CHAPTER FIFTEEN

1
CHAPTER FIFTEEN

• BOND PORTFOLIO MANAGEMENT

2
BOND PORTOLIOS

• METHODS OF MANAGMENT
• Passive
• rests on the belief that bond markets are
  semi-strong efficient
• current bond prices viewed as accurately
  reflecting all publicly available information

3
BOND PORTOLIOS

• METHODS OF MANAGMENT
• Active
• rests on the belief that the market is not so
  efficient
• some investors have the opportunity to earn
  above-average returns

4
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• for a typical bond making periodic coupon
  payments and a terminal principal payment

5
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• THEOREM 1
• If a bonds market price increases
• then its yield must decrease
• conversely if a bonds market price decreases
• then its yield must increase

6
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• THEOREM 2
• If a bonds yield doesnt change over its life,
• then the size of the discount or premium will
  decrease as its life shortens

7
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• THEOREM 3
• If a bonds 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

8
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• THEOREM 4
• A decrease in a bonds yield will raise the
  bonds price by an amount that is greater in size
  than the corresponding fall in the bonds price
  that would occur if there were an equal-sized
  increase in the bonds yield
• the price-yield relationship is convex

9
BOND PRICING THEOREMS

• 5 BOND PRICING THEOREMS
• THEOREM 5
• the percentage change in a bonds price owing to
  a change in it yield will be smaller if the
  coupon rate is higher

10
CONVEXITY

• CONVEXITY
• DEFINITION a measure of the curvedness of the
  price-yield relationship

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CONVEXITY

• THE PRICE-YIELD RELATIONSHIP

Price
YTM
12
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

13
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

14
DURATION

• FORMULA
• where P0 the current market price of the
  bond
• PV(Ct ) the present value of the coupon
  payments
• t time periods

15
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

16
DURATION

• DURATION IS A PRICE-RISK INDICATOR
• FORMULA
• rewritten
• where y the bonds yield to maturity

17
DURATION

• MODIFIED DURATION
• FORMULA
• reflects the bonds price change for a one
  percent change in the yield

18
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

19
DURATION

• THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION

P
C
YTM
0
20
IMMUNIZATION

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

21
IMMUNIZATION

• HOW TO ACCOMPLISH IMMUNIZAITON
• 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

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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

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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

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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

25
ACTIVE MANAGEMENT

• TYPES OF ACTIVE MANAGEMENT
• Contingent Immunization
• portfolio managed actively as long as favorable
  results are obtained
• if unfavorable, then immunize the portfolio

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PASSIVE MANAGEMENT

• TYPES OF PASSIVE MANAGEMENT
• INDEXATION
• the portfolio is formed to track a chosen index

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• END OF CHAPTER 15