1. Managing Bond Portfolios
Chapter 16

2. Basic Strategies Active strategy Passive 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’d)
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. 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.

6. Duration: Calculation

7. Duration Calculation: Spreadsheet 16.18%
Time
Payment
PV of CF
Weight
C1 X
Bond
years
(10%) C4 .5 40
38.095
.0395
.0197 1 40
36.281
.0376
.0376
1.5 40
34.553
.0358
.0537
2.0
1040 .
8871
1.7742
sum
1.000
1.8852

8. 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

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. 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. Rules for Duration (cont’d)
Rule 7 The duration for a corporate bond is equal to:

12. Duration and Convexity
Price
Pricing Error from convexity
Duration
Yield

13. Correction for Convexity

14. Passive Management 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

15. Active Management: Swapping Strategies
Substitution swap
Inter-market swap
Rate anticipation swap
Pure yield pickup
Tax swap

16. Yield Curve Ride Yield to Maturity % Maturity 3 mon 6 mon 9 mon
Maturity
3 mon 6 mon mon

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.

18. Interest Rate Swaps
Contract between two parties to exchange a series of cash flows
One party pays a fixed rate and receives a variable rate
One party pays a variable rate and receives a fixed rate
Payments based on notional principal

19. Swap Example Figure 16-11 6.95% 7.05% 7% Swap Dealer Company A
Company B
LIBOR
LIBOR
LIBOR