Chapter 5
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Chapter 5. Bond Management. 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    If  Arbitrage sell long-term bond yield  P   .

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Chapter 5

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Chapter 5

Chapter 5

Bond Management


A the term structure of interest rates term to maturity vs ytm

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

    If

     Arbitrage sell long-term bond yield

     P


B the liquidity preference theory hicks 1946

(B) The Liquidity Preference Theory,Hicks 1946

YTM

Yield with liquidity premium

Yield without liquidity premium

N


C market segmentation theory gulberson 1957

(C) Market Segmentation Theory, Gulberson 1957


D cir theory 1979 cox ingersoll and ross

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


B fixed income portfolio management

B. Fixed-Income Portfolio Management

1. Duration

the weighted average of the times to each coupon or principal payment made by the bond


B fixed income portfolio management1

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


B fixed income portfolio management2

B. Fixed-Income Portfolio Management

(2)Duration vs. Interest rate sensitivity

MD= ―(ΔP/P)/[ΔYTM/(1+YTM)]


B fixed income portfolio management3

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


B fixed income portfolio management4

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


B fixed income portfolio management5

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


B fixed income portfolio management6

e. The duration of a level

perpetuity is (1+YTM)/YTM

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


B fixed income portfolio management7

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


B fixed income portfolio management8

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


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