CHAPTER FIFTEEN
BOND PORTFOLIO
MANAGEMENT
BOND PORTOLIOS

METHODS OF MANAGMENT
• Passive
rests on the belief that bond markets are semistrong efficient
current bond prices viewed as accurately
reflecting all publicly available information
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
BOND 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 increase
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
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
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 equalsized increase in the bond’s yield
the price-yield relationship is convex
BOND 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 the
coupon rate is higher
CONVEXITY

CONVEXITY
• DEFINITION:
a measure of the
curvedness of the price-yield relationship
CONVEXITY

THE PRICE-YIELD RELATIONSHIP
Price
YTM
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
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
D
where

T

t 1
 PV ( C

P0

t
)

t

P0 = the current market price of
the bond
PV(Ct )= the present value of the
coupon payments
t = time periods
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
DURATION

DURATION IS A PRICE-RISK
INDICATOR
• FORMULA
p
  D  (1  ytm ) 
p
rewritten  p
p
 y
  D 
1  y



where y = the bond’s yield to maturity
DURATION

MODIFIED DURATION
• FORMULA:
D
m
D

1 y
• reflects the bond’s % price change for a
one percent change in the yield
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
0
YTM
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
durations
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
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
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
ACTIVE MANAGEMENT

TYPES OF ACTIVE MANAGEMENT
• Contingent Immunization
portfolio managed actively as long as favorable
results are obtained
if unfavorable, then immunize the portfolio
PASSIVE MANAGEMENT

TYPES OF PASSIVE MANAGEMENT
• INDEXATION
the portfolio is formed to track a chosen index
END OF CHAPTER 15