This document discusses different methods for managing bond portfolios, including passive and active management. It also outlines five bond pricing theorems and defines key concepts like convexity and duration. Immunization is introduced as a technique for matching a portfolio's duration to promised cash flows. Active strategies include horizon analysis and bond swapping, while passive strategies involve indexation.
2. 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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3. 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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4. BOND PRICING THEOREMS
• 5 BOND PRICING THEOREMS
– for a typical bond making periodic coupon
payments and a terminal principal payment
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5. 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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6. 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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7. 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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8. 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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9. 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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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
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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
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14. DURATION
• FORMULA
T
P V (Ct )
D t
where P0 = the 1 market price of
t current P 0
the bond
PV(Ct )= the present value of the
coupon payments
t = time periods
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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
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16. DURATION
• DURATION IS A PRICE-RISK INDICATOR
– FORMULA
p
rewritten D (1 ytm )
p
where y = thep yield maturity
bond’s D y
to
1 y
p
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17. DURATION
• MODIFIED DURATION
– FORMULA:
D
Dm
1 y
– reflects the bond’s % price change for a one
percent change in the yield
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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
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20. 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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21. 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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22. 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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23. 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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24. 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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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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26. PASSIVE MANAGEMENT
• TYPES OF PASSIVE MANAGEMENT
– INDEXATION
• the portfolio is formed to track a chosen index
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