2. 1 The Risk and Term Structure of Interest Rates Chapter 6

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4. 3 Why Do Bonds With Same Maturity Have Different Prices? Some might be riskier than others. Some might be riskier than others. Some might be more liquid than others. Some might be more liquid than others. Some might have lower taxes than others. Some might have lower taxes than others. Collectively, these influences are called “risk structure of interest rates.” Collectively, these influences are called “risk structure of interest rates.” Of course, if prices of various bonds differ so do their yield to maturity. Of course, if prices of various bonds differ so do their yield to maturity.

5. 4 Risk Structure of Interest Rates Default risk - inability of the bond issuer to pay interest or face value. Default risk - inability of the bond issuer to pay interest or face value. Liquidity risk - inability to find a buyer when one decides to sell her bond before it matures. Liquidity risk - inability to find a buyer when one decides to sell her bond before it matures. Income tax - interest earnings on municipal bonds are free from federal income tax. Income tax - interest earnings on municipal bonds are free from federal income tax.

6. 5 Default Risk US Treasury bonds are risk free. US Treasury bonds are risk free. Congress can raise taxes. Congress can raise taxes. Federal government can print money. Federal government can print money. The interest difference between a default- free bond and one with default risk is called “risk premium.” The interest difference between a default- free bond and one with default risk is called “risk premium.” Buyers of bonds have to get higher interest bonds (lower price bonds) to persuade them to buy the riskier bonds. Buyers of bonds have to get higher interest bonds (lower price bonds) to persuade them to buy the riskier bonds.

7. 6 Long-Term Bond Yields, 1919–2008 Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941– 1970; Federal Reserve: www.federalreserve.gov/releases/h15/data.htm www.federalreserve.gov/releases/h15/data.htm.

8. 7 Why Do Similar Bonds With Different Maturities Have Different Prices? Two bonds could be identical in their risk structure but they may have different yield to maturity if their maturities differ. Two bonds could be identical in their risk structure but they may have different yield to maturity if their maturities differ. This is called “term structure of interest rates.” This is called “term structure of interest rates.”

9. 8 Interest Rates on U.S. Government Bonds with Different Maturities Sources: Federal Reserve: www.federalreserve.gov/releases/h15/data.htm www.federalreserve.gov/releases/h15/data.htm.

10. 9 Increase in Default Risk on Corporate Bonds

11. 10 Application: The Subprime Collapse and the Baa-Treasury Spread

12. 11 Series 1 is Moody’s Baa Corporate Bond Yield. Series 2 is 1-yr Treasury Constant Maturity Rate. Series 3 is the difference between the two. Source: http://www.stls.frb.org/fred/data/irates.html (Discontinued).http://www.stls.frb.org/fred/data/irates.html

13. 12 http://research.stlouisfed.org/fred2/ categories/22/1 During the 2001 recession, Baa yields fell from 8.5% to 8%; treasuries fell from 6% to below 4%, adding 3.5% to the risk premium.

14. 13 Decline in Corporate Bond Risk P1 Q of US bondsQ of corporate bonds P2 White arrow shows the risk premium initially. Red arrow is the new risk premium.

15. 14 Risk Premium During recessions default risk generally rises. During recessions default risk generally rises. Rating agencies evaluate single companies and issue a rating indicating the default risk of the company’s bonds. Rating agencies evaluate single companies and issue a rating indicating the default risk of the company’s bonds. Rating agencies also evaluate the default risk of foreign bonds. Rating agencies also evaluate the default risk of foreign bonds.

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17. 16 http://www.economist.com/finance/displaystory.cfm?story_id=8628827

18. 17 Liquidity The more liquid an asset is, the quicker and cheaper it can be converted to cash. The more liquid an asset is, the quicker and cheaper it can be converted to cash. Cheaper means lower transaction cost. Cheaper means lower transaction cost. The more liquid an asset is the higher the demand for it. The more liquid an asset is the higher the demand for it. What happens to the risk premium if corporate bonds become less liquid? What happens to the risk premium if corporate bonds become less liquid?

19. 18 Corporate Bonds Become Less Liquid Q of Corporate BondsQ of T-bonds i i i i P P Initially, corporate bond market and T-bond market are at equilibrium at the intersection of white S and D. Corporate bonds have lower P and higher I. Less liquidity increases the D for T- bonds and reduces the D for corporate bonds. Interest rates on corporate bonds rise, on T-bonds fall.

20. 19 Municipal Bonds Municipal bonds have lower interest rates than T-bonds. Municipal bonds have lower interest rates than T-bonds. Municipal bonds are not risk-free. Municipal bonds are not risk-free. Cleveland defaulted in early 1970s. Cleveland defaulted in early 1970s. New York defaulted in late 1970s. New York defaulted in late 1970s. Orange County, California defaulted in 1994. Orange County, California defaulted in 1994. Is there a contradiction? Is there a contradiction?

