B. Managing Bond Portfolios

1.  Interest rate risk

• Bond prices and yields are inversely related

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a.  Interest rate sensitivity

• Increase in a bond's yield to maturity results in a smaller price change than a decrease

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(1) Impact of maturity

• Prices of long-term bonds more sensitive to interest rate changes than short-term bonds

• Interest rate risk is less than proportional to bond maturity

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(2)  Impact of coupon

• Interest rate risk is inversely related to the coupon rate

- Prices of low-coupon bonds more sensitive to changes in interest rates than high-coupon bonds

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(3) Impact of yield to maturity

• Price sensitivity inversely related to the yield to maturity

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b.  Duration

• Average maturity of a bond's cash flows

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• Measure of interest rate sensitivity

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c.  Factors affecting duration

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(1) Duration of a zero-coupon bond equals its time to maturity

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(2) Duration is higher when coupon rate is lower

• Higher weights on earlier payments

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(3) Duration increases with time to maturity

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(4) Duration higher when yield to maturity  is lower

• Lesser impact on distant cash flows

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(5) Duration of a level perpetuity

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• Excel

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2.  Passive bond management

• Assume bond prices are fairly set, try only to control risk of bond portfolio

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a. Immunization

• Insulate portfolios from interest rate risk altogether

- Protect current net worth against interest rate fluctuations

- May have obligation to make future payments, e.g., pension funds

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• Price risk - change in interest rates causes capital gains or losses

• Reinvestment risk - change in interest rates affects returns on coupons

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• Matching duration of liabilities and assets balances price and reinvestment risk

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(1) Procedure

•  Calculate duration of the liability

• Calculate duration of asset portfolio

• Find the asset mix that sets duration of assets equal to duration of liability

• Fully fund the obligation

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(2) Rebalancing

• May need to rebalance portfolio if interest rates change and/or time passes

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(3)  Cash flow matching

• Match cash flows from a portfolio with the cash flows of an obligation

• Dedication strategy - cash flow matching  over multiple periods

• Not widely used because it limits the choice of bonds

3.  Convexity

• Duration is an approximation

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• Convexity of bond = curvature of price-yield curve

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4.  Active bond management

• Believe information or insight is superior

- Interest rates

- Mispricing

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a.  Substitution swap

• Exchange nearly identical bonds, assuming a mispricing of one

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b.  Intermarket spread swap

• Believe yield spread between two sectors of the bond market are out of line

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c.  Rate anticipation swap

• Exchange into bonds with longer duration if interest rates are expected to fall

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d.  Pure yield pickup swap

• Exchange into higher-yield bonds

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e.  Tax swap

• Exchange bonds to exploit some tax advantage