1. Chapter 7. Risk and Term Structure of Interest Rates Risk Structure Term Structure Risk Structure Term Structure

2. Not all interest rates are created equal! many interest rates at one time But interest rates do move together over time many interest rates at one time But interest rates do move together over time

3. Interest rate structure Why do yields differ? Risk structure  bonds/debt with same maturity but different characteristics Term structure  Bond with same characteristics but different maturities Why do yields differ? Risk structure  bonds/debt with same maturity but different characteristics Term structure  Bond with same characteristics but different maturities

4. Interest rates: a snapshot 1/07 1/08 3 mo Tbill4.98%2.75% 3 mo Com Paper5.17%3.25% 10 yr. Tnote4.76%3.74% 10 yr. AAA corp5.4%5.33% 10 yr. BAA corp6.34%6.54% 30 yr. mortgage 6.22%5.76% 1/07 1/08 3 mo Tbill4.98%2.75% 3 mo Com Paper5.17%3.25% 10 yr. Tnote4.76%3.74% 10 yr. AAA corp5.4%5.33% 10 yr. BAA corp6.34%6.54% 30 yr. mortgage 6.22%5.76%

5. measurementmeasurement difference between two interest rates  spread measured in  percentage points  basis points  1 percentage pt. = 100 basis pts. difference between two interest rates  spread measured in  percentage points  basis points  1 percentage pt. = 100 basis pts.

6. example 1 3 mo. Tbill 2.75% 3 mo. Commercial paper 3.25% spread  0.5 percentage pts.  50 basis pts. 3 mo. Tbill 2.75% 3 mo. Commercial paper 3.25% spread  0.5 percentage pts.  50 basis pts.

7. example 2 10 yr Tnote3.74% 10 BAA corporate6.54% spread  2.8 percentage pts.  280 basis pts. 10 yr Tnote3.74% 10 BAA corporate6.54% spread  2.8 percentage pts.  280 basis pts.

8. I. Risk Structure of Interest Rates debt with same maturity, but different characteristics  default risk  tax treatment debt with same maturity, but different characteristics  default risk  tax treatment

10. PatternsPatterns Baa > AAA > U.S. Treasury  size of the spread varies Baa > AAA > U.S. Treasury  size of the spread varies

11. A. Default Risk risk of not receiving timely payment of principal and interest depends on  creditworthiness of issuer  structure of bond risk of not receiving timely payment of principal and interest depends on  creditworthiness of issuer  structure of bond

12. U.S. government debt zero default risk backed by “full faith and credit” of U.S. government why?  power to tax largest economy  power to issue stable currency zero default risk backed by “full faith and credit” of U.S. government why?  power to tax largest economy  power to issue stable currency

13. Other issuers private foreign municipal all have some default risk rated for default risk private foreign municipal all have some default risk rated for default risk

14. Bond ratings bond issuer pays rating agency  Moody’s, S&P, Fitch  p. 151 or p. 149 high credit rating  = low default risk bond ratings may change over time  Downgrades or upgrades bond issuer pays rating agency  Moody’s, S&P, Fitch  p. 151 or p. 149 high credit rating  = low default risk bond ratings may change over time  Downgrades or upgrades

15. Investment grade Moodys’S&P Aaa AAA Aa (Aa1, Aa2, Aa3) AA (AA+, AA, AA-) AA BaaBBB Moodys’S&P Aaa AAA Aa (Aa1, Aa2, Aa3) AA (AA+, AA, AA-) AA BaaBBB

16. Noninvestment, speculative BaBB BB BaBB BB Highly Speculative (High-yield, “Junk”) CaaCCC CaCC CC D (in default) CaaCCC CaCC CC D (in default)

17. examplesexamples AAA  GE, Toyota, Berkshire Hathaway, Pfizer AA  Wells Fargo, Merck, Merrill Lynch, Gillette, NYC GO bonds, Rochester, Syracuse, Onondaga Co. A  Caterpillar, Boeing, Dow Chemical, Coca Cola, California GO bonds, BBB  DaimlerChrysler, Union Pacific, Mattel, Home Depot AAA  GE, Toyota, Berkshire Hathaway, Pfizer AA  Wells Fargo, Merck, Merrill Lynch, Gillette, NYC GO bonds, Rochester, Syracuse, Onondaga Co. A  Caterpillar, Boeing, Dow Chemical, Coca Cola, California GO bonds, BBB  DaimlerChrysler, Union Pacific, Mattel, Home Depot

18. BB  GM, Sears B  Ford, Clear Channel, Univision CCC  Revlon, Sirius, Pep Boys, JoAnn, ToysRUs CC  Primus C  Wolverine Tube BB  GM, Sears B  Ford, Clear Channel, Univision CCC  Revlon, Sirius, Pep Boys, JoAnn, ToysRUs CC  Primus C  Wolverine Tube

19. DefaultsDefaults Most likely in industrial sector Defaults over past 10 years:  Zenith Delta, Northwest  EnronDelphi  Daewoo  Purina Mills Most likely in industrial sector Defaults over past 10 years:  Zenith Delta, Northwest  EnronDelphi  Daewoo  Purina Mills

