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**R. GLENN HUBBARD ANTHONY PATRICK O’BRIEN**

Money, Banking, and the Financial System

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**The Risk Structure and Term Structure of Interest Rates**

5 C H A P T E R The Risk Structure and Term Structure of Interest Rates LEARNING OBJECTIVES After studying this chapter, you should be able to: 5.1 Explain why bonds with the same maturity can have different interest rates 5.2 Explain why bonds with different maturities can have different interest rates

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**The Risk Structure and Term Structure of Interest Rates**

5 C H A P T E R The Risk Structure and Term Structure of Interest Rates WHY INVEST IN TREASURY BILLS IF THEIR INTEREST RATES ARE SO LOW? In February 2010, Moody’s Investors Service hinted that large budget deficits could affect the Aaa rating of government bonds. Also in 2010, Treasure bills offered very low interest rates, yet investors bought them even though Treasury bonds offered much higher rates. In the corporate bond market, investors were also buying bonds with very low yields. In this chapter, we study why these unusual situations occur. An Inside Look at Policy on page 148 describes the testimony before Congress of rating agencies about the ratings of mortgage-backed securities.

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Key Issue and Question Issue: During the financial crisis, the bond rating agencies were criticized for having given high ratings to securities that proved to be very risky. Question: Should the government more closely regulate the credit rating agencies?

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5.1 Learning Objective Explain why bonds with the same maturity can have different interest rates.

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**The Risk Structure of Interest Rates**

Why might bonds that have the same maturities—for example, all the bonds that will mature in 30 years—have different interest rates, or yields to maturity? Four factors account for these differences: Risk Liquidity Information costs Taxation Risk structure of interest rates The relationship among interest rates on bonds that have different characteristics but the same maturity. Default Risk Bonds differ with respect to default risk (sometimes called credit risk), which is the risk that the bond issuer will fail to make payments of interest or principal. The Risk Structure of Interest Rates

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Default Risk Bonds differ with respect to default risk (sometimes called credit risk), which is the risk that the bond issuer will fail to make payments of interest or principal. Measuring Default Risk The default risk premium on a bond is the difference between the interest rate on the bond and the interest rate on a Treasury bond that has the same maturity. Many investors rely on credit rating agencies to provide them with information on the creditworthiness of corporations and governments that issue bonds. Bonds with higher risk will have a higher interest rate. Bond rating A single statistic that summarizes a rating agency’s view of the issuer’s likely ability to make the required payments on its bonds. The Risk Structure of Interest Rates

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**The Risk Structure of Interest Rates**

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**Changes in Default Risk and in the Default Risk Premium**

Figure 5.1 (1 of 2) Determining Default Risk Premium in Yields Investors require a great deal of extra return to compensate them for a very high level of risk on the bond. In other words, the bond’s default risk premium must be very high. The initial default risk premium can be seen by comparing yields associated with the prices P1T and P1C. Because the price of the safer U.S. Treasury bond is greater than that of the riskier corporate bond, we know that the yield on the corporate bond must be greater than the yield on the Treasury bond to compensate investors for bearing risk. The Risk Structure of Interest Rates

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**Changes in Default Risk and in the Default Risk Premium**

Figure 5.1 (2 of 2) Determining Default Risk Premium in Yields As the default risk on corporate bonds increases, in panel (a), the demand for corporate bonds shifts to the left. In panel (b), the demand for Treasury bonds shifts to the right. The price of corporate bonds falls to P2C, and the price of Treasury bonds rises to P2T, so the yield on Treasury bonds falls relative to the yield on corporate bonds. Therefore, the default risk premium has increased.• The Risk Structure of Interest Rates

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**Changes in Default Risk and in the Default Risk Premium**

During recessions, the default risk on corporate bonds typically increases, which can cause a flight to quality. Figure 5.2 (1 of 2) Rising Default Premiums during Recessions The default premium typically rises during a recession. For the 2001 recession, the figure shows a fairly typical pattern, with the spread between the interest rate on corporate bonds and the interest rate on Treasury bonds rising from about 2 percentage points before the recession to more than 3 percentage points during the recession. The Risk Structure of Interest Rates

