m05_hubb3538_1e_im_c05 (1)

Chapter 5The Risk Structure and Term Structure of Interest Rates

Brief Chapter Summary and Learning Objectives

5.1 The Risk Structure of Interest Rates (pages 124–134)Explain why bonds with the same maturity can have different interest rates. Bonds that have the same maturity may differ with respect to other characteristics that investors

believe are important, such as risk, liquidity, information costs, and taxation. Bonds with more favorable characteristics have lower interest rates because investors are willing

to accept lower expected returns on those bonds.

5.2 The Term Structure of Interest Rates (pages 135–147)Explain why bonds with different maturities can have different interest rates. The liquidity premium theory, the most complete theory of the term structure, 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.

The slope of the yield curve shows the short-term interest rates that bond market participants expect in the future and can be used to help forecast inflation and economic activity.

Key Terms and Concepts

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.

Default risk (or credit risk) The risk that the bond issuer will fail to make payments of interest or principal.

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.

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

Municipal bonds Bonds issued by state and local governments.

Risk structure of interest rates The relationship among interest rates on bonds that have different characteristics but the same maturity.

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.

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.

Term structure of interest rates The relationship among the interest rates on bonds that are otherwise

© 2012 Pearson Education, Inc. Publishing as Prentice Hall

47 Hubbard & O’Brien • Money, Banking, and the Financial System, First Edition

in value the longer the maturity of the bond. similar, but that have different maturities.

Chapter Outline

Why Invest in Treasury Bills if Their Interest Rates are So Low?

The three largest rating credit rating agencies are Moody’s Investors Service, Standard & Poor’s Corporation, and Fitch Ratings. The U.S. government’s projected large budget deficits caused Moody’s to announce in early 2010 that the government’s bond rating would be reduced. Table 5.1 on page 125 summarizes the bond ratings for each credit agency.

5.1 The Risk Structure of Interest Rates (pages 124–134)

Learning Objective: Explain why bonds with the same maturity can have different interest rates.A. Default Risk

Bonds with a higher default risk, the risk that the bond issuer will fail to make payments of interest and principal, pay higher interest rates. 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 with the same maturity. An increased perceived risk of default leads to a decline in the demand for a bond, resulting in a lower price and higher interest rate. During recessions, investors seek safety, leading to an increase in the demand for U.S. Treasury bonds and a decrease in the demand for corporate bonds, resulting in a higher risk premium for corporate bonds.

Teaching Tips

At the height of the financial crisis in the fall of 2008, the default risk premium for bonds of companies rated Baa by Moody’s surpassed 6%, higher than any time since the 1930s. Have students discuss how this can be used as a measure of the severity of the financial crisis (i.e., difficulty of investment-grade corporations in obtaining credit).

B. Liquidity and Information CostsAn 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, resulting in a higher price and a lower interest rate.

C. Tax TreatmentInvestor’s care about the after-tax return on their investments; that is, the return the investors have left after paying their taxes. Other things equal, a bond that is not subject to taxes pays a lower interest rate than one that is taxable. The coupons on municipal bonds are typically not subject to federal, state, or local taxes. The coupons on Treasury bonds are subject to federal tax, but not to state or local taxes. The coupons on corporate bonds can be subject to federal, state, and local taxes.

5.2 The Term Structure of Interest Rates (pages 135–147)

Learning Objective: Explain why bonds with different maturities can have different interest rates.A. Explaining the Term Structure

One way to analyze the term structure is by looking at the Treasury yield curve, which is the relationship on a particular day among the interest rates on Treasury bonds of different maturities. See Figure 5.4 on page 135 for the Treasury yield curve for 2009 and 2010. Any explanation of the term structure should be able to account for three important facts: Interest rates on long-term bonds are usually higher than interest rates on short-term bonds. Interest rates on short-term bonds are occasionally higher than interest rates on long-term


Chapter 5 The Risk Structure and Term Structure of Interest Rates 48

bonds. Interest rates on bonds of all maturities tend to rise and fall together.



