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# Chapter 11 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Chapter 11' - schuyler

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Presentation Transcript

### 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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• 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

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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

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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.

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• 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

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• 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 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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• 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

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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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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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• Substitution swap

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

• 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

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• 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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