Interest rate risk-types_of_bonds

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Interest rate risk-types_of_bonds

  1. 1. IMPACT ON FIXED INCOME SECURITIES INTEREST RATE RISK
  2. 2. Bonds, bond prices and interest rates <ul><li>Bond prices and yields </li></ul><ul><li>Bond market equilibrium </li></ul><ul><li>Bond risks </li></ul>
  3. 3. Bonds: 3 types <ul><li>Zero coupon bonds </li></ul><ul><ul><li>e.g. Tbills </li></ul></ul><ul><li>Fixed payment loans </li></ul><ul><ul><li>e.g. mortgages, car loans </li></ul></ul><ul><li>Coupon bonds </li></ul><ul><ul><li>e.g. Tnotes, Tbonds </li></ul></ul>
  4. 4. Zero coupon bonds <ul><li>Discount bonds </li></ul><ul><ul><li>purchased price less than face value </li></ul></ul><ul><ul><li>-- F > P </li></ul></ul><ul><ul><li>face value at maturity </li></ul></ul><ul><ul><li>no interest payments </li></ul></ul>
  5. 5. Example <ul><li>91 day Tbill, </li></ul><ul><li>P = Rs.9850, F = Rs.10,000 </li></ul><ul><li>YTM solves </li></ul>
  6. 7. yield on a discount basis (127) <ul><li>how Tbill yields are actually quoted </li></ul><ul><li>approximates the YTM </li></ul>i db = F - P F x 360 d
  7. 8. example <ul><li>91 day Tbill, </li></ul><ul><li>P = Rs.9850, F = Rs.10,000 </li></ul><ul><li>discount yield = </li></ul>
  8. 9. <ul><li>i db < YTM </li></ul><ul><li>why? </li></ul><ul><ul><li>F in denominator </li></ul></ul><ul><ul><li>360 day year </li></ul></ul>
  9. 10. <ul><li>Fixed-payment loan </li></ul><ul><ul><li>loan is repaid with equal (monthly) payments </li></ul></ul><ul><ul><li>each payment is combination of principal and interest </li></ul></ul>
  10. 11. example 2: fixed pmt. loan <ul><li>Rs.20,000 car loan, 5 years </li></ul><ul><li>monthly pmt. = Rs.500 </li></ul><ul><li>so Rs.15,000 is price today </li></ul><ul><li>cash flow is 60 pmts. of Rs.500 </li></ul><ul><li>what is i? </li></ul>
  11. 12. <ul><li>i is annual rate </li></ul><ul><ul><li>(effective annual interest rate) </li></ul></ul><ul><li>but payments are monthly, & compound monthly </li></ul><ul><li>(1+i m ) 12 = i </li></ul><ul><li>i m = i 1/12 -1 </li></ul><ul><li>i m is the periodic rate </li></ul><ul><li>note: APR = i m x 12 </li></ul>
  12. 13. i m =1.44% i=(1+. 0144) 12 – 1 =18.71%
  13. 14. <ul><li>how to solve for i? </li></ul><ul><ul><li>trial-and-error </li></ul></ul><ul><ul><li>table </li></ul></ul><ul><ul><li>financial calculator </li></ul></ul><ul><ul><li>spreadsheet </li></ul></ul>
  14. 15. Coupon Bond
  15. 16. Bond Yields <ul><li>Yield to maturity (YTM) </li></ul><ul><ul><li>chapter 4 </li></ul></ul><ul><li>Current yield </li></ul><ul><li>Holding period return </li></ul>
  16. 17. Yield to Maturity (YTM) <ul><li>a measure of interest rate </li></ul><ul><li>interest rate where </li></ul>P = PV of cash flows
