CHAPTER FIFTEEN
BOND PORTFOLIO
MANAGEMENT
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 informationBOND 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 returnsBOND PRICING THEOREMS
5 BOND PRICING THEOREMS
• for a typical bond making periodic coupon
payments and a terminal principal payment
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 increaseBOND 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 shortensBOND 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 shortensBOND 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 convexBOND PRICING THEOREMS
5 BOND PRICING THEOREMS
• THEOREM 5
the percentage change in a bond’s price owing to a change in it yield will be smaller if thecoupon rate is higher
CONVEXITY
CONVEXITY
• DEFINITION: a measure of the
curvedness of the price-yield relationship
CONVEXITY
THE PRICE-YIELD RELATIONSHIP
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
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
DURATION
FORMULA
where P
0= the current market price of the bond
PV(C
t)= the present value of the coupon payments
T
t
t
t
P
C D PV
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 indicatorDURATION
DURATION IS A PRICE-RISK INDICATOR
• FORMULA
rewritten
( 1 ytm )
p D
p
y
p D
DURATION
MODIFIED DURATION
• FORMULA:
• reflects the bond’s % price change for a one percent change in the yield
y D
mD
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
DURATION
THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION
P
C
IMMUNIZATION
DEFINITION: a bond portfolio
management technique which allows
the manager to be relatively certain of a
given promised cash stream
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 durationsIMMUNIZATION
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
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 estimatedACTIVE 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
ACTIVE MANAGEMENT
TYPES OF ACTIVE MANAGEMENT
• Contingent Immunization
portfolio managed actively as long as favorable results are obtained
if unfavorable, then immunize the portfolioPASSIVE MANAGEMENT
