liquidity, and the income tax treatment of the bond’s interest payments. As a bond’s default risk increases, the risk premium on that bond (the spread between its interest rate and the interest rate on a default-free Treasury bond) rises. The greater liquidity of Treasury bonds also explains why their interest rates are lower than interest rates on less liquid bonds. If a bond has a favorable tax treatment, as do municipal bonds, whose interest payments are exempt from federal income taxes, its interest rate will be lower. Effects of the Bush Tax Cut on Bond Interest Rates The Bush tax cut passed in 2001 scheduled a reduction of the top income tax bracket from 39% to 35% over a ten-year period. What is the effect of this income tax decrease on interest rates in the municipal bond market relative to those in the Treasury bond market? Our supply and demand analysis provides the answer. A decreased income tax rate for rich people means that the after-tax expected return on tax-free municipal bonds relative to that on Treasury bonds is lower, because the interest on Treasury bonds is now taxed at a lower rate. Because municipal bonds now become less desirable, their demand decreases, shifting the demand curve to the left, which lowers their price and raises their interest rate. Conversely, the lower income tax rate makes Treasury bonds more desirable; this change shifts their demand curve to the right, raises their price, and lowers their interest rates. Our analysis thus shows that the Bush tax cut raises the interest rates on municipal bonds relative to interest rates on Treasury bonds. Term Structure of Interest Rates We have seen how risk, liquidity, and tax considerations (collectively embedded in the risk structure) can influence interest rates. Another factor that influences the interest rate on a bond is its term to maturity: Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different. A plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations is called a yield curve, and it describes the term structure of interest rates for particular types of bonds, such as government bonds. The “Following the Financial News” box shows several yield curves for Treasury securities that were published in the Wall Street Journal. Yield curves can be classified as upward-sloping, flat, and downward-sloping (the last sort is often referred to as an inverted yield curve). When yield curves slope upward, as in the “Following the Financial News” box, the long-term interest rates are above the shortterm interest rates; when yield curves are flat, short- and long-term interest rates are the same; and when yield curves are inverted, long-term interest rates are below short-term interest rates. Yield curves can also have more complicated shapes in which they first slope up and then down, or vice versa. Why do we usually see 128 PART II Financial Markets Following the Financial News Yield Curves The Wall Street Journal publishes a daily plot of the yield curves for Treasury securities, an example of which is presented here. It is typically found on page 2 of the “Money and Investing” section. The numbers on the vertical axis indicate the interest rate for the Treasury security, with the maturity given by the numbers on the horizontal axis. For example, the yield curve marked “Yesterday” indicates that the interest rate on the three-month Treasury bill yesterday was 1.25%, while the one-year bill had an interest rate of 1.35% and the ten-year bond had an interest rate of 4.0%. As you can see, the yield curves in the plot have the typical upward slope. Source: Wall Street Journal, Wednesday, January 22, 2003, p. C2. Treasury Yield Curve Yield to maturity of current bills, notes and bonds. 5.0% Yesterday 1 month ago 1 year ago 4.0 3.0 2.0 1.0 1 3 mos. 6 2 yrs. 5 10 30 maturity Source: Reuters www.ratecurve.com/yc2.html Check out today’s yield curve. upward slopes of the yield curve as in the “Following the Financial News” box but sometimes other shapes? Besides explaining why yield curves take on different shapes at different times, a good theory of the term structure of interest rates must explain the following three important empirical facts: 1. As we see in Figure 4, interest rates on bonds of different maturities move together over time. 2. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term interest rates are high, yield curves are more likely to slope downward and be inverted. 3. Yield curves almost always slope upward, as in the “Following the Financial News” box. Three theories have been put forward to explain the term structure of interest rates; that is, the relationship among interest rates on bonds of different maturities reflected in yield curve patterns: (1) the expectations theory, (2) the segmented markets theory, and (3) the liquidity premium theory, each of which is described in the following sections. The expectations theory does a good job of explaining the first two facts on our list, but not the third. The segmented markets theory can explain fact 3 but not the other two facts, which are well explained by the expectations theory. Because each theory explains facts that the other cannot, a natural way to seek a better understanding of the term structure is to combine features of both theories, which leads us to the liquidity premium theory, which can explain all three facts. If the liquidity premium theory does a better job of explaining the facts and is hence the most widely accepted theory, why do we spend time discussing the other two theories? There are two reasons. First, the ideas in these two theories provide the CHAPTER 6 The Risk and Term Structure of Interest Rates 129 Interest Rate (%) 16 14 Three-to Five-Year Averages 12 10 8 20-Year Bond Averages 6 4 Three-Month Bills (Short-Term) 2 0 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 F I G U R E 4 Movements over Time of Interest Rates on U.S. Government Bonds with Different Maturities Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15 /data.htm#top. groundwork for the liquidity premium theory. Second, it is important to see how economists modify theories to improve them when they find that the predicted results are inconsistent with the empirical evidence. Expectations Theory The expectations theory of the term structure states the following commonsense proposition: The interest rate on a long-term bond will equal an average of short-term interest rates that people expect to occur over the life of the long-term bond. For example, if people expect that short-term interest rates will be 10% on average over the coming five years, the expectations theory predicts that the interest rate on bonds with five years to maturity will be 10% too. If short-term interest rates were expected to rise even higher after this five-year period so that the average short-term interest rate over the coming 20 years is 11%, then the interest rate on 20-year bonds would equal 11% and would be higher than the interest rate on five-year bonds. We can see that the explanation provided by the expectations theory for why interest rates on bonds of different maturities differ is that short-term interest rates are expected to have different values at future dates. The key assumption behind this theory is that buyers of bonds do not prefer bonds of one maturity over another, so they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity. Bonds that have this characteristic are said to be perfect substitutes. What this means in practice is that if bonds with different maturities are perfect substitutes, the expected return on these bonds must be equal.