Chapter 11
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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.

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Chapter 11

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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.


More on Duration

  • Duration increases with maturity

  • A higher coupon results in a lower duration

  • Duration is shorter than maturity for all bonds except zero coupon bonds

  • Duration is equal to maturity for zero coupon bonds

  • All else equal, duration is shorter at higher interest rates


Duration/Price Relationship

D = Duration

Price change is proportional to duration and not to maturity

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

D* = modified duration

D*= D / (1+y)

DP/P = - D* x Dy


Interest Rate Risk

Interest 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:

  • 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.

  • 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.



  • Immunization: An investment strategy designed to ensure the investor earns the promised ytm.

  • A form of passive management, two versions

    • 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



  • Net worth immunization

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


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

    • May be a suboptimal strategy

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

    • Requires rebalancing of the portfolio periodically, which then incurs transaction costs

      • Rebalancing is required when interest rates move

      • Rebalancing is required over time


    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


    Convexity: Definition and Usage

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

    The prediction model including convexity is:


    Swapping Strategies - active

    • Substitution swap

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

    • Intermarket spread swap

      • Exploiting deviations in spreads between two market segments

    • 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


    Swapping Strategies

    • 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.

    • 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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