  17. 18. Current yield <ul><li>approximation of YTM for coupon bonds </li></ul>i c = annual coupon payment bond price
  18. 19. <ul><li>better approximation when </li></ul><ul><ul><li>maturity is longer </li></ul></ul><ul><ul><li>P is close to F </li></ul></ul>
  19. 20. example <ul><li>2 year Tnotes, F = Rs.10,000 </li></ul><ul><li>P = Rs.9750, coupon rate = 6% </li></ul><ul><li>current yield </li></ul>i c = 600 9750 = 6.15%
  20. 21. <ul><li>Current yield = 6.15% </li></ul><ul><li>True YTM = 7.37% </li></ul><ul><li>Lousy approximation </li></ul><ul><ul><li>only 2 years to maturity </li></ul></ul><ul><ul><li>selling 2.5% below F </li></ul></ul>
  21. 22. Holding period return <ul><li>sell bond before maturity </li></ul><ul><li>return depends on </li></ul><ul><ul><li>holding period </li></ul></ul><ul><ul><li>interest payments </li></ul></ul><ul><ul><li>resale price </li></ul></ul>
  22. 23. example <ul><li>2 year Tnotes, F = Rs.10,000 </li></ul><ul><li>P = Rs.9750, coupon rate = 6% </li></ul><ul><li>sell right after 1 year for Rs.9900 </li></ul><ul><ul><li>Rs.300 at 6 mos. </li></ul></ul><ul><ul><li>Rs.300 at 1 yr. </li></ul></ul><ul><ul><li>Rs.9900 at 1 yr. </li></ul></ul>
  23. 24. i/2 = 3.83% i = 7.66%
  24. 25. <ul><li>why i/2? </li></ul><ul><li>interest compounds annually not semiannually </li></ul>
  25. 26. The Bond Market <ul><li>Bond supply </li></ul><ul><li>Bond demand </li></ul><ul><li>Bond market equilibrium </li></ul>
  26. 27. Bond supply <ul><li>bond issuers/ borrowers </li></ul><ul><li>look at Qs as a function of price, yield </li></ul>
  27. 28. <ul><li>lower bond prices </li></ul><ul><ul><li>higher bond yields </li></ul></ul><ul><ul><li>more expensive to borrow </li></ul></ul><ul><ul><li>lower Qs of bonds </li></ul></ul><ul><li>so bond supply slopes up with price </li></ul>
  28. 29. Bond price Q of bonds S
  29. 30. <ul><li>Changes in bond price/yield </li></ul><ul><ul><li>Move along the bond supply curve </li></ul></ul><ul><li>What shifts bond supply? </li></ul>
  30. 31. Shifts in bond supply <ul><li>Change in government borrowing </li></ul><ul><ul><li>Increase in gov’t borrowing </li></ul></ul><ul><ul><ul><li>Increase in bond supply </li></ul></ul></ul><ul><ul><ul><li>Bond supply shifts right </li></ul></ul></ul>
  31. 32. P Qs S S’
  32. 33. <ul><li>a change in business conditions </li></ul><ul><ul><li>affects incentives to expand production </li></ul></ul>exp. profits supply of bonds (shift rt.) <ul><ul><li>exp. economic expansion shifts bond supply rt. </li></ul></ul>
  33. 34. <ul><li>a change in expected inflation </li></ul><ul><ul><li>rising inflation decreases real cost of borrowing </li></ul></ul>exp. inflation supply of bonds (shift rt.)
