2. Chapter 11 Managing Fixed-Income Investments

3. 11-2 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Managing Fixed Income Securities: Basic Strategies Active strategy Active strategy –Trade on interest rate predictions –Trade on market inefficiencies Passive strategy Passive strategy –Control risk –Balance risk and return

4. 11-3 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998

5. 11-4 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Pricing Relationships Inverse relationship between price and yield 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 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 Long-term bonds tend to be more price sensitive than short-term bonds

6. 11-5 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Pricing Relationships (cont.) As maturity increases, price sensitivity increases at a decreasing rate 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 a bond’s coupon rate Price sensitivity is inversely related to the yield to maturity at which the bond is selling Price sensitivity is inversely related to the yield to maturity at which the bond is selling

7. 11-6 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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

8. 11-7 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Other duration “rules” A bond’s duration (and interest sensitivity) are higher the lower is the coupon rate (all else the same) A bond’s duration (and interest sensitivity) are higher the lower is the coupon rate (all else the same) Duration and interest rate sensitivity usually increase with maturity (all else the same) Duration and interest rate sensitivity usually increase with maturity (all else the same) Duration and interest rate sensitivity are higher when yields are lower (all else the same) Duration and interest rate sensitivity are higher when yields are lower (all else the same) Duration for perpetuity = 1/(1+y) Duration for perpetuity = 1/(1+y)

9. 11-8 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Duration: Calculation

10. 11-9 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Duration Calculation

11. 11-10 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Consider a 5-year, 10% coupon bond. Yield = 14%.

12. 11-11 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Duration/Price Relationship Price change is proportional to duration and not to maturity  P/P = -D x [  (1+y) / (1+y) D * = modified duration D * = D / (1+y)  P/P = - D * x  y

13. 11-12 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Approximating price changes Consider our 10%, 5-year bond. Yields are initially at 14% and the duration of the bond is 4.1. Consider our 10%, 5-year bond. Yields are initially at 14% and the duration of the bond is 4.1. Suppose rates fall by 200 basis points. Estimate the percentage change in the bond’s price. Estimate the price (& compare to actual price). Suppose rates fall by 200 basis points. Estimate the percentage change in the bond’s price. Estimate the price (& compare to actual price).

14. 11-13 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Estimating price sensitivity Price Duration Pricing Error from convexity

15. 11-14 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Using duration and convexity to estimate price changes. Correction for convexity:

16. 11-15 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Convexity Estimate of percentage price change = 0.074997 Estimate of price = $927.3751

17. 11-16 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Uses of Duration Summary measure of length or effective maturity for a portfolio Summary measure of length or effective maturity for a portfolio Immunization of interest rate risk (passive management) Immunization of interest rate risk (passive management) –Net worth immunization –Target date immunization Measure of price sensitivity for changes in interest rate Measure of price sensitivity for changes in interest rate

18. 11-17 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Target date immunization Consider the two components of interest rate risk Consider the two components of interest rate risk –price risk –reinvestment rate risk Suppose rates are at 14% and you have a 4.1 year horizon. Suppose rates are at 14% and you have a 4.1 year horizon. Consider the bond with a 10% annual coupon, 5 years, and duration of 4.1 years Consider the bond with a 10% annual coupon, 5 years, and duration of 4.1 years

19. 11-18 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Target date immunization

20. 11-19 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Target or Horizon Date Immunization Set D p = Horizon Date or Target date Set D p = Horizon Date or Target date –then price risk (sale price of the bond) and reinvestment risk (accumulated value of the coupon payments) offset one another Rebalancing (must monitor & update) Rebalancing (must monitor & update) –Changing interest rates –The passage of time

21. 11-20 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Other approaches Cash flow matching Cash flow matching dedication strategy dedication strategy horizon matching (not analysis) horizon matching (not analysis) contingent immunization contingent immunization

22. 11-21 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Active Bond Management: Swapping Strategies Substitution swap Substitution swap Intermarket swap Intermarket swap Rate anticipation swap Rate anticipation swap –D = HD => immunized –D > HD => net price risk –D net reinvestment rate risk Pure yield pickup Pure yield pickup Tax swap Tax swap

23. 11-22 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Rate anticipation Consider a bond with 10 years to maturity, 8% coupon (paid annually), priced at $877.11. Current interest rates = 10% Consider a bond with 10 years to maturity, 8% coupon (paid annually), priced at $877.11. Current interest rates = 10% –Duration = 7.04 –Suppose your HD = 4 years –You expect interest rates will decline –Since D > HD => net price risk

24. 11-23 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Rate anticipation

25. 11-24 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Interest rate swap Contract between two parties to trade the cash flows corresponding to different securities without actually exchanging the securities directly. Contract between two parties to trade the cash flows corresponding to different securities without actually exchanging the securities directly. Plain vanilla: convert interest payments based on a floating rate into payments based on a fixed rate (or vice versa) Plain vanilla: convert interest payments based on a floating rate into payments based on a fixed rate (or vice versa) –Notional