CHAPTER FIFTEEN BOND PORTFOLIO MANAGEMENT BOND PORTOLIOS n

CHAPTER FIFTEEN BOND PORTFOLIO MANAGEMENT

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

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

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

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

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

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

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 equalsized increase in the bond’s yield 3 the price-yield relationship is convex

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

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

CONVEXITY n THE PRICE-YIELD RELATIONSHIP Price YTM

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

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

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

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

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

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

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

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

IMMUNIZATION n DEFINITION: a bond portfolio management technique which allows the manager to be relatively certain of a given promised cash stream

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

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

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

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

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

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

END OF CHAPTER 15