20. Municipal defaults NYC 1975, Cleveland 1978 Largest: Washington Power SS  Over $2 billion  (failed nuclear plants in 1970s) The Cicero Commons (2003) Wilkes-Barre, PA (2002) NYC 1975, Cleveland 1978 Largest: Washington Power SS  Over $2 billion  (failed nuclear plants in 1970s) The Cicero Commons (2003) Wilkes-Barre, PA (2002)

21. default risk & yield investors are risk averse higher default risk lower credit rating higher yield

22. If Treasuries are the benchmark Bond yield = Treasury yield + default premium If Treasuries are the benchmark Bond yield = Treasury yield + default premium

23. so default risk explains Treasury yields AAA Corp yields BAA Corp yields <<

24. default risk is not constant! varies over the business cycle  higher in recessions  lower in expansions Tnote vs. BAA yield  1/07 158 basis pts. (6.34% vs. 4.76%)  1/08 280 basis pts. (6.54% vs. 3.74%) varies over the business cycle  higher in recessions  lower in expansions Tnote vs. BAA yield  1/07 158 basis pts. (6.34% vs. 4.76%)  1/08 280 basis pts. (6.54% vs. 3.74%)

26. B. Tax treatment Q. why do municipal bonds have lower yields than Tbonds?  muni’s less liquid  muni’s not default-free A. tax treatment Q. why do municipal bonds have lower yields than Tbonds?  muni’s less liquid  muni’s not default-free A. tax treatment

27. municipal bond interest exempt from federal income tax possibly exempt from state income tax  if issuer & bondholder are in same state exempt from federal income tax possibly exempt from state income tax  if issuer & bondholder are in same state

28. Treasury bond interest exempt from state income tax Corporate bond interest fully taxable

29. example: federal taxes bond where F=$10,000 coupon rate = 10% annual coupon pmts = $1000 bond where F=$10,000 coupon rate = 10% annual coupon pmts = $1000

30. municipal bond before taxes:  $1000 in interest pmts. after taxes:  $1000 in interest pmts before taxes:  $1000 in interest pmts. after taxes:  $1000 in interest pmts

31. Corporate bond before taxes:  $1000 interest pmts. after taxes  (25% marginal rate)  $1000(1-.25) = $750 interest pmts. before taxes:  $1000 interest pmts. after taxes  (25% marginal rate)  $1000(1-.25) = $750 interest pmts.

32. So, after taxes muni has 10% coupon rate corp has 7.5% coupon rate After tax yield = i(1- tax rate) muni can offer a lower yield and still be competitive muni has 10% coupon rate corp has 7.5% coupon rate After tax yield = i(1- tax rate) muni can offer a lower yield and still be competitive

33. tax treatment explains Treasury yields muni yields Corp yields < <

34. impact of tax rates higher tax brackets derive more benefit from muni’s changing tax rates will affect the corporate-municipal yield spread higher tax brackets derive more benefit from muni’s changing tax rates will affect the corporate-municipal yield spread

35. II. Term structure of interest rates bonds with the same characteristics, but different maturities bonds with the same characteristics, but different maturities

36. focus on Treasury yields  same default risk, tax treatment  many choices of maturity -- 4 weeks to 10 years focus on Treasury yields  same default risk, tax treatment  many choices of maturity -- 4 weeks to 10 years

37. Treasury yields over time

38. relationship between yield & maturity is NOT constant  sometimes short-term yields are highest,  Most of the time, long-term yields are highest relationship between yield & maturity is NOT constant  sometimes short-term yields are highest,  Most of the time, long-term yields are highest

39. A. Yield curve plot of maturity vs. yield slope of curve indicates relationship between maturity and yield The living yield curve plot of maturity vs. yield slope of curve indicates relationship between maturity and yield The living yield curve

40. upward sloping yields rise w/ maturity (common) maturity yield

41. downward sloping (inverted) yield falls w/ maturity (rare) maturity yield

42. flatflat yield varies little with maturity maturity yield

43. 3 facts about the yield curve based on historical data on U.S. Treasury yields 1. interest rates on bonds of different maturities generally move together based on historical data on U.S. Treasury yields 1. interest rates on bonds of different maturities generally move together

44. 2. ST bond yields are more volatile than LT bond yields 3. The yield curve usually slopes up. 2. ST bond yields are more volatile than LT bond yields 3. The yield curve usually slopes up.

