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Chapter 9

Chapter 9. Bond Prices and Yields. Bond Characteristics. Face or par value Coupon rate Coupon payment Maturity Yield to maturity. Accrued interest and quoted bond prices. Accrued Interest = (Annual coupon payment/2)x(days since last coupon payment/days separate coupon payment)

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Chapter 9

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  1. Chapter9 Bond Prices and Yields

  2. Bond Characteristics • Face or par value • Coupon rate • Coupon payment • Maturity • Yield to maturity

  3. Accrued interest and quoted bond prices Accrued Interest = (Annual coupon payment/2)x(days since last coupon payment/days separate coupon payment) Invoice price = quoted price + accrued interest

  4. Provisions of Bonds • Secured or unsecured • Call provision • Convertible provision • Put provision (putable bonds) • Floating rate bonds • Sinking funds

  5. Bond Pricing T  ParValue C P T t = + B + T + ( 1 r ) T ( 1 r ) = t 1 Bond price = PV of Annuity + PV of lump sum CF PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity

  6. Example: Price of 8%,semiannual coupon payment, 10-yr. with yield at 6% 20 1 1 å P = ´ + ´ 40 1000 t 20 B ( 1 . 03 ) ( 1 . 03 ) = t 1 P = 1 , 148 . 77 B Coupon = 4%*1,000 = 40 (Semiannual) Discount Rate = 3% (Semiannual Maturity = 10 years or 20 periods Par Value = 1,000

  7. Exercise in class • A coupon bond which pays interest semi-annually, has a par value of $1,000, matures in 5 years, and has a yield to maturity of 8%. If the coupon rate is 10%, the intrinsic value of the bond today will be __________. A) $855.55 B) $1,000 C) $1,081 D) $1,100 2. A coupon bond which pays interest of $40 annually, has a par value of $1,000, matures in 5 years, and is selling today at a $159.71 discount from par value. The actual yield to maturity on this bond is __________. A) 5% B) 6% C) 7% D) 8%

  8. Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship • When yields get very high the value of the bond will be very low • When yields approach zero, the value of the bond approaches the sum of the cash flows

  9. Prices and Yield Price Yield

  10. Alternative Measures of Yield • Current Yield • Annual coupon payment/current bond price • Yield to Call • Call price replaces par • Call date replaces maturity • Example: • Suppose the 8% coupon (semiannual payment), 30-year maturity bond sells for $1,150 and is callable in 10 years at a call price of $1,100. What is the yield to maturity and yield to call? • Given: PMT: 40; N: 60; FV:1000; PV: -1150  YTM = 6.82% • Given: PMT: 40, N: 20; FV:1100; PV: -1150  YTC = 6.64%

  11. Alternative Measures of Yield • Holding Period Yield • Considers actual reinvestment of coupons • Considers any change in price if the bond is held less than its maturity • You purchased a 5-year annual interest coupon bond one year ago. Its coupon interest rate was 6% and its par value was $1,000. At the time you purchased the bond, the yield to maturity was 4%. If you sold the bond after receiving the first interest payment and the bond's yield to maturity had changed to 3%, your annual total rate of return on holding the bond for that year would have been __________. A) 5.00% B) 5.51% C) 7.61% D) 8.95%

  12. Exercise in class • A coupon bond which pays interest of $50 annually, has a par value of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The current yield on this bond is __________. A) 5% B) 5.46% C) 5.94% D) 6.00% 2. A callable bond pays annual interest of $60, has a par value of $1,000, matures in 20 years but is callable in 10 years at a price of $1,100, and has a value today of $1055.84. The yield to call on this bond is __________. A) 6.00% B) 6.58% C) 7.20% D) 8.00%

  13. Premium and Discount Bonds • Premium Bond • Coupon rate exceeds yield to maturity • Bond price will decline to par over its maturity • Discount Bond • Yield to maturity exceeds coupon rate • Bond price will increase to par over its maturity

  14. Figure 9.6 Premium and Discount Bonds over Time

  15. Default Risk and Ratings • Rating companies • Moody’s Investor Service • Standard & Poor’s • Fitch • Rating Categories • Investment grade • Speculative grade (BBB or BaB below)

  16. Figure 9.8 Definitions of Each Bond Rating Class

  17. Factors Used by Rating Companies • Coverage ratios • Leverage ratios • Liquidity ratios • Profitability ratios • Cash flow to debt

  18. Term Structure of Interest Rates • Relationship between yields to maturity and maturity • Yield curve - a graph of the yields on bonds relative to the number of years to maturity • Usually Treasury Bonds • Have to be similar risk or other factors would be influencing yields

  19. Figure 9.10 Yields on Long-Term Bonds

  20. Figure 9-11 Yield Curves

  21. Theories of Term Structure • Expectations • Long term rates are a function of expected future short term rates • Upward slope means that the market is expecting higher future short term rates • Downward slope means that the market is expecting lower future short term rates • Liquidity Preference • Upward bias over expectations • The observed long-term rate includes a risk premium

  22. Problems with Traditional Theories Expectations theory • The term structure is almost always upward sloping, but interest rates have not always risen. • It is often the case that the term structure turns down at very long maturities. Maturity preference theory • The U.S. government borrows much more heavily short term than long term. • Many of the biggest buyers of fixed-income securities, such as pension funds, have a strong preference for long maturities

  23. Market segmentation theory • The U.S. government borrows at all maturities. • Many institutional investors, such as mutual funds, are more than willing to move maturities to obtain more favorable rates. • There are bond trading operations that exist just to exploit even very small perceived premiums.