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**Changes in Default Risk and in the Default Risk Premium**

Note: The corporate bond rate is for Baa-rated bonds. The Treasury bond rate is for 10-year Treasury notes. Figure 5.2 (2 of 2) Rising Default Premiums during Recessions For the 2007–2009 recession, the figure shows that the increase in the default risk premium was much larger. It rose from less than 2 percentage points before the recession began to more than 6 percentage points at the height of the financial crises in the fall of 2008.• The Risk Structure of Interest Rates

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**Do Credit Rating Agencies Have a Conflict of Interest?**

Making the Connection Do Credit Rating Agencies Have a Conflict of Interest? John Moody began the modern bond rating business by publishing Moody’s Analyses of Railroad Investments in 1909. By the 1920s, the work of rating agencies expanded to cover an increasing number of industries. In the post-World War II period, prosperity diminished the role of rating agencies, but by the late 1970s, recession, inflation, and government regulations once again expanded the work of rating agencies. When the rating agencies began charging firms and governments—rather than investors—for their services, a conflict of interest emerged. During the financial crisis, rating agencies came under increased scrutiny. In July 2010, Congress passed the Dodd-Frank Wall Street Reform and Consumer Protection Act, and a new Office of Credit Ratings was created within the Securities and Exchange Commission (SEC) to oversee the work of credit rating agencies. The Risk Structure of Interest Rates

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**Liquidity and Information Costs**

Investors care about liquidity, so they are willing to accept a lower interest rate on more liquid investments than on less liquid—or illiquid—investments, all other things being equal. Similarly, investors care about the costs of acquiring information on a bond. An increase in a bond’s liquidity or a decrease in the cost of acquiring information about the bond will increase the demand for the bond. During the financial crisis of 2007–2009, homeowners were defaulting on many of the mortgages contained in the bonds. To make matters worse, investors came to realize that they did not fully understand these bonds and had difficulty finding information contained in the mortgage-backed bonds. The Risk Structure of Interest Rates

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Tax Treatment Investors care about the after-tax return on their investments—that is, the return the investors have left after paying their taxes. How the Tax Treatment of Bonds Differs Municipal bonds Bonds issued by state and local governments. GE bond: FV = $1,000; coupon = 8%; t = 40%. Then tax = $80 – 80(1 – 0.04) = $32. Coupon after tax: $80 - $32 = $48. Return after tax: $48/$1,000 = 4.8%. Treasury FV = $1,000; coupon = 8%; t = 25%. Then tax = $80 – 80(1 – 0.025) = $20. Coupon after tax: $80 - $20 = $60. Return after tax: $60/$1,000 = 6.0%. The Risk Structure of Interest Rates

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**How the Tax Treatment of Bonds Differs**

The coupons on corporate bonds can be subject to federal, state, and local taxes. The coupons on Treasury bonds are subject to federal tax but not to state or local taxes. The coupons on municipal bonds are typically not subject to federal, state, or local taxes. It is important to recall that bond investors can receive two types of income from owning bonds: (1) interest income from coupons and (2) capital gains (or losses) from price changes on the bonds. Interest income is taxed at the same rates as wage and salary income. Capital gains are taxed at a lower rate than interest income. Capital gains are also taxed only if they are realized, which means that the investor sells the bond for a higher price than he or she paid for it. Unrealized capital gains are not taxed. The Risk Structure of Interest Rates

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**The Effect of Tax Changes on Interest Rates**

Figure 5.3 The Effect of Changes in Taxes on Bond Prices If the federal income tax rate increases, tax-exempt municipal bonds will be more attractive to investors, and Treasury bonds will be less attractive. In panel (a), the demand curve for municipal bonds shifts to the right, from DMuni1 to DMuni2, increasing the price from PM1 to PM2 and lowering the interest rate. In panel (b), the demand curve for Treasury bonds shifts to the left, from DTreas1 to DTreas2, lowering the price from PT1 to PT2 and raising the interest rate.•

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**5.1 How Would a VAT Affect Interest Rates?**

