CHAPTER TWENTY-TWO

BOND PORTFOLIO MANAGEMENT

1

BOND PORTOLIOS

• METHODS OF MANAGEMENT

– Passive

• rests on the belief that bond markets are semi-strong efficient

• current bond prices viewed as accurately reflecting all publicly available information

2

BOND PORTOLIOS

• METHODS OF MANAGEMENT

– Active

• rests on the belief that the market is not so efficient

• some investors have the opportunity to earn above-average returns

3

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– for a typical bond making periodic coupon payments and a terminal principal payment

4

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– THEOREM 1

• If a bond’s market price increases

• then its yield must decrease

• conversely if a bond’s market price decreases

• then its yield must increase

5

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– THEOREM 2

• If a bond’s yield doesn’t change over its life,

• then the size of the discount or premium will decrease as its life shortens

6

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– THEOREM 3

• If a bond’s yield does not change over its life

• then the size of its discount or premium will decrease

• at an increasing rate as its life shortens

7

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– THEOREM 4

• A decrease in a bond’s yield will raise the bond’s price by an amount that is greater in size than the corresponding fall in the bond’s price that would occur if there were an equal-sized increase in the bond’s yield

• the price-yield relationship is convex

8

BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS

– THEOREM 5

• the percentage change in a bond’s price owing to a change in its yield will be smaller if the coupon rate is higher

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CONVEXITY

CONVEXITY DEFINITION:

– a measure of the curvedness of the price-yield relationship

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CONVEXITY

• THE PRICE-YIELD RELATIONSHIP

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YTM

Price

CONVEXITY

• THEOREM 1 TELLS US

– price and yield are inversely related but not in a linear fashion (see graph)

– an increase in yield is associated with a drop in bond price

– but the size of the change in price when yield rises is greater than the size of the price change when yield falls

12

DURATION

• DEFINITION:

– measures the “average maturity” of a stream of bond payments

– it is the weighted average time to full recovery of the principal and interest payments

13

DURATION

• FORMULA

where P0 = the current market price of the bond

PV(Ct )= the present value of the coupon payments

t = time periods

14

T

t

t tP

CPVD

1 0

)(

DURATION

• THE RELATION OF DURATION TO PRICE CHANGES

– THEOREM 5 implies

• bonds with same maturity date but different coupon rates may react differently to changes in the interest rate

• duration is a price-risk indicator

15

DURATION

• DURATION IS A PRICE-RISK INDICATOR– FORMULA

rewritten

where y = the bond’s yield to maturity

16

)1( ytmDp

p

y

yD

p

p

1

DURATION

• MODIFIED DURATION

– FORMULA:

– reflects the bond’s % price change for a one percent change in the yield

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y

DDm

1

DURATION

• THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION

– whereas duration would have us believe that the relationship between yield and price change is linear

– convexity shows us otherwise

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DURATION

• THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION

19

YTM

P

C

0

IMMUNIZATION

• DEFINITION: a bond portfolio management technique which allows the manager to be relatively certain of a given promised cash stream

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IMMUNIZATION

• HOW TO ACCOMPLISH IMMUNIZATION– Duration of a portfolio of bonds

• equals the weighted average of the individual bond durations in the portfolio

– Immunization• calculate the duration of the promised outflows

• invest in a portfolio of bonds with identical durations

21

IMMUNIZATION

• PROBLEMS WITH IMMUNIZATION

– default and call risk ignored

– multiple nonparallel shifts in a nonhorizontal yield curve

– costly rebalancing ignored

– choosing from a wide range of candidate bond portfolios is not very easy

22

ACTIVE MANAGEMENT

• TYPES OF ACTIVE MANAGEMENT

– Horizon Analysis

• simple holding period selected for analysis

• possible yield structures at the end of period are considered

• sensitivities to changes in key assumptions are estimated

23

ACTIVE MANAGEMENT

• TYPES OF ACTIVE MANAGEMENT

– Bond Swapping

• exchanging bonds to take advantage of superior ability to predict yields

• Categories:– substitution swap

– intermarket spread swap

– rate anticipation swap

– pure yield pickup swap

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ACTIVE MANAGEMENT

• TYPES OF ACTIVE MANAGEMENT

– Contingent Immunization

• portfolio managed actively as long as favorable results are obtained

• if unfavorable, then immunize the portfolio

25

PASSIVE MANAGEMENT

• TYPES OF PASSIVE MANAGEMENT

– INDEXATION

• the portfolio is formed to track a chosen index

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