B. The Expectations Theory of the Term StructureThe expectations theory holds that the interest rates 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. Since interest rates on long-term bonds are usually higher than interest rates on short-term bonds, the expectations theory implies that future short-term rates are typically expected to rise at any particular point in time, which is unrealistic.

C. The Segmented Markets Theory of the Term StructureThe segmented markets theory assumes bonds of different maturity are in separate markets. Factors that affect the demand for Treasury bills or other short-term bonds will have no effect on the demand for Treasury bonds or other long-term bonds. Since long-term bonds carry higher interest-rate risk and tend to be less liquid, investors need to be compensated by receiving higher interest rates on long-term bonds than on short-term bonds. The segmented markets theory fails to explain why short-term interest rates are sometimes higher than long-term interest rates as well as why interest rates tend to move together.

D. The Liquidity Premium TheoryThe liquidity premium theory 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.

E. Using the Term Structure to Forecast Economic VariablesThe slope of the yield curve shows the short-term interest rates that bond market participants expect in the future. If fluctuations in expected real interest rates are small, the yield curve contains expectations of future inflation rates. The yield curve can also indicate likely future economic activity. With only one exception, every time the yield on the 3-month bill was higher than the yield on the 10-year note, a recession followed within a year.

Table 5.4 on page 145 summarizes and compares the three theories of term structure of interest rates: expectations theory, segmented markets theory, and liquidity premium theory.

Teaching Tips

In the summer of 2010, some commentators expressed fear of rapidly increasing inflation in the next few years. Meanwhile, interest rates are long-term bonds, such as the five-year and ten-year Treasury bonds, were about 1.5% and 3%, respectively. Have students discuss what this implies about the bond markets’ view of future inflation. Are low interest rates on bonds consistent with expectations of rapidly increasing inflation?



Solutions to the End-of-Chapter Questions and Problems

Answers to Thinking Critically Questions

1. The downgrading of the credit ratings increased the default risk on the affected securities. Information costs were also affected; so long as the rating agencies are paid for their services by the firms that issue securities, investors are likely to spend more resources evaluating securities rather than to simply trust the ratings. Bond yields rise as default risk and information costs rise.

2. Although the conflict of interest was in place in the 1970s, it was not until the 2000s that the popularity of credit ratings of mortgage-backed securities became widespread. These securities were more difficult to evaluate than traditional bonds. There were substantial financial rewards for granting the securities investment grade ratings. Rather than develop new, more accurate ratings models, firms succumbed to the pressure to give their clients the ratings they wanted.

5.1 The Risk Structure of Interest Rates

Learning objective: Explain why bonds with the same maturity can have different interest rates.

Review Questions

1.1 The risk structure of interest rates is the relationship among the interest rates on bonds that have different characteristics but the same maturity. The differences between interest rates among bonds with the same maturities exists because of different default risk, liquidity, information costs, and taxation.

1.2 Default risk is the risk that the bond issuer will fail to make payments of interest and principal. The default risk is measured as the difference between the interest rate on the bond and the interest rate on a U.S. Treasury bond with the same maturity.

1.3 A bond issuer’s creditworthiness is the projected rating of a company’s or a government’s ability to pay off the bond. A bond rating is a rating assigned to a company or a government that rates its creditworthiness. The major credit rating agencies are Moody’s Investors Service, Standard and Poor’s Corporation, and Fitch Ratings.

1.4 When a company’s rating is lowered, there is less demand for the bond, shifting the demand curve to the left. This lowers price and increases the yield.



1.5 Investors favor liquidity, so a bond that is not liquid would have less demand compared to an equivalent bond with more liquidity. This would mean a lower price for the illiquid bond and a higher yield. A bond with high information costs would have lower demand than an equivalent bond that has lower information costs. Investors favor full information, so this would push the price of the high information cost bond down and the yield up.

1.6 Interest income from coupons and capital gains/losses from price changes. Capital gains are taxed at the income tax rate (within one year) and at a lower rate (capital gains tax) if held for more than one year. Coupon payments are taxed at the income tax rate.

