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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.

11-2

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

11-3

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

11-4

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.

11-5

Immunization

- 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

- Target date immunization

11-6

Immunization

- Net worth immunization
- The equity of an institution can be immunized by matching the duration of the assets to the duration of the liabilities.

11-7

Cash Flow Matching and Dedication Not widely pursued, too limiting in terms of choice of bonds May not be feasible due to lack of availability of investments needed

- Cash flow from the bond and the obligation exactly offset each other
- Automatically immunizes a portfolio from interest rate movements

11-8

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

11-9

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

11-10

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:

11-11

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

- Choosing a duration different than your investment horizon to exploit a rate change.

11-12

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

11-13

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