Solved Problem 5.1 How Would a VAT Affect Interest Rates? Suppose the federal government eliminates the federal income tax and replaces it with a VAT. Explain the effect of this policy change on the interest rates on municipal bonds, corporate bonds, and Treasury bonds. Draw three graphs, one for each market, to illustrate your answer. The Risk Structure of Interest Rates

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**5.1 How Would a VAT Affect Interest Rates? Solving the Problem**

Solved Problem 5.1 How Would a VAT Affect Interest Rates? Solving the Problem Step 1 Review the chapter material. Step 2 Analyze the effect of the tax policy change on the interest rate on municipal bonds. The Risk Structure of Interest Rates

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**5.1 How Would a VAT Affect Interest Rates?**

Solved Problem 5.1 How Would a VAT Affect Interest Rates? Solving the Problem (continued) Step 3 Analyze the effect of the tax policy change on the interest rate on corporate bonds. Step 4 Analyze the effect of the tax policy change on the interest rate on Treasury bonds. Step 5 Summarize your findings. Replacing the federal income tax with a VAT would increase the interest rate on municipal bonds and lower the interest rates on corporate bonds and Treasury bonds. The Risk Structure of Interest Rates

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**The Risk Structure of Interest Rates**

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**Is the U.S. Treasury Likely to Default on Its Bonds?**

Making the Connection Is the U.S. Treasury Likely to Default on Its Bonds? Bonds issued by governments are called sovereign debt. Recent examples of sovereign debt defaults include Russia and Argentina. In the nineteenth century, many U.S. states also defaulted on their bonds. Circa 2010, investors feared that several European countries might default on their debt. Investors typically consider U.S. Treasury bonds to be default-risk free, but rating agencies worry that very large projected budget deficits will increase the volume of Treasury bonds issued and that the resulting interest payments will take an ever increasing fraction of the federal budget. Governments can raise taxes or create money to make the interest payments, but these two alternatives can be painful. In 2010, investors in the United States and elsewhere didn’t seem to think that the U.S. Treasury would default on its bonds because they were willing to buy them at interest rates that were too low to include a default premium. The Risk Structure of Interest Rates

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5.2 Learning Objective Explain why bonds with different maturities can have different interest rates.

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**The Term Structure of Interest Rates**

Term structure of interest rates The relationship among the interest rates on bonds that are otherwise similar but that have different maturities. The Treasury yield curve shows the relationship on a particular day among the interest rates on Treasury bonds with different maturities. When short-term rates are lower than long-term rates, we have an upward-sloping yield curve. Infrequently, there are times when short-term interest rates are higher than long-term interest rates, resulting in a downward-sloping yield curve. The Term Structure of Interest Rates

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**The Treasury Yield Curve**

Figure 5.4 The Treasury Yield Curve This figure shows the Treasury yield curves for June 22, 2009, and June 22, 2010.• The Term Structure of Interest Rates

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Figure 5.5 The Interest Rates on 3-Month Treasury Bills and 10-Year Treasury Notes, January 1970–May 2010 The figure shows that most of the time since 1970, the interest rates on 3-month Treasury bills (indicated by the red line) have been lower than the interest rates on 10-year Treasury notes (indicated by the blue line). During a few periods, though, the interest rate on the 3-month Treasury bill has been higher than the interest rate on the 10-year Treasury note.• The Term Structure of Interest Rates

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**Negative Interest Rates on Treasury Bills?**

Making the Connection Negative Interest Rates on Treasury Bills? Can the nominal interest rate ever be negative? A negative nominal interest rate means that the lender is actually paying the borrower interest in return for borrowing the lender’s money. What lender would ever do that? In fact, at times during the Great Depression of the 1930s and again during the financial crisis of 2007–2009, investors were willing to accept negative interest rates on the Treasury bills by paying prices that were higher than the bills’ face values. Because interest rates on other short-term investments, such as bank certificates of deposit or money market mutual fund shares, were also very low, investors were giving up relatively little to temporarily park their funds in default-risk free Treasury bills. The Term Structure of Interest Rates

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**Explaining the Term Structure**

