Chapter 11 Managing Fixed-Income Investments

11-2 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Managing Fixed Income Securities: Basic Strategies Active strategy Active strategy –Trade on interest rate predictions –Trade on market inefficiencies Passive strategy Passive strategy –Control risk –Balance risk and return

11-3 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Pricing Relationships Inverse relationship between price and yield 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 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 Long-term bonds tend to be more price sensitive than short-term bonds

11-4 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Pricing Relationships (cont.) As maturity increases, price sensitivity increases at a decreasing rate 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 a bond’s coupon rate Price sensitivity is inversely related to the yield to maturity at which the bond is selling Price sensitivity is inversely related to the yield to maturity at which the bond is selling

11-5 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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

11-6 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Duration: Calculation

11-7 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Duration Calculation

11-8 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Consider a 5-year, 10% coupon bond. Yield = 14%.

11-9 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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

11-10 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Approximating price changes Consider our 10%, 5-year bond. Yields are initially at 14% and the duration of the bond is 4.1. 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). Suppose rates fall by 200 basis points. Estimate the percentage change in the bond’s price. Estimate the price (& compare to actual price).

11-11 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Estimating price sensitivity Price Duration Pricing Error from convexity

11-12 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Using duration and convexity to estimate price changes. Correction for convexity:

11-13 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Convexity Estimate of percentage price change = Estimate of price = $

11-14 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Uses of Duration Summary measure of length or effective maturity for a portfolio Summary measure of length or effective maturity for a portfolio Immunization of interest rate risk (passive management) Immunization of interest rate risk (passive management) –Net worth immunization –Target date immunization Measure of price sensitivity for changes in interest rate Measure of price sensitivity for changes in interest rate

11-15 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Target date immunization Suppose rates are at 14% and you have a 4.1 year horizon. 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 Consider the bond with a 10% annual coupon, 5 years, and duration of 4.1 years

11-16 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Target date immunization

11-17 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Immunization and rebalancing Changing interest rates Changing interest rates The passage of time The passage of time

11-18 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Other approaches Cash flow matching Cash flow matching dedication strategy dedication strategy horizon analysis horizon analysis contingent immunization contingent immunization

11-19 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Active Bond Management: Swapping Strategies Substitution swap Substitution swap Intermarket swap Intermarket swap Rate anticipation swap Rate anticipation swap Pure yield pickup Pure yield pickup Tax swap Tax swap

11-20 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Interest rate swap Contract between two parties to trade the cash flows corresponding to different securities without actually exchanging the securities directly. 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) Plain vanilla: convert interest payments based on a floating rate into payments based on a fixed rate (or vice versa) –Notional