45. Understanding the yield curve what causes the 3 facts? what does the shape of the yield curve tell us? must understand why/how maturity affects yield what causes the 3 facts? what does the shape of the yield curve tell us? must understand why/how maturity affects yield

46. 2 theories of term structure assumptions about investor preference implications for maturity and yield check implications against 3 facts about yield curve assumptions about investor preference implications for maturity and yield check implications against 3 facts about yield curve

47. B. The Expectations Theory Assume: bond buyers do not have any preference about maturity i.e. bonds of different maturities are perfect substitutes Assume: bond buyers do not have any preference about maturity i.e. bonds of different maturities are perfect substitutes

48. if assumption is true, then investors care only about expected return  for example,  if expect better return from short- term bonds, only hold short-term bonds if assumption is true, then investors care only about expected return  for example,  if expect better return from short- term bonds, only hold short-term bonds

49. but investors hold both short-term an long-term bonds so, must EXPECT similar return: long-term yields = average of the expected future short-term yields but investors hold both short-term an long-term bonds so, must EXPECT similar return: long-term yields = average of the expected future short-term yields

50. exampleexample 5 year time horizon investors indifferent between (1) holding 5-year bond (2) holding 1year bonds, 5 yrs. in a row as long as expected return is same 5 year time horizon investors indifferent between (1) holding 5-year bond (2) holding 1year bonds, 5 yrs. in a row as long as expected return is same

51. expected one-year interest rates: 5%, 6%, 7%, 8%, 9% over next 5 years so 5-year bond must yield (approx) expected one-year interest rates: 5%, 6%, 7%, 8%, 9% over next 5 years so 5-year bond must yield (approx)

52. maturity yield 1 yr.5 yrs. 5% 7% yield curve if ST rates are expected to rise, yield curve slopes up if ST rates are expected to rise, yield curve slopes up

53. under exp. theory, slope of yield curve tells us direction of expected future short-term rates

54. ST rates expected to fall maturity yield

55. ST rates expected to stay the same maturity yield

56. ST rates expected to rise, then fall maturity yield

57. theory vs. reality does the theory explain the 3 facts? 1. interest rates move together? YES. If ST rates rise, then average will rise (LT rate) does the theory explain the 3 facts? 1. interest rates move together? YES. If ST rates rise, then average will rise (LT rate)

58. 2. ST rates are more volatile YES. If LT rates are an average of ST rates, then they will be less volatile 2. ST rates are more volatile YES. If LT rates are an average of ST rates, then they will be less volatile

59. 3. yield curve usually slopes up NO. Under expectations theory, this means we would expect interest rates to rise most of the time BUT we don’t (rates have trended down for 20 yrs.) 3. yield curve usually slopes up NO. Under expectations theory, this means we would expect interest rates to rise most of the time BUT we don’t (rates have trended down for 20 yrs.)

60. what went wrong? back to assumption: bonds of different maturities are perfect substitutes but this is not likely  long term bonds have greater price volatility  short term bonds have reinvestment risk back to assumption: bonds of different maturities are perfect substitutes but this is not likely  long term bonds have greater price volatility  short term bonds have reinvestment risk

61. B. Liquidity Premium Theory assume: bonds of different maturities are imperfect substitutes, and investors PREFER ST bonds  Less inflation risk, less interest rate risk assume: bonds of different maturities are imperfect substitutes, and investors PREFER ST bonds  Less inflation risk, less interest rate risk

62. so if true, investors hold ST bonds UNLESS LT bonds offer higher yield as incentive higher yield = liquidity premium so if true, investors hold ST bonds UNLESS LT bonds offer higher yield as incentive higher yield = liquidity premium

63. so, LT yield = average exp. ST yields + liquidity premium so, LT yield = average exp. ST yields + liquidity premium

64. exampleexample 5 years 1 yr. bond yields: 5%, 6%, 7%, 8%, 9% AND 5yr. bond has 1% liquidity prem. 5 years 1 yr. bond yields: 5%, 6%, 7%, 8%, 9% AND 5yr. bond has 1% liquidity prem.

65. theory vs. reality does the theory explain the 3 facts? 1. & 2? YES. LT rates are still based in part on exp. about ST rates does the theory explain the 3 facts? 1. & 2? YES. LT rates are still based in part on exp. about ST rates

66. 3. yield curve usually slopes up YES. IF LT bond yields have a liquidity premium, then usually LT yields > ST yields or yield curve slopes up. 3. yield curve usually slopes up YES. IF LT bond yields have a liquidity premium, then usually LT yields > ST yields or yield curve slopes up.

67. ProblemProblem How do we interpret yield curve? slope due to 2 things: (1) exp. about future ST rates (2) size of liquidity premium do not know size of liq. prem. How do we interpret yield curve? slope due to 2 things: (1) exp. about future ST rates (2) size of liquidity premium do not know size of liq. prem.

68. if liquidity premium is small, then ST rates are expected to rise if liquidity premium is small, then ST rates are expected to rise maturity yield yield curve small liquidity premium

69. if liquidity premium is larger, then ST rates are expected to stay the same if liquidity premium is larger, then ST rates are expected to stay the same maturity yield yield curve large liquidity premium

70. C. What does the yield curve tell us? expected future ST rates? expected inflation? business cycle? expected future ST rates? expected inflation? business cycle?

71. slope of yield curve is useful in predicting recessions slight upward slope  normal GDP growth steep upward slope  recovery from recession slope of yield curve is useful in predicting recessions slight upward slope  normal GDP growth steep upward slope  recovery from recession

72. flat curve  uncertainty  could mean recession, or slow growth inverted curve  exp. lower interest rates  followed by slowdown or recession flat curve  uncertainty  could mean recession, or slow growth inverted curve  exp. lower interest rates  followed by slowdown or recession