1. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-1 Managing Bond Portfolios Chapter 16

2. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-2 Active strategy -Trade on interest rate predictions -Trade on market inefficiencies Passive strategy -Control risk -Balance risk and return Managing Fixed Income Securities: Basic Strategies

3. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-3 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

4. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-4 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. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-5 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

6. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-6 Duration: Calculation

7. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-7 8% Bond Time years PaymentPV of CF (10%) WeightC1 X C4.54038.095.0395.0197 14036.281.0376 1.5 2.0 40 1040 sum 34.553 855.611 964.540.0358.8871 1.000.0537 1.7742 1.8852 Duration Calculation: Example using Table 16.3

8. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-8 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

9. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-9 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.

10. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-10 Rules for Duration (cont’d) Rules 5 The duration of a level perpetuity is equal to: Rule 6 The duration of a level annuity is equal to:

11. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-11 Rules for Duration (cont’d) Rule 7 The duration for a corporate bond is equal to:

12. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-12 Yield Price Duration Pricing Error from convexity Duration and Convexity

13. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-13 Correction for Convexity Correction for Convexity:

14. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-14 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

15. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-15 Substitution swap Inter-market swap Rate anticipation swap Pure yield pickup Tax swap Active Bond Management: Swapping Strategies

16. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-16 Maturity Yield to Maturity % 3 mon 6 mon 9 mon 1.5 1.25.75 Yield Curve Ride

17. McGraw-Hill/Irwin Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved. 16-17 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.