The Risk and Term Structure of Interest Rates

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

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

4. Risk Structure of Interest Rates • 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. • Income tax - interest earnings on municipal bonds are free from federal income tax.

5. Default Risk • US Treasury bonds are risk free. • Congress can raise taxes. • Federal government can print money. • 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.

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 .

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. • This is called “term structure of interest rates.”

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

9. Increase in Default Risk on Corporate Bonds

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

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).

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.

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

14. Risk Premium • 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 also evaluate the default risk of foreign bonds.

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

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

18. Corporate Bonds Become Less Liquid i i P i i P Q of Corporate Bonds Q of T-bonds 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.

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

20. Tax Advantage of Municipal Bonds • 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. • $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.

21. The Effect of Tax Elimination on Municipal Bonds i P P i i P Q of Muni Bonds Q of T-bonds 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.

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

23. Term Structure of Interest Rates • 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.

24. Yield Curves • 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. • 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.

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

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 • 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 • Flat  short- and long-term rates are the same • Inverted  long-term rates are below short-term rates

27. Facts • Interest rates on bonds of different maturities move together over time • 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 • Yield curves almost always slope upward

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

29. Expectations Theory • 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 high, yield curves are more likely to be downward sloping. • Doesn’t explain why yield curves are usually upward sloping.

30. Expectations Theory • Assume bonds with different maturities are perfect substitutes. • Demand for bonds with higher yield will be higher. • Their prices will go up and their yields will decline. • 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?

31. An Example • 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. • 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%.

32. Expectations Theory • 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. • If short-term rates are unusually high (low), people will expect them to move down (up) in the future. • Inverted (regular) yield curve. • Chances of interest rates moving in either direction are equal. We shouldn’t see primarily upward sloping yield curves.

33. Segmented Markets Theory • 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. • Interest rates on these bonds will be determined by the specific supply and demand of the short and long bond markets.

34. Segmented Markets Theory • 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. • Why do interest rates move together? • Segmented Markets Theory cannot explain this. • Why when short-term interest rates are high, yield curves are inverted? • Segmented Markets Theory cannot explain this.

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. • Liquidity premium on a five-year bond will be lower than a ten-year bond. • Bonds of different maturities are partial (not perfect) substitutes

36. Liquidity Premium Theory • 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. • An inverted curve indicates a sharp fall in the expected future short term rates.

37. Preferred Habitat Theory 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 Investors are likely to prefer short-term bonds over longer-term bonds

38. Liquidity Premium (Preferred Habitat) and Expectations Theory

39. Why the Yield Curve Became Inverted in 2000? • 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. • Do we have a lower liquidity premium than before? • Unlikely. • Is there an unusual supply-demand condition in the long-term bond market? • 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

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.