bond portfolio management
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BOND PORTFOLIO MANAGEMENT
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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
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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
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BOND PRICING THEOREMS
• 5 BOND PRICING THEOREMS– for a typical bond making periodic coupon
payments and a terminal principal payment
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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
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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
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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
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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
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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
YTM
Price
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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
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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
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DURATION
• FORMULA
where P0 = the current market price of the bond
PV(Ct )= the present value of the coupon payments
t = time periods
T
t
t tP
CPVD
1 0
)(
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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
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DURATION
• DURATION IS A PRICE-RISK INDICATOR– FORMULA
rewritten
where y = the bond’s yield to maturity
)1( ytmDp
p
y
yD
p
p
1
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DURATION
• MODIFIED DURATION– FORMULA:
– reflects the bond’s % price change for a one percent change in the yield
y
DDm
1
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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
YTM
P
C
0
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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
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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
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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
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PASSIVE MANAGEMENT
• TYPES OF PASSIVE MANAGEMENT– INDEXATION
• the portfolio is formed to track a chosen index