Any explanation of the term structure should be able to account for three important facts: 1. Interest rates on long-term bonds are usually higher than interest rates on short-term bonds. 2. Interest rates on short-term bonds are occasionally higher than interest rates on long-term bonds. 3. Interest rates on bonds of all maturities tend to rise and fall together. Economists have advanced three theories to explain these facts: the expectations theory, the segmented markets theory, and the liquidity premium theory or preferred habitat theory. We examine these theories next. The Term Structure of Interest Rates

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**The Expectations Theory of the Term Structure**

Expectations theory A theory of the term structure of interest rates that holds that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bond. The two key assumptions of the expectations theory are: 1. Investors have the same investment objectives. 2. For a given holding period, investors view bonds of different maturities as being perfect substitutes for one another. That is, holding a 10-year bond for 10 years is the same to investors as holding a five-year bond for five years and another five-year bond for a second five years. The Term Structure of Interest Rates

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**The Expectations Theory Applied in a Simple Example**

Suppose that you intend to invest $1,000 for two years and are considering one of two strategies: The buy-and-hold strategy. With this strategy, you buy a two-year bond and hold it until maturity. After two years, the $1,000 investment will have grown to $1,000(1 + i2t)(1 + i2t). The rollover strategy. With this strategy, you buy a one-year bond today and hold it until it matures in one year. At that time, you buy a second one-year bond, and you hold it until it matures at the end of the second year. After two years, you will expect your $1,000 investment to have grown to $1,000(1 + i1t) (1 + ie it+1). With the rollover strategy, you must form an expectation of what the interest rate on the one-year bond will be. We will assume that this is a two-year discount bond. This simplification allows us to avoid having to deal with coupon payments, although the result would not change if we added that complication. The Term Structure of Interest Rates

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**The Expectations Theory Applied in a Simple Example**

A key point to understand is that under the assumptions of the expectations theory, the returns from the two strategies must be the same. Arbitrage should result in the returns from the two strategies being the same. Therefore, we can write: This equality can be reduced to: This equation tells us that the interest rate on the two-year bond is an average of the interest rate on the one-year bond today and the expected interest rate on the one-year bond one year from now. Generally, the interest rate on an n-year bond—where n can be any number of years—is equal to: $1, 𝑖 2𝑡 1+ 𝑖 2𝑡 =$1, 𝑖 1𝑡 1+ 𝑖 1𝑡+1 𝑒 . 𝑖 2𝑡 = 𝑖 1𝑡 + 𝑖 1𝑡+1 𝑒 2 . 𝑖 𝑛𝑡 = 𝑖 1𝑡 + 𝑖 1𝑡+1 𝑒 + 𝑖 1𝑡+2 𝑒 + 𝑖 1𝑡+3 𝑒 𝑖 1𝑡+(𝑛−1 𝑒 𝑛 . The Term Structure of Interest Rates

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**Interpreting the Term Structure Using the Expectations Theory**

The term structure provides us with information on what bond investors must expect to happen to short-term rates in the future. For example, if i1t = 2% and i2t = 3%, then 𝑖 1𝑡+1 𝑒 = 2(3%) – 2% = 4%. Similarly, we can calculate the expected one-year rate two years from now, using the expected one-year rate one year from now that we just calculated: 3%= 2%+ Expected one−year rate one year from now 2 =4% 4%= 2% + 4% + Expected one−year rate one year from now 3 =6% The Term Structure of Interest Rates

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**Interpreting the Term Structure Using the Expectations Theory**

More generally, according to the expectations theory: An upward-sloping yield curve is the result of investors expecting future short-term rates to be higher than the current short-term rate. A flat yield curve is the result of investors expecting future short-term rates to be the same as the current short-term rate. A downward-sloping yield curve is the result of investors expecting future short-term rates to be lower than the current short-term rate. The Term Structure of Interest Rates

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**(c) fall relative to current levels.•**

Figure 5.6 Using the Yield Curve to Predict Interest Rates: The Expectations Theory Under the expectations theory, the slope of the yield curve shows that future short-term interest rates are expected to (a) rise, (b) remain the same, or (c) fall relative to current levels.• The Term Structure of Interest Rates

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**Shortcomings of the Expectations Theory**

