CHAPTER FIFTEEN BOND PORTFOLIO MANAGEMENT

BOND PORTOLIOS METHODS OF MANAGMENT Passive rests on the belief that bond markets are semi- strong 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 The theorems deal with how bond prices move in response to changes in the bonds’ yields-to-maturity. for a typical bond making periodic coupon payments and a terminal principal payment

BOND PRICING THEOREMS 5 BOND PRICING THEOREMS THEOREM 1 If a bonds market price increases then its yield must decrease conversely if a bonds market price decreases then its yield must increase

BOND PRICING THEOREMS 5 BOND PRICING THEOREMS THEOREM 2 If a bonds yield doesnt 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 bonds 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 bonds yield will raise the bonds price by an amount that is greater in size than the corresponding fall in the bonds price that would occur if there were an equal-sized increase in the bonds yield the price-yield relationship is convex

BOND PRICING THEOREMS 5 BOND PRICING THEOREMS THEOREM 5 the percentage change in a bonds price owing to a change in it yield will be smaller if the coupon rate is higher Notes: this theorem does not apply to bonds with a life of one year or to bonds that have no maturity date.

CONVEXITY DEFINITION: a measure of the curvedness of the price-yield relationship The first and fourth bond pricing theorems have led to the concept in bond valuation known as convexity.

CONVEXITY THE PRICE-YIELD RELATIONSHIP YTM Price

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

DURATION Calculation Taking the present value of each cash flow Multiplying each one by the respective amount of time until it is received Summing the resulting figures Dividing this sum by the market price of the bond

DURATION Consider a bond with annual coupon payments of $80, a remaining life of three years, and a par value of $1,000. Duration=? YTM=10%

DURATION A zero coupon bond will have a duration equal to its remaining life T Because there is only one cash flow associated with such a bond For any coupon-bearing bond its duration will always be less than the amount of time to its maturity date T.

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 rewritten where y = the bonds yield to maturity

DURATION The prices of the bonds may adjust by notably different amounts when there is a given change in interest rates. However, bonds with the same duration will react quite similarly. When the yields of two bonds having the same duration change by the same percentage, then the prices of the two bonds will change by approximately equal percentages.

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 YTM P C 0

DURATION Because the relationship between yield changes and bond price changes is convex, not linear, the use of equation will underestimate the new price associated with either an increase or a decrease in the bond’s yield. However, for small changes in yields the error is relatively small, and thus, as an approximation, equation works reasonably well.

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