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 aboveaverage 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
9
CONVEXITY
CONVEXITY DEFINITION:
– a measure of the curvedness of the price-yield
relationship
10
CONVEXITY
• THE PRICE-YIELD RELATIONSHIP
Price
YTM
11
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
 PV (Ct )
D  
P0
t 1 
T

t

where P0 = the current market price of
the bond
PV(Ct )= the present value of the
coupon payments
t = time periods
14
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
p
  D(1  ytm)
p
rewritten
 y
p
  D
1 y
p





where y = the bond’s yield to maturity
16
DURATION
• MODIFIED DURATION
D
– FORMULA:
Dm 
1 y
– reflects the bond’s % price change for a one
percent change in the yield
17
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
18
DURATION
• THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION
P
C
0
YTM
19
IMMUNIZATION
• DEFINITION: a bond portfolio
management technique which allows the
manager to be relatively certain of a given
promised cash stream
20
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
24
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
26