The expectations theory explains an upward-sloping yield curve as being the result of investors expecting future short-term rates to be higher than the current short-term rate. But if the yield curve is typically upward sloping, investors must be expecting short-term rates to rise most of the time. This explanation seems unlikely because at any particular time, short-term rates are about as likely to fall as to rise. The Term Structure of Interest Rates

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**5.2a Is There Easy Money to Be Made from the Term Structure?**

Solved Problem 5.2a Is There Easy Money to Be Made from the Term Structure? The term interest carry trade is sometimes used to refer to borrowing at a low short-term interest rate and using the borrowed funds to invest at a higher long-term interest rate. a. How would you advise an investor who is thinking of following a carry trade strategy? What difficulties would you point out in the strategy? b. If the yield curve was inverted, or downward sloping, would a carry trade strategy still be possible? Briefly explain. The Term Structure of Interest Rates

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**5.2a Is There Easy Money to Be Made from the Term Structure?**

Solved Problem 5.2a Is There Easy Money to Be Made from the Term Structure? Solving the Problem Step 1 Review the chapter material. Step 2 Use the expectations theory of the term structure to answer the questions in part (a). If the expectations theory is correct, the average of the expected short-term interest rates over the life of a long-term investment should be roughly equal to the interest rate on the long-term investment, which would wipe out any potential profits from the interest carry trade. Moreover, if interest rates rise more rapidly than expected, the price of the long-term investment will decline, and the investor will suffer a capital loss. Step 3 Answer part (b) by explaining whether the interest carry trade would still be possible if the yield curve were inverted. If the yield curve were inverted, with long-term rates lower than short-term rates, an institutional investor could borrow long term and invest the funds at the higher short-term rates. In this case, the investor would be subject to reinvestment risk, or the risk that after the short-term investment has matured, the interest rate on new short-term investments will have declined. The Term Structure of Interest Rates

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**The Segmented Markets Theory of the Term Structure**

Segmented markets theory A theory of the term structure of interest rates that holds that the interest rate on a bond of a particular maturity is determined only by the demand and supply of bonds of that maturity. The segmented markets theory addresses the shortcomings of the expectations theory by making two related observations: 1. Investors in the bond market do not all have the same objectives. 2. Investors do not see bonds of different maturities as being perfect substitutes for each other. Markets for bonds of different maturities are separated from each other, or segmented. Investors who participate in the market for bonds of one maturity do not participate in markets for bonds of other maturities. The Term Structure of Interest Rates

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**The Segmented Markets Theory of the Term Structure**

Relative to short-term bonds, long-term bonds have two shortcomings: They are subject to greater interest-rate risk, and they are often less liquid. The reason why the yield curve is typically upward sloping is that more investors are in the market for short-term bonds, causing their prices to be higher and their interest rates lower, and fewer investors are in the market for long-term bonds, causing their prices to be lower and their interest rates higher. The segmented markets theory, however, cannot explain why short-term interest rates would ever be greater than long-term interest rates (a downward-sloping yield curve), or why interest rates of all maturities tend to rise and fall together. The Term Structure of Interest Rates

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**The Liquidity Premium Theory**

Liquidity premium theory (or preferred habitat theory) A theory of the term structure of interest rates that holds that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bond, plus a term premium that increases in value the longer the maturity of the bond. Term premium The additional interest investors require in order to be willing to buy a long-term bond rather than a comparable sequence of short-term bonds. The Term Structure of Interest Rates

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**The Liquidity Premium Theory**

In effect, then, the liquidity premium theory adds a term premium to the expectations theory’s equation linking the interest rate on a long-term bond to the interest rate on short-term bonds. 𝑖 2𝑡 = 𝑖 1𝑡 + 𝑖 1𝑡+1 𝑒 2 + 𝑖 2𝑡 𝑇𝑃 , where is the term premium on a two-year bond. 𝑖 2𝑡 𝑇𝑃 Or, more generally, the interest rate on an n-period bond is equal to: 𝑖 𝑛𝑡 = 𝑖 1𝑡 + 𝑖 1𝑡+1 𝑒 + 𝑖 1𝑡+2 𝑒 + 𝑖 1𝑡+3 𝑒 𝑖 1𝑡+(𝑛−1 𝑒 𝑛 + 𝑖 2𝑡 𝑇𝑃 . The Term Structure of Interest Rates

