McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Managing Bond Portfolios CHAPTE R 10

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 10.1 Change in Bond Price as a Function of YTM

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration: Calculation t t t w[CF y ice   () ]1 Pr Dtw t T t    1 CFCashFlowforperiodt t 

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Calculation

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 10.3 Duration as a Function of Maturity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration/Price Relationship Price change is proportional to duration and not to maturity  P/P = -D x [  y / (1+y)] D * = modified duration D * = D / (1+y)  P/P = - D * x  y

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Immunization In Practice Example Page Immunization and rebalancing Cash flow matching and dedication

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Correction for Convexity )( y ConvexityyD P P    Modify the pricing equation: Convexity is Equal to:             N t t t t t y CF P )1(y)(1 1 Where: CF t is the cash flow (interest and/or principal) at time t.

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 10.6 Bond Price Convexity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Active Bond Management: Swapping Strategies Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Contingent Immunization Allow the managers to actively manage until the bond portfolio falls to a threshold level Once the threshold value is hit the manager must then immunize the portfolio Active with a floor loss level

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 10-8 Contingent Immunization

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Swaps Interest rate swap basic characteristics One party pays fixed and receives variable Other party pays variable and receives fixed Principal is notional Growth in market Started in 1980 