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Ch11

Ch11. Managing Bond Portfolios. 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. Bond Pricing Relationships.

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Ch11

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  1. Ch11 Managing Bond Portfolios

  2. 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

  3. 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

  4. 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

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

  6. 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

  7. Figure 11.2 Cash Flows of 8-yr Bond with 9% annual coupon and 10% YTM

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

  9. Duration Calculation

  10. Figure 10.3 Duration as a Function of Maturity

  11. 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

  12. 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

  13. Immunization Passive management Net worth immunization Target date immunization

  14. Cash Flow Matching and Dedication Automatically immunizes a portfolio from interest rate movements Cash flow from the bond and the obligation exactly offset each other Not widely pursued Sometimes not even possible

  15. 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 15

  16. Exercise 12 A bank has $50 million in assets, $47 million in liabilities and $3 million in shareholders' equity. If the duration of its liabilities are 1.3 and the bank wants to immunize its net worth against interest rate risk and thus set the duration of equity equal to zero, it should select assets with an average duration of __________.  a   1.22b.  1.50c.  1.60d.   2.00 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% increasec.   1.53% increased.   2.43% decrease 16

  17. 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% 17

  18. Pricing Error from Convexity Price Pricing Error from Convexity Duration Yield 18

  19. 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.

  20. Figure 11.6 Bond Price Convexity 20

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