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CHAPTER FIFTEEN BOND PORTFOLIO MANAGEMENT

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BOND PORTOLIOS n METHODS OF MANAGMENT Passive 3 rests on the belief that bond markets are semi- strong efficient 3 current bond prices viewed as accurately reflecting all publicly available information

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BOND PORTOLIOS n METHODS OF MANAGMENT Active 3 rests on the belief that the market is not so efficient 3 some investors have the opportunity to earn above-average returns

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS for a typical bond making periodic coupon payments and a terminal principal payment

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS THEOREM 1 3 If a bond’s market price increases 3 then its yield must decrease 3 conversely if a bond’s market price decreases 3 then its yield must increase

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS THEOREM 2 3 If a bond’s yield doesn’t change over its life, 3 then the size of the discount or premium will decrease as its life shortens

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS THEOREM 3 3 If a bond’s yield does not change over its life 3 then the size of its discount or premium will decrease 3 at an increasing rate as its life shortens

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS THEOREM 4 3 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 3 the price-yield relationship is convex

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BOND PRICING THEOREMS n 5 BOND PRICING THEOREMS THEOREM 5 3 the percentage change in a bond’s price owing to a change in it yield will be smaller if the coupon rate is higher

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CONVEXITY n CONVEXITY DEFINITION: a measure of the curvedness of the price-yield relationship

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CONVEXITY n THE PRICE-YIELD RELATIONSHIP YTM Price

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CONVEXITY n 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 n 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 n FORMULA where P 0 = the current market price of the bond PV(C t )= the present value of the coupon payments t = time periods

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DURATION n THE RELATION OF DURATION TO PRICE CHANGES THEOREM 5 implies 3 bonds with same maturity date but different coupon rates may react differently to changes in the interest rate 3 duration is a price-risk indicator

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DURATION n DURATION IS A PRICE-RISK INDICATOR FORMULA rewritten where y = the bond’s yield to maturity

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DURATION n MODIFIED DURATION FORMULA: reflects the bond’s % price change for a one percent change in the yield

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DURATION n 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 n THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION YTM P C 0

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IMMUNIZATION n 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 n HOW TO ACCOMPLISH IMMUNIZAITON Duration of a portfolio of bonds 3 equals the weighted average of the individual bond durations in the portfolio Immunization 3 calculate the duration of the promised outflows 3 invest in a portfolio of bonds with identical durations

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IMMUNIZATION n 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 n TYPES OF ACTIVE MANAGEMENT Horizon Analysis 3 simple holding period selected for analysis 3 possible yield structures at the end of period are considered 3 sensitivities to changes in key assumptions are estimated

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ACTIVE MANAGEMENT n TYPES OF ACTIVE MANAGEMENT Bond Swapping 3 exchanging bonds to take advantage of superior ability to predict yields 3 Categories: – substitution swap – intermarket spread swap – rate anticipation swap – pure yield pickup swap

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ACTIVE MANAGEMENT n TYPES OF ACTIVE MANAGEMENT Contingent Immunization 3 portfolio managed actively as long as favorable results are obtained 3 if unfavorable, then immunize the portfolio

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PASSIVE MANAGEMENT n TYPES OF PASSIVE MANAGEMENT INDEXATION 3 the portfolio is formed to track a chosen index

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END OF CHAPTER 15

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