1. Bonds, bond prices and interest rates Bonds, bond prices and interest rates Bond prices and yields Bond market equilibrium Bond risks Bond prices and yields Bond market equilibrium Bond risks

2. Bonds: 4 types zero coupon bonds  e.g. Tbills fixed payment loans  e.g. mortgages, car loans coupon bonds  e.g. Tnotes, Tbonds consols zero coupon bonds  e.g. Tbills fixed payment loans  e.g. mortgages, car loans coupon bonds  e.g. Tnotes, Tbonds consols

3. Zero coupon bonds discount bonds  purchased price less than face value -- F > P  face value at maturity  no interest payments discount bonds  purchased price less than face value -- F > P  face value at maturity  no interest payments

4. exampleexample 91 day Tbill, P = $9850, F = $10,000 YTM solves 91 day Tbill, P = $9850, F = $10,000 YTM solves

6. yield on a discount basis (127) how Tbill yields are actually quoted approximates the YTM how Tbill yields are actually quoted approximates the YTM i db = F - P F x 360 d

7. exampleexample 91 day Tbill, P = $9850, F = $10,000 discount yield = 91 day Tbill, P = $9850, F = $10,000 discount yield =

8. i db < YTM why?  F in denominator  360 day year i db < YTM why?  F in denominator  360 day year

9. fixed-payment loan  loan is repaid with equal (monthly) payments  each payment is combination of principal and interest fixed-payment loan  loan is repaid with equal (monthly) payments  each payment is combination of principal and interest

10. example 2: fixed pmt. loan $20,000 car loan, 5 years monthly pmt. = $500 so $15,000 is price today cash flow is 60 pmts. of $500 what is i? $20,000 car loan, 5 years monthly pmt. = $500 so $15,000 is price today cash flow is 60 pmts. of $500 what is i?

11. i is annual rate  (effective annual interest rate) but payments are monthly, & compound monthly (1+i m ) 12 = i i m = i 1/12 -1 i m is the periodic rate note: APR = i m x 12 i is annual rate  (effective annual interest rate) but payments are monthly, & compound monthly (1+i m ) 12 = i i m = i 1/12 -1 i m is the periodic rate note: APR = i m x 12

12. i m =1.44% i=(1+. 0144) 12 – 1 =18.71%

13. how to solve for i?  trial-and-error  table  financial calculator  spreadsheet how to solve for i?  trial-and-error  table  financial calculator  spreadsheet

14. (chapter 4) Coupon bond

15. Bond Yields Yield to maturity (YTM)  chapter 4 Current yield Holding period return Yield to maturity (YTM)  chapter 4 Current yield Holding period return

16. Yield to Maturity (YTM) a measure of interest rate interest rate where a measure of interest rate interest rate where P =PV of cash flows

17. Current yield approximation of YTM for coupon bonds i c = annual coupon payment bond price

18. better approximation when  maturity is longer  P is close to F better approximation when  maturity is longer  P is close to F

19. exampleexample 2 year Tnotes, F = $10,000 P = $9750, coupon rate = 6% current yield 2 year Tnotes, F = $10,000 P = $9750, coupon rate = 6% current yield i c = 600 9750 = 6.15%

20. current yield = 6.15% true YTM = 7.37% lousy approximation  only 2 years to maturity  selling 2.5% below F current yield = 6.15% true YTM = 7.37% lousy approximation  only 2 years to maturity  selling 2.5% below F

21. Holding period return sell bond before maturity return depends on  holding period  interest payments  resale price sell bond before maturity return depends on  holding period  interest payments  resale price

22. exampleexample 2 year Tnotes, F = $10,000 P = $9750, coupon rate = 6% sell right after 1 year for $9900  $300 at 6 mos.  $300 at 1 yr.  $9900 at 1 yr. 2 year Tnotes, F = $10,000 P = $9750, coupon rate = 6% sell right after 1 year for $9900  $300 at 6 mos.  $300 at 1 yr.  $9900 at 1 yr.

23. i/2 = 3.83% i = 7.66%

24. why i/2? interest compounds annually not semiannually why i/2? interest compounds annually not semiannually

25. The Bond Market Bond supply Bond demand Bond market equilibrium Bond supply Bond demand Bond market equilibrium

26. Bond supply bond issuers/ borrowers look at Qs as a function of price, yield bond issuers/ borrowers look at Qs as a function of price, yield

27. lower bond prices  higher bond yields  more expensive to borrow  lower Qs of bonds so bond supply slopes up with price lower bond prices  higher bond yields  more expensive to borrow  lower Qs of bonds so bond supply slopes up with price

28. Bond price Q of bonds S

29. Changes in bond price/yield  Move along the bond supply curve What shifts bond supply? Changes in bond price/yield  Move along the bond supply curve What shifts bond supply?