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Solved Problem 5.2b Using the Liquidity Premium Theory to Calculate Expected Interest Rates? Using the table above, what did investors expect the interest rate to be on the one-year Treasury bill two years from that time if the term premium on a two-year Treasury note was 0.05% and the term premium on a three-year Treasury note was 0.10%? The Term Structure of Interest Rates

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Solved Problem 5.2b Using the Liquidity Premium Theory to Calculate Expected Interest Rates? Solving the Problem Step 1 Review the chapter material. Step 2 Use the liquidity premium equation that links the interest rate on a long-term bond to the interest rates on short-term bonds to calculate the interest rate that investors expected on the one-year Treasury bill one year from February 19, 2010. Step 3 Answer the problem by using the result from step 2 to calculate the interest rate investors expected on the one-year Treasury bill two years from February 19, 2010. 𝑖 2𝑡 =0.95%= 0.39%+ 𝑖 1𝑡+1 𝑒 %, or, 𝑖 1𝑡+1 𝑒 =1.41% 𝑖 3𝑡 =1.51%= 0.39%+1.41%+ 𝑖 1𝑡+2 𝑒 %, or, 𝑖 1𝑡+2 𝑒 =2.43% The Term Structure of Interest Rates

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**The Term Structure of Interest Rates**

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**Using the Term Structure to Forecast Economic Variables**

The slope of the yield curve shows the short-term interest rates that bond market participants expect in the future. In addition, if fluctuations in expected real interest rates are small, the yield curve contains expectations of future inflation rates. For example, If the real interest rate is expected to remain constant, you can interpret an upward-sloping yield curve to mean that inflation is expected to rise, leading investors to expect higher nominal interest rates. Economists and market participants also look to the slope of the yield curve to predict the likelihood of a recession. Models of the term structure reveal that in every recession since 1953, the term spread has narrowed significantly. That is, the yield on the 10-year Treasury note has declined significantly relative to the yield on the 3-month Treasury bill. The Term Structure of Interest Rates

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**Using the Term Structure to Forecast Economic Variables**

Figure 5.7 Interpreting the Yield Curve Models of the term structure, such as the liquidity premium theory, help analysts use data on the Treasury yield curve to forecast the future path of the economy.• The Term Structure of Interest Rates

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**Using the Term Structure to Forecast Economic Variables**

During recessions, interest rates typically fall, and short-term rates tend to fall more than long-term rates. In this situation, the liquidity premium theory of the term structure predicts that long-term rates should fall relative to short-term rates, making the yield curve inverted. The Term Structure of Interest Rates

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**Answering the Key Question**

At the beginning of this chapter, we asked the question: “Should the government more closely regulate credit rating agencies?” Like other policy questions we will encounter in this book, this question has no definitive answer. During the financial crisis of 2007–2009, many bonds had much higher levels of default risk than the credit rating agencies had indicated. Some observers argued that the rating agencies had a conflict of interest in being paid by the firms whose bond issues they rate. Other observers, though, argued that the ratings may have been accurate when given, but the creditworthiness of the bonds declined rapidly following the unexpected severity of the housing bust and the resulting financial crisis.

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**AN INSIDE LOOK AT POLICY**

Executives from Moody’s, Standard and Poor’s Describe Pressure to Grant High Ratings LOS ANGELES TIMES, Credit Rating Executives Say They Were Pressured to Give Good Ratings Key Points in the Article In 2008, Congress investigated allegations of pressure on the rating agencies to grant investment-grade ratings to certain financial instruments. The conflict of interest started back in the 1970s, when rating agencies switched from selling ratings to investors to selling ratings to the firms whose bonds they rated. Credit agencies provided the Congressional subcommittee with evidence of extensive downgrading of mortgage-backed securities between 2004 and 2007. After downgrading those securities, their price fell and the yields rose. Investors increased their demand for safer Treasury bonds, causing their prices to rise and yields to fall.

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**AN INSIDE LOOK AT POLICY**

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Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 6 The Risk and Term Structure of Interest Rates.

Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 6 The Risk and Term Structure of Interest Rates.

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