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Managing Bond Portfolios: Strategies and Pricing Relationships

Learn about the active and passive strategies for managing bond portfolios, bond pricing relationships, duration calculation, immunization techniques, pricing error from convexity, and bond swapping strategies.

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Managing Bond Portfolios: Strategies and Pricing Relationships

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  1. CHAPTER 10 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. 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

  8. Duration Calculation

  9. Figure 10.3 Duration as a Function of Maturity

  10. 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

  11. 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

  12. Immunization In Practice • Example Page334-335 • Immunization and rebalancing • Cash flow matching and dedication

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

  14. 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.

  15. Figure 10.6 Bond Price Convexity

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

  17. 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

  18. Figure 10-8 Contingent Immunization

  19. 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

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