21. 20 Tax Advantage of Municipal Bonds Earnings from municipal bonds are exempt from federal income tax. Earnings from municipal bonds are exempt from federal income tax. A person at 33% income tax bracket can earn a higher after-tax return from a riskier municipal bond than a risk-free T-bond. A person at 33% income tax bracket can earn a higher after-tax return from a riskier municipal bond than a risk-free T-bond. $1000 face-value T-bond with 10% coupon rate selling for $1000 would yield $67 after-tax income to this person. $1000 face-value T-bond with 10% coupon rate selling for $1000 would yield $67 after-tax income to this person. $1000 face-value muni-bond with 8% coupon rate selling for $1000 would yield $80 after-tax income to this person. $1000 face-value muni-bond with 8% coupon rate selling for $1000 would yield $80 after-tax income to this person.

22. 21 The Effect of Tax Elimination on Municipal Bonds Q of Muni Bonds Q of T-bonds P P i i Assuming similar risk and liquidity we start with same P and i. Eliminating taxes for munis would increase the demand for them, While reducing the demand for T-bonds. i P

23. 22 What Would Happen If the Top Tax Rate Were Increased? D for munis will increase. D for munis will increase. D for T-bonds will decrease. D for T-bonds will decrease. P of munis will rise. P of munis will rise. P of T-bonds will drop. P of T-bonds will drop. Interest rates on munis will fall. Interest rates on munis will fall. Interest rates on T-bonds will rise. Interest rates on T-bonds will rise.

24. 23 Term Structure of Interest Rates Bonds with identical risk, liquidity and tax considerations may have different interest rates because of their maturity. Bonds with identical risk, liquidity and tax considerations may have different interest rates because of their maturity. Typically, bonds with maturity far into the future have higher interest rates than bonds that will mature soon. Typically, bonds with maturity far into the future have higher interest rates than bonds that will mature soon.

25. 24 Yield Curves Yields of different maturity but identical risk, liquidity, tax characteristics are plotted. Yields of different maturity but identical risk, liquidity, tax characteristics are plotted. Yield curves typically move upwards, but sometimes they are flat or downward sloping. Yield curves typically move upwards, but sometimes they are flat or downward sloping. When short term interest rates are high yield curves may be inverted. When short term interest rates are high yield curves may be inverted. Yield curves at different dates usually show that short and long term interest rates move up and down together. Yield curves at different dates usually show that short and long term interest rates move up and down together.

26. 25 Term-structure of Interest Rates Source: http://www.stls.frb.org/docs/publications/mt/2000/cover4.pdfhttp://www.stls.frb.org/docs/publications/mt/2000/cover4.pdf

27. 26 Term Structure of Interest Rates Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different Yield curve—a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations Yield curve—a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations Upward-sloping  long-term rates are above short-term rates Upward-sloping  long-term rates are above short-term rates Flat  short- and long-term rates are the same Flat  short- and long-term rates are the same Inverted  long-term rates are below short-term rates Inverted  long-term rates are below short-term rates

28. 27 Facts 1. 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 rates are high, yield curves are more likely to slope downward and be inverted 3. Yield curves almost always slope upward

29. 28 Explaining Yield Curves The expectations theory The expectations theory The segmented markets theory The segmented markets theory The liquidity premium theory The liquidity premium theory

30. 29 Expectations Theory Explains why interest rates move together. Explains why interest rates move together. Explains why when short-term interest rates are low, yield curves are more likely to be upward sloping. Explains why when short-term interest rates are low, yield curves are more likely to be upward sloping. Explains why when short-term interest rates are high, yield curves are more likely to be downward sloping. Explains why when short-term interest rates are high, yield curves are more likely to be downward sloping. Doesn’t explain why yield curves are usually upward sloping. Doesn’t explain why yield curves are usually upward sloping.

31. 30 Expectations Theory Assume bonds with different maturities are perfect substitutes. Assume bonds with different maturities are perfect substitutes. Demand for bonds with higher yield will be higher. Demand for bonds with higher yield will be higher. Their prices will go up and their yields will decline. Their prices will go up and their yields will decline. Yields on different maturity bonds will be equal. Yields on different maturity bonds will be equal. How can you have an upward (or downward) sloping yield curve if the expected yields on different maturity bonds is the same? How can you have an upward (or downward) sloping yield curve if the expected yields on different maturity bonds is the same?

32. 31 An Example Suppose you consider to save your funds for a period of four years. Suppose you consider to save your funds for a period of four years. You can put these funds in a four-year bond or you can put them in four successive one-year bonds. You can put these funds in a four-year bond or you can put them in four successive one-year bonds. Expectations theory says the returns from these two choices should be the same. Expectations theory says the returns from these two choices should be the same. If the expected yearly returns for the next four years are 6%, 7%, 8%, and 9%, then the return on the four-year bond should be 7.5%. If the expected yearly returns for the next four years are 6%, 7%, 8%, and 9%, then the return on the four-year bond should be 7.5%.

