1. Chapter 5
Bond Management

2. A. The term structure of interest rates ---Term to Maturity vs. YTM
(A) The expectation theory, Fisher 1896 If
 Arbitrage buy long-term bond yield
 P  
 Arbitrage sell long-term bond yield
 P  

3. (B) The Liquidity Preference Theory,Hicks 1946
YTM
Yield with liquidity premium
Yield without liquidity premium N

4. (C) Market Segmentation Theory, Gulberson 1957

5. (D) CIR Theory, 1979 Cox, Ingersoll and Ross

6. B. Fixed-Income Portfolio Management
1. Duration
the weighted average of the times to each coupon or principal payment made by the bond

7. B. Fixed-Income Portfolio Management
(1) Macaulay's Duration, 1938 Macaulay (MD)
MD=1{[C1/(1+Y)]/P0}+2{[C2/(1+Y)2]/P0}
+...+T{[(CT+F)/(1+Y) ]/P0}
= {[tCT/(1+Y) ]+[FT/(1+Y) ]}/P0

8. B. Fixed-Income Portfolio Management
(2) Duration vs. Interest rate sensitivity
MD= ―(ΔP/P)/[ΔYTM/(1+YTM)]

9. B. Fixed-Income Portfolio Management
(3) Bond Rules
a. The duration of a zero-coupon bond
equals its time to maturity
< Proof >:
MD = / P0 = T(P0/ P0) =T

10. B. Fixed-Income Portfolio Management
b. Holding time to maturity and YTM constant, a bond's duration and interest rate sensitivity are higher when the coupon rate is lower i.e. MD/i<0

11. B. Fixed-Income Portfolio Management
c. Holding the coupon rate constant, a bond's duration and interest rate sensitivity generally increase with its time to maturity
i.e. MD/t >0

12. B. Fixed-Income Portfolio Management
d. Holding other factors constant,the duration and interest rate sensitivity of a coupon bond are higher when the bond's yield to maturity is lower  i.e. MD/YTM < 0
e. The duration of a level
perpetuity is (1+YTM)/YTM

13. B. Fixed-Income Portfolio Management
2. Immunization:
strategies used by investors to shield their overall
financial status from exposure to interest rate
fluctuations
 Rebalancing portfolio
As interest rates and asset durations change, a manager must
rebalance the portfolio of fixed income assets continually to
realign its duration with the duration of the obligation

14. B. Fixed-Income Portfolio Management
Single bond, Single payment [Immunization rule]
MD of the bond = MD of the liability
Bond portfolio, Single payment [Immunization rule]
Weighted Average MD of the bond portfolio
= MD of the liability