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# Chapter 5 PowerPoint PPT Presentation

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   .

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

YTM

N

## 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 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 Management

(2)Duration vs. Interest rate sensitivity

MD= ―(ΔP/P)/[ΔYTM/(1+YTM)]

## 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 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 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

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 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 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