33. 32 Expectations Theory If short term interest rates have been inching up (down), people will expect them to increase (decrease) in the future, too. If short term interest rates have been inching up (down), people will expect them to increase (decrease) in the future, too. Short and long-term rates will move together. Short and long-term rates will move together. If short-term rates are unusually high (low), people will expect them to move down (up) in the future. If short-term rates are unusually high (low), people will expect them to move down (up) in the future. Inverted (regular) yield curve. Inverted (regular) yield curve. Chances of interest rates moving in either direction are equal. We shouldn’t see primarily upward sloping yield curves. Chances of interest rates moving in either direction are equal. We shouldn’t see primarily upward sloping yield curves.

34. 33 Segmented Markets Theory Assumption: different maturity bonds are not substitutes. Assumption: different maturity bonds are not substitutes. People with a short holding period will buy short-term bonds, people with a long holding period will buy long-term bonds. People with a short holding period will buy short-term bonds, people with a long holding period will buy long-term bonds. Interest rates on these bonds will be determined by the specific supply and demand of the short and long bond markets. Interest rates on these bonds will be determined by the specific supply and demand of the short and long bond markets.

35. 34 Segmented Markets Theory Why do yield curves usually have an upward slope? Why do yield curves usually have an upward slope? Typically, long-term bonds will carry higher interest rate risk so will have a lower demand, lower price and higher interest rate. Typically, long-term bonds will carry higher interest rate risk so will have a lower demand, lower price and higher interest rate. Why do interest rates move together? Why do interest rates move together? Segmented Markets Theory cannot explain this. Segmented Markets Theory cannot explain this. Why when short-term interest rates are high, yield curves are inverted? Why when short-term interest rates are high, yield curves are inverted? Segmented Markets Theory cannot explain this. Segmented Markets Theory cannot explain this.

36. 35 Liquidity Premium Theory Interest rate on a long-term bond will be equal to the average of expected short term returns plus a liquidity premium that reflects the lower demand for long-term (high interest rate risk) bonds. Interest rate on a long-term bond will be equal to the average of expected short term returns plus a liquidity premium that reflects the lower demand for long-term (high interest rate risk) bonds. Liquidity premium on a five-year bond will be lower than a ten-year bond. Liquidity premium on a five-year bond will be lower than a ten-year bond. Bonds of different maturities are partial (not perfect) substitutes Bonds of different maturities are partial (not perfect) substitutes

37. 36 Liquidity Premium Theory Even if the expected future interest rates were to remain constant, liquidity premium will show an upward sloping yield curve. Even if the expected future interest rates were to remain constant, liquidity premium will show an upward sloping yield curve. Yield curve will be mildly rising if future short term rates were expected to fall. Yield curve will be mildly rising if future short term rates were expected to fall. An inverted curve indicates a sharp fall in the expected future short term rates. An inverted curve indicates a sharp fall in the expected future short term rates.

38. 37 Preferred Habitat Theory Investors have a preference for bonds of one maturity over another Investors have a preference for bonds of one maturity over another They will be willing to buy bonds of different maturities only if they earn a somewhat higher expected return They will be willing to buy bonds of different maturities only if they earn a somewhat higher expected return Investors are likely to prefer short-term bonds over longer-term bonds Investors are likely to prefer short-term bonds over longer-term bonds

39. 38 Liquidity Premium (Preferred Habitat) and Expectations Theory

40. 39 Why the Yield Curve Became Inverted in 2000? Do we expect a lower inflation 10, 30 years in the future? Do we expect a lower inflation 10, 30 years in the future? Perhaps; but a current inflation rate of 3-3.5% is already low. Perhaps; but a current inflation rate of 3-3.5% is already low. Do we have a lower liquidity premium than before? Do we have a lower liquidity premium than before? Unlikely. Unlikely. Is there an unusual supply-demand condition in the long-term bond market? Is there an unusual supply-demand condition in the long-term bond market? Yes. The federal government announced retirement of debt. Yes. The federal government announced retirement of debt. Read the one-page explanation of St. Louis Fed at http://research.stlouisfed.org/publications/mt/20000401/cover.pdf Read the one-page explanation of St. Louis Fed at http://research.stlouisfed.org/publications/mt/20000401/cover.pdf http://research.stlouisfed.org/publications/mt/20000401/cover.pdf

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42. 41 Yield Curves for U.S. Government Bonds Sources: Federal Reserve Bank of St. Louis; U.S. Financial Data, various issues; Wall Street Journal, various dates.

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