30. Shifts in bond supply Change in government borrowing  Increase in gov’t borrowing Increase in bond supply Bond supply shifts right Change in government borrowing  Increase in gov’t borrowing Increase in bond supply Bond supply shifts right

31. P Qs S S’

32. a change in business conditions  affects incentives to expand production a change in business conditions  affects incentives to expand production exp. profits supply of bonds (shift rt.)  exp. economic expansion shifts bond supply rt.

33. a change in expected inflation  rising inflation decreases real cost of borrowing a change in expected inflation  rising inflation decreases real cost of borrowing exp. inflation supply of bonds (shift rt.)

34. Bond Demand bond buyers/ lenders/ savers look at Qd as a function of bond price/yield bond buyers/ lenders/ savers look at Qd as a function of bond price/yield

35. Bond yield Qd of bonds price of bond Qd of bonds so bond demand slopes down with respect to price

36. Bond price Quantity of bonds D

37. Changes in bond price/yield  Move along the bond demand curve What shifts bond demand? Changes in bond price/yield  Move along the bond demand curve What shifts bond demand?

38. Wealth  Higher wealth increases asset demand Bond demand increases Bond demand shifts right Wealth  Higher wealth increases asset demand Bond demand increases Bond demand shifts right

39. P Qd D D

40. a change in expected inflation  rising inflation decreases real return a change in expected inflation  rising inflation decreases real return inflation expected to demand for bonds (shift left)

41. a change in exp. interest rates  rising interest rates decrease value of existing bonds a change in exp. interest rates  rising interest rates decrease value of existing bonds int. rates expected to demand for bonds (shift left)

42. a change in the risk of bonds relative to other assets relative risk of bonds demand for bonds (shift left)

43. a change in liquidity of bonds relative to other assets relative liquidity of bonds demand for bonds (shift rt.)

44. Bond market equilibrium changes when bond demand shifts, and/or bond supply shifts shifts cause bond prices AND interest rates to change changes when bond demand shifts, and/or bond supply shifts shifts cause bond prices AND interest rates to change

45. Example 1: the Fisher effect expected inflation 3%

46. exp. inflation rises to 4%  bond demand -- real return declines -- Bd decreases  bond supply -- real cost of borrowing declines -- Bs increases exp. inflation rises to 4%  bond demand -- real return declines -- Bd decreases  bond supply -- real cost of borrowing declines -- Bs increases

47. bond price falls interest rate rises bond price falls interest rate rises

48. Fisher effect expected inflation rises, nominal interest rates rise expected inflation rises, nominal interest rates rise

49. Example 2: economic slowdown

50. bond demand  decline in income, wealth  Bd decreases  P falls, i rises bond supply  decline in exp. profits  Bs decreases  P rises, i falls bond demand  decline in income, wealth  Bd decreases  P falls, i rises bond supply  decline in exp. profits  Bs decreases  P rises, i falls

51. shift Bs > shift in Bd interest rate falls shift Bs > shift in Bd interest rate falls

52. Why shift Bs > shift Bd? changes in wealth are small response to change in exp. profits is large  large cyclical swings in investment changes in wealth are small response to change in exp. profits is large  large cyclical swings in investment

53. interest rate is pro-cyclical

54. Why are bonds risky? 3 sources of risk  Default  Inflation  Interest rate 3 sources of risk  Default  Inflation  Interest rate

55. Default risk Risk that the issuer fails to make promised payments on time Zero for U.S. gov’t debt Other issuers: corporate, municipal, foreign have some default risk Greater default risk means a greater yield Risk that the issuer fails to make promised payments on time Zero for U.S. gov’t debt Other issuers: corporate, municipal, foreign have some default risk Greater default risk means a greater yield

56. Inflation risk Most bonds promise fixed dollar payments  Inflation erodes the real value of these payments Future inflation is unknown Larger for longer term bonds Most bonds promise fixed dollar payments  Inflation erodes the real value of these payments Future inflation is unknown Larger for longer term bonds

57. Interest rate risk Changing interest rates change the value (price) of a bond in the opposite direction. All bonds have interest rate risk  But it is larger for the long term bonds Changing interest rates change the value (price) of a bond in the opposite direction. All bonds have interest rate risk  But it is larger for the long term bonds