1. McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Bond Portfolios CHAPTER 10

2. 10-2 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. 10-3 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. 10-4 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. 10-5 Figure 10.1 Change in Bond Price as a Function of YTM

6. 10-6 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. 10-7 Figure 10.2 Cash Flows of 8-yr Bond with 9% annual coupon and 10% YTM

8. 10-8 Duration: Calculation t t t w[CF y ice   () ]1 Pr Dtw t T t    1 CFCashFlowforperiodt t 

9. 10-9 Duration Calculation

10. 10-10 Figure 10.3 Duration as a Function of Maturity

11. 10-11 Duration/Price Relationship Price change is proportional to duration and not to maturity Price change is proportional to duration and not to maturity  P/P = -D x [  y / (1+y)] D * = modified duration D * = D / (1+y)  P/P = - D * x  y

12. 10-12 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. 10-13 Figure 10.4 Growth of Invested Funds

14. 10-14 Figure 10.5 Immunization

15. 10-15 Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity

16. 10-16 Correction for Convexity )( 2 1 2 y ConvexityyD P P    Modify the pricing equation: Convexity is Equal to:             N t t t t t y CF P 1 2 2 )1(y)(1 1 Where: CF t is the cash flow (interest and/or principal) at time t.

17. 10-17 Figure 10.6 Bond Price Convexity

18. 10-18 Figure 10.7 Convexity of Two Bonds

19. 10-19 Active Bond Management: Swapping Strategies Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap

20. 10-20 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. 10-21 Figure 10-8 Contingent Immunization

22. 10-22 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