  34. 35. Bond Demand <ul><li>bond buyers/ lenders/ savers </li></ul><ul><li>look at Qd as a function of bond price/yield </li></ul>
  35. 36. <ul><li>so bond demand slopes down with respect to price </li></ul>Bond yield Qd of bonds price of bond Qd of bonds
  36. 37. Bond price Quantity of bonds D
  37. 38. <ul><li>Changes in bond price/yield </li></ul><ul><ul><li>Move along the bond demand curve </li></ul></ul><ul><li>What shifts bond demand? </li></ul>
  38. 39. <ul><li>Wealth </li></ul><ul><ul><li>Higher wealth increases asset demand </li></ul></ul><ul><ul><ul><li>Bond demand increases </li></ul></ul></ul><ul><ul><ul><li>Bond demand shifts right </li></ul></ul></ul>
  39. 40. P Qd D D
  40. 41. <ul><li>a change in expected inflation </li></ul><ul><ul><li>rising inflation decreases real return </li></ul></ul>inflation expected to demand for bonds (shift left)
  41. 42. <ul><li>a change in exp. interest rates </li></ul><ul><ul><li>rising interest rates decrease value of existing bonds </li></ul></ul>int. rates expected to demand for bonds (shift left)
  42. 43. <ul><li>a change in the risk of bonds relative to other assets </li></ul>relative risk of bonds demand for bonds (shift left)
  43. 44. <ul><li>a change in liquidity of bonds relative to other assets </li></ul>relative liquidity of bonds demand for bonds (shift rt.)
  44. 45. Bond market equilibrium <ul><li>changes when bond demand shifts, </li></ul><ul><li>and/or bond supply shifts </li></ul><ul><li>shifts cause bond prices AND interest rates to change </li></ul>
  45. 46. Example 1: the Fisher effect <ul><li>expected inflation 3% </li></ul>
  46. 47. <ul><li>exp. inflation rises to 4% </li></ul><ul><ul><li>bond demand </li></ul></ul><ul><ul><li>-- real return declines </li></ul></ul><ul><ul><li>-- Bd decreases </li></ul></ul><ul><ul><li>bond supply </li></ul></ul><ul><ul><li>-- real cost of borrowing declines </li></ul></ul><ul><ul><li>-- Bs increases </li></ul></ul>
  47. 48. <ul><li>bond price falls </li></ul><ul><li>interest rate rises </li></ul>
  48. 49. Fisher effect <ul><li>expected inflation rises, </li></ul><ul><li>nominal interest rates rise </li></ul>
  49. 50. Example 2: economic slowdown
  50. 51. <ul><li>bond demand </li></ul><ul><ul><li>decline in income, wealth </li></ul></ul><ul><ul><li>Bd decreases </li></ul></ul><ul><ul><li>P falls, i rises </li></ul></ul><ul><li>bond supply </li></ul><ul><ul><li>decline in exp. profits </li></ul></ul><ul><ul><li>Bs decreases </li></ul></ul><ul><ul><li>P rises, i falls </li></ul></ul>
  51. 52. <ul><li>shift Bs > shift in Bd </li></ul><ul><li>interest rate falls </li></ul>
  52. 53. Why shift Bs > shift Bd? <ul><li>changes in wealth are small </li></ul><ul><li>response to change in exp. profits is large </li></ul><ul><ul><li>large cyclical swings in investment </li></ul></ul>
  53. 54. <ul><li>interest rate is pro-cyclical </li></ul>
  54. 55. Why are bonds risky? <ul><li>3 sources of risk </li></ul><ul><ul><li>Default </li></ul></ul><ul><ul><li>Inflation </li></ul></ul><ul><ul><li>Interest rate </li></ul></ul>
  55. 56. Default risk <ul><li>Risk that the issuer fails to make promised payments on time </li></ul><ul><li>Zero for U.S. gov’t debt </li></ul><ul><li>Other issuers: corporate, municipal, foreign have some default risk </li></ul><ul><li>Greater default risk means a greater yield </li></ul>
  56. 57. Inflation risk <ul><li>Most bonds promise fixed dollar payments </li></ul><ul><ul><li>Inflation erodes the real value of these payments </li></ul></ul><ul><li>Future inflation is unknown </li></ul><ul><li>Larger for longer term bonds </li></ul>
  57. 58. Interest rate risk <ul><li>Changing interest rates change the value (price) of a bond in the opposite direction. </li></ul><ul><li>All bonds have interest rate risk </li></ul><ul><ul><li>But it is larger for the long term bonds </li></ul></ul>

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