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CHAPTER 10

CHAPTER 10. 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.

henry-hughes
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CHAPTER 10

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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. Figure 10.2 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 å = ´ 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. 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

  13. Figure 10.4 Growth of Invested Funds

  14. Figure 10.5 Immunization

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

  16. 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.

  17. Figure 10.6 Bond Price Convexity

  18. Figure 10.7 Convexity of Two Bonds

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

  20. 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

  21. Figure 10-8 Contingent Immunization

  22. 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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