1.7 The bond issued by Houston is a municipal bond and its coupons are not subject to federal, state, or local taxes. The bond issued by GE is a corporate bond and its coupons are subject to federal taxes, and typically to state and local taxes. The coupons of the U.S. Treasury bond are subject to federal tax, but not state or local taxes.

Problems and Applications

1.8 a “Obligations” refers to the obligation the bond issuer has to pay the bond holder.b. Credit risk is the risk of default.

1.9. a. A municipal bond is a bond issued by a state or local government. b. Municipal bonds have different tax treatments and different ways of measuring default risk.

1.10 The profitability of Republic Services 30 years from now is more uncertain than its profitability 10 years from now.

1.11 The bond ratings model relies on the rating agencies to rate bonds and to charge firms for the service of viewing the bond ratings. This creates a conflict of interest because a large firm that pays the rating agencies may have a large investment in a company that the rating agencies are supposed to downgrade. The rating agencies, because of the fee-for-service model, have an incentive to provide ratings that their customers–the large firms–want.

1.12 Managers of firms may have more incentive to take risk than the bond holder would desire. The manager may have a bonus tied to performance and may value higher risk than the bond holder values. Rating agencies bridge the information asymmetry gap between investors and firm managers.

1.13 Taxing the coupon reduces the after-tax coupon paid to the bond purchaser. This makes the bond less desirable. This would reduce the price and increase the yield.

1.14 The rise in the top marginal tax rate on the federal personal income tax would increase the desirability of holding municipal bonds. As a result, the demand curve for municipal bonds will shift to the right, increasing their price. The tax on income from U.S. Treasury bonds will increase. This will cause the demand curve for U.S. Treasury bonds to shift to the left, decreasing their price.



1.15 a. The price of the bonds tumbled because of the risk of default. b. Because the Romanian government could not take steps to solve their budget crisis, the risk of

default on their bonds increased.

1.16 With higher budget deficits, debt accumulates and the potential for default increases. A lower rating would lower Treasury bond prices and raise yields.

1.17 An increase in risk of default would shift demand for Treasury bonds to the left pushing price down and yield up.



1.18 a. Junk status is a low credit rating from the credit agencies. Greek debt are bonds that Greece sells to finance its budget deficits.

b. The spread is the difference in yield (6.71%) from a safe bond (Germany) and the bond in question (Greece). The spread represents the risk premium.

1.19 Bob’s bond would be better because only the 3% interest income is taxed, not the 4% capital gain. Bob’s after-tax return would equal 0.03(1 0.33) 0.04 0.0601 or 6.01%. Juanita’s after-tax return would equal 0.08(1 0.33) 0.0536 or 5.36%.

1.20 The coupon on the state bond will not be subject to tax, so its pre-tax yield will also be 8%. The pre-tax yield on the federal perpetuity equals 0.08/(1 0.396) 0.1325 or 13.25%.

1.21 A junk bond is a bond with a high level of default risk. The yields of junk bonds will rise at the bottom of a business cycle because of the increase in default risk that an economic downturn brings. The yields will fall as the economy recovers and default is less likely.

5.2 The Term Structure of Interest RatesLearning objective: Explain why bonds with different maturities can have different interest rates.

Review Questions

2.1 The term structure of interest rates is the relationship among the interest rates on bonds that are otherwise similar, but differ in maturity. The Treasury yield curve graphically illustrates the term structure of interest rates by illustrating for a particular day the interest rates on treasury bonds of different maturities.



2.2 The three key facts about the term structure are 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; and 3) interest rates on bonds of all maturities tend to rise and fall together.

2.3 The three theories of the term structure are: 1) Segmented market theory: Holds that the market for bonds of different maturities are completely separated from each other. 2) Liquidity premium theory: Holds that interest rates on long-term bonds are averages of the expected interest rates on short-term bonds plus a term premium. 3) Expectations theory: Holds that interest rates on long-term bonds are an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bond.

