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Chapter 11

Chapter 11. Managing Fixed-Income Investments. Managing Fixed Income Securities: Basic Strategies. Active strategy Trade on interest rate predictions Trade on market inefficiencies Passive strategy Control risk Balance risk and return. Bond Pricing Relationships.

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Chapter 11

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  1. Chapter 11 Managing Fixed-Income Investments

  2. Managing Fixed Income Securities: Basic Strategies • Active strategy • Trade on interest rate predictions • Trade on market inefficiencies • Passive strategy • Control risk • Balance risk and return

  3. Bond Pricing Relationships • Inverse relationship between price and yield • An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield • Long-term bonds tend to be more price sensitive than short-term bonds

  4. Bond Pricing Relationships (cont.) • As maturity increases, price sensitivity increases at a decreasing rate • Price sensitivity is inversely related to a bond’s coupon rate • Price sensitivity is inversely related to the yield to maturity at which the bond is selling

  5. Duration A measure of the effective maturity of a bond The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment Duration is shorter than maturity for all bonds except zero coupon bonds Duration is equal to maturity for zero coupon bonds

  6. Duration: Calculation

  7. Duration Calculation

  8. Consider a 5-year, 10% coupon bond. Yield = 14%.

  9. Duration/Price Relationship Price change is proportional to duration and not to maturity P/P = -D x [(1+y) / (1+y) D* = modified duration D* = D / (1+y) P/P = - D* x y

  10. Approximating price changes • Consider our 10%, 5-year bond. Yields are initially at 14% and the duration of the bond is 4.1. • Suppose rates fall by 200 basis points. Estimate the percentage change in the bond’s price. Estimate the price (& compare to actual price).

  11. Price Pricing Error from convexity Duration Estimating price sensitivity

  12. Using duration and convexity to estimate price changes. Correction for convexity:

  13. Convexity Estimate of percentage price change = 0.074997 Estimate of price = $927.3751

  14. Uses of Duration • Summary measure of length or effective maturity for a portfolio • Immunization of interest rate risk (passive management) • Net worth immunization • Target date immunization • Measure of price sensitivity for changes in interest rate

  15. Target date immunization • Suppose rates are at 14% and you have a 4.1 year horizon. • Consider the bond with a 10% annual coupon, 5 years, and duration of 4.1 years

  16. Target date immunization

  17. Immunization and rebalancing • Changing interest rates • The passage of time

  18. Other approaches • Cash flow matching • dedication strategy • horizon analysis • contingent immunization

  19. Active Bond Management: Swapping Strategies • Substitution swap • Intermarket swap • Rate anticipation swap • Pure yield pickup • Tax swap

  20. Interest rate swap • Contract between two parties to trade the cash flows corresponding to different securities without actually exchanging the securities directly. • Plain vanilla: convert interest payments based on a floating rate into payments based on a fixed rate (or vice versa) • Notional

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