  24. Forward Rates Implied in the Yield Curve + + + - n n 1 ( 1 ) ( 1 ) ( 1 ) y y f = - n n 1 n 2 1 ( 1 . 12 ) ( 1 . 11 ) ( 1 . 1301 ) = For example, using a 1-yr and 2-yr rates Longer term rate, y(n) = 12% Shorter term rate, y(n-1) = 11% Forward rate, a one-year rate in one year = 13.01%

  25. Exercise in class Consider the following $1,000 par value zero-coupon bonds: The expected one-year interest rate two years from now should be __________. A) 7.00% B) 8.00% C) 9.00% D) 10.00%

  26. Ch10 Managing Bond Portfolios

  27. Managing Fixed Income Securities: Basic Strategies • Active strategy • Trade on interest rate predictions • Trade on market inefficiencies • Passive strategy • Control risk • Balance risk and return

  28. Bond Pricing Relationships • Inverse relationship between price and yield • An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield • Long-term bonds tend to be more price sensitive than short-term bonds

  29. Bond Pricing Relationships (cont.) • As maturity increases, price sensitivity increases at a decreasing rate • Price sensitivity is inversely related to a bond’s coupon rate • Price sensitivity is inversely related to the yield to maturity at which the bond is selling

  30. Figure 10.1 Change in Bond Price as a Function of YTM

  31. Duration • A measure of the effective maturity of a bond • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment • Duration is shorter than maturity for all bonds except zero coupon bonds • Duration is equal to maturity for zero coupon bonds

  32. Figure 10.2 Cash Flows of 8-yr Bond with 9% annual coupon and 10% YTM

  33. Duration: Calculation t = + Pr ice ( 1 y ) ] w [CF t t T å = ´ D t w t = t 1 = CF Cash Flow for period t t

  34. Duration Calculation

  35. Figure 10.3 Duration as a Function of Maturity

  36. Duration/Price Relationship Price change is proportional to duration and not to maturity DP/P = -D x [Dy / (1+y)] D* = modified duration D* = D / (1+y) DP/P = - D* x Dy

  37. Example 34 A bond pays annual interest. Its coupon rate is 7%. Its value at maturity is $1,000. It matures in three years. Its yield to maturity is presently 8%. The duration of this bond is __________. A) 2.60 B) 2.73 C) 2.81 D) 3.00 A bond presently has a price of $1,030. The present yield on the bond is 8.00%. If the yield changes from 8.00% to 8.10%, the price of the bond will go down to $1,020. The duration of this bond is __________. A) -10.5 B) -8.5 C) 9.7 D) 10.5

  38. Uses of Duration • Summary measure of length or effective maturity for a portfolio • Immunization of interest rate risk (passive management) • Net worth immunization • Target date immunization • Measure of price sensitivity for changes in interest rate

  39. Example 322 A bond is presently worth $1,080.00 and its yield to maturity is 8%. If the yield to maturity goes down to 7.84%, the value of the bond will go to __________ if the duration of the bond is 9. A) $1,034.88 B) $1,036.00 C) $1,094.00 D) $1,123.60 An 8%, 30-year bond has a yield-to-maturity of 10% and a modified duration of 8.0 years. If the market yield drops by 15 basis points, there will be a __________ in the bond's price. A) 1.15% decrease B) 1.20% increase C) 1.53% increase D) 2.43% decrease create a portfolio with a duration of 4 years, using a 5 year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest ________ of the portfolio value in the zero-coupon bond. A) 50% B) 55% C) 60% D) 75%

  40. Figure 10.4 Growth of Invested Funds

  41. Figure 10.5 Immunization

  42. Pricing Error from Convexity Price Pricing Error from Convexity Duration Yield

  43. Correction for Convexity Modify the pricing equation: D P 1 2 = - ´ D + ´ ´ D D y Convexity ( y ) 2 P Convexity is Equal to: é ù N 1 ( ) CF å + t 2 t ê ú t 2 t ´ + + P (1 y) ( 1 y ) ë û = t 1 Where: CFt is the cash flow (interest and/or principal) at time t.

  44. Figure 10.6 Bond Price Convexity

  45. Figure 10.7 Convexity of Two Bonds

  46. Active Bond Management: Swapping Strategies • Substitution swap • Intermarket swap • Rate anticipation swap • Pure yield pickup • Tax swap

  47. Contingent Immunization • Allow the managers to actively manage until the bond portfolio falls to a threshold level • Once the threshold value is hit the manager must then immunize the portfolio • Active with a floor loss level

  48. Figure 10-8 Contingent Immunization

  49. Interest Rate Swaps • Interest rate swap basic characteristics • One party pays fixed and receives variable • Other party pays variable and receives fixed • Principal is notional • Growth in market • Started in 1980 • Estimated over $60 trillion today • Hedging applications

  50. Chapter13 Financial Statement Analysis

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