Chapter 11

Managing Bond

Portfolios

Interest Rate Sensitivity(Duration we will cover in Finc420)

The concept: • Any security that gives an investor more money back

sooner (as a % of your investment) will have lower price volatility when interest rates change.

• Maturity is a major determinant of bond price sensitivity to interest rate changes, but

• It is not the only factor; in particular the coupon rate and the current ytm are also major determinants.

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More on Duration1. Duration increases with maturity

2. A higher coupon results in a lower duration

3. Duration is shorter than maturity for all bonds except zero coupon bonds

4. Duration is equal to maturity for zero coupon bonds

5. All else equal, duration is shorter at higher interest rates

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Duration/Price Relationship• Price change is proportional to duration

and not to maturity

P/P = -D x [y / (1+y)]

D* = modified duration

D* = D / (1+y)

P/P = - D* x y

D = Duration

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Interest Rate RiskInterest rate risk is the possibility that an investor does not earn the promised ytm because of interest rate changes.

A bond investor faces two types of interest rate risk:

1.Price risk: The risk that an investor cannot sell the bond for as much as anticipated. An increase in interest rates reduces the sale price.

2.Reinvestment risk: The risk that the investor will not be able to reinvest the coupons at the promised yield rate. A decrease in interest rates reduces the future value of the reinvested coupons.

The two types of risk are potentially offsetting.

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Immunization• Immunization: An investment strategy

designed to ensure the investor earns the promised ytm.

• A form of passive management, two versions1. Target date immunization

• Attempt to earn the promised yield on the bond over the investment horizon.

• Accomplished by matching duration of the bond to the investment horizon

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Immunization

2. Net worth immunization

• The equity of an institution can be immunized by matching the duration of the assets to the duration of the liabilities.

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Cash Flow Matching and Dedication

• Cash flow from the bond and the obligation exactly offset each other

– Automatically immunizes a portfolio from interest rate movements

• Not widely pursued, too limiting in terms of choice of bonds

• May not be feasible due to lack of availability of investments needed

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Problems with Immunization

1. May be a suboptimal strategy

2. Does not work as well for complex portfolios with option components, nor for large interest rate changes

3. Requires rebalancing of the portfolio periodically, which then incurs transaction costs– Rebalancing is required when interest rates move– Rebalancing is required over time

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The Need for Convexity(calculation in Finc 420)

• Duration is only an approximation

• Duration asserts that the percentage price change is linearly related to the change in the bond’s yield– Underestimates the increase in bond prices

when yield falls– Overestimates the decline in price when the

yield rises

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Convexity: Definition and Usage

2yConvexity2/1)y1(

yD

P

P

n

1t

2t

t2

)tt()y1(

CF

)y1(P

1Convexity

Where: CFt is the cash flow (interest and/or principal) at time t and y = ytm

The prediction model including convexity is:

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Swapping Strategies - active1. Substitution swap

– Exchanging one bond for another with very similar characteristics but more attractively priced

2. Intermarket spread swap– Exploiting deviations in spreads between two market segments

3. Rate anticipation swap– Choosing a duration different than your investment horizon to

exploit a rate change.• Rate increase: Choose D > Investment horizon• Rate decrease: Choose D < Investment horizon

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Swapping Strategies4. Pure yield pickup

– Switching to a higher yielding bond, may be longer maturity if the term structure is upward sloping or may be lower default rating.

5. Tax swap– Swapping bonds for tax purposes, for example

selling a bond that has dropped in price to realize a capital loss that may be used to offset a capital gain in another security

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