1. CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Cover image

2. 16- 2 Cover image  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. Bond Pricing Relationships

3. 16- 3 Cover image Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity

4. 16- 4 Cover image  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. Bond Pricing Relationships (cont’d)

5. 16- 5 Cover image Table 16.1 Prices of an 8% Coupon Bond (Coupons Paid Semiannually)

6. 16- 6 Cover image Table 16.2 Prices of Zero-Coupon Bond (Coupons Paid Semiannually)

7. 16- 7 Cover image  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. Duration

8. 16- 8 Cover image Figure 16.2 Cash Flows Paid by 9% Coupon, Annual Payment Bond with an 8-Year Maturity and 10% Yield to Maturity

9. 16- 9 Cover image Duration: Calculation

10. 16- 10 Cover image Spreadsheet 16.1 Calculating the Duration of Two Bonds

11. 16- 11 Cover image 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 Duration/Price Relationship

12. 16- 12 Cover image Rules for Duration Rule 1 The duration of a zero-coupon bond equals its time to maturity. Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower. Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity. Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower. Rules 5 The duration of a level perpetuity is equal to: (1+y) / y

13. 16- 13 Cover image Figure 16.3 Bond Duration versus Bond Maturity

14. 16- 14 Cover image Table 16.3 Bond Duration (Initial Bond Yield 8% APR)

15. 16- 15 Cover image Figure 16.4 Bond Price Convexity (30-Year Maturity, 8% Coupon; Initial Yield to Maturity = 8%

16. 16- 16 Cover image Correction for Convexity Correction for Convexity:

17. 16- 17 Cover image Figure 16.5 Convexity of Two Bonds

18. 16- 18 Cover image Figure 16.6 Price –Yield Curve for a Callable Bond

19. 16- 19 Cover image Figure 16.7 Price – Yield Curve for a Mortgage- Backed Security

20. 16- 20 Cover image Figure 16.8 Panel AP: Cash Flows to Whole Mortgage Pool; Panels B – D Cash Flows to Three Tranches

21. 16- 21 Cover image  Bond-Index Funds  Immunization of interest rate risk: –Net worth immunization Duration of assets = Duration of liabilities –Target date immunization Holding Period matches Duration  Cash flow matching and dedication Passive Management

22. 16- 22 Cover image Figure 16.9 Stratification of Bonds into Cells

23. 16- 23 Cover image Table 16.4 Terminal value of a Bond Portfolio After 5 Years (All Proceeds Reinvested)

24. 16- 24 Cover image Figure 16.10 Growth of invested Funds

25. 16- 25 Cover image Figure 16.11 Immunization

26. 16- 26 Cover image Table 16.5 Market Value of Balance Sheet

27. 16- 27 Cover image  Substitution swap  Intermarket swap  Rate anticipation swap  Pure yield pickup  Tax swap Active Management: Swapping Strategies

28. 16- 28 Cover image Maturity Yield to Maturity % 3 mon 6 mon 9 mon 1.5 1.25.75 Yield Curve Ride

29. 16- 29 Cover image Contingent Immunization  A combination of active and passive management.  The strategy involves active management with a floor rate of return.  As long as the rate earned exceeds the floor, the portfolio is actively managed.  Once the floor rate or trigger rate is reached, the portfolio is immunized.

30. 16- 30 Cover image Figure 16.12 Contingent Immunization