Problems and Applications

2.4 Consider what a $1 investment in each option would equal after three years:

Option (a) (1.08)(1.11)(1.07) $1.282

Option (b) (1.1)(1.1)(1.07) $1.295

Option (c) (1.085)3 1.277.

Option (b) offers the highest return.

2.5 a. $1,000(1.064) $1262.48b. $1,000(1.0553)(1.09) $1,279.92c. $1,000(1.052)(1.07)(1.09) $1,285.85d. $1,000(1.04)(1.065)(1.07)(1.09) $1,291.79.

You should choose option (d).

2.6 2-year: (3 4)/2 3.5%

3-year: (3 4 5)/3 4%

4-year: (3 4 5 3)/4 3.75%

2.7 Investors would buy a Treasury bill instead of a Treasury bond because of the potential default risk (which increases the longer the maturity), the threat of price depreciation if interest rates rise, and the desire for liquidity.

2.8 A carry trade (interest carry trade) refers to borrowing at a low short-term interest rate and using the borrowed funds to invest at a higher long-term interest rate. With the expectations theory, the average of the expected short-term interest rates over the life of the long-term investment should be roughly equal to the interest on the long-term investment, which would wipe out any potential profits from the interest carry trade. Moreover, if interest rates rise more than expected, the price of the long-term investment will decline, and the investor will suffer a capital loss.

2.9 The Treasury would be subject to borrowing risk, in that after the short-term bills have matured, the interest on new short-term bills may have risen. The much higher interest rates on Treasury notes and bonds are because the market expects future short-term interest rates to rise.



2.10 Expected real interest rate = nominal interest rate minus expected inflation rate. The nominal yield is 1%, the inflation rate is negative 2%, hence the expected real return should be 1%.

2.11 Investors expected the one-year interest rate on Treasury bills in two years to be 2.33%. They expected the one-year interest rate on Treasury bills in one year to be 1.4%.



2.12 a. It would matter because in the past inverted yield curves had very high short-term interest rates, which have a negative effect on economic growth. In this period when the yield curve is inverted, short-term rates are low.

b. The structural fall in the term premium refers to the fall in the additional interest an investor requires to purchase a long-term bond rather than a short-term bond. A structural fall in the term premium would flatten the yield curve itself, independent of any effect of an expected recession.

c. No, Chairman Bernanke’s interpretation was wrong in the sense that a severe recession started December of 2007.

2.13. a. An inverted yield curve.b. Because the market must expect future short-term interest rates to fall and long-term

bonds include a term premium.

2.14 There is a risk of default, but treasury bonds compared to any other investment are the safest possible asset. Other types of risk are a probable cause in this article and include interest rate risk, the risk of prices falling, and the opportunity cost of being in bonds when other markets (equities) rally.

2.15 The short end of the yield curve shifts up, and the long end of the yield curve shifts down, as shown in the graph below.

2.16 An upward-sloping yield curve implies healthy economic conditions. According to expectations theory, an upward-sloping yield curve indicates that investors expect interest rates to rise. The expectation that interest rates will rise means that people expect stronger economic conditions, and hence no recession.

2.17 a. Proxy means “in place of.” Generally speaking, the two-year Treasury note market will reflect the current thinking about economic conditions. This will provide evidence for what the Federal Reserve will do to the Fed Funds rate.



b. Bond traders bid the price of bonds to adjust to what the expectation of the Fed Funds rate will be. This creates arbitrage profits because as traders buy and sell bonds based on the expectations of what the Federal Reserve will do, they will capture the capital gains when the Federal Reserve actually makes its move.



Data Exercises

D5.1 Short-term rates were higher than long-term rates in the mid-1970s, as well as the early 1980s.

D5.2 On November 24, 2010, the yield curve had a steep slope with the one-year Treasury bill yield of 0.25 and the 30-year Treasury bond yield of 4.22. Concerns about inflation and government budget deficits kept expected future short-term interest rates relatively high pushing up current long-term rates.


m05_hubb3538_1e_im_c05 (1)

Documents

rates investors

term structure

municipal bonds bonds

risk structure

rates pages

longterm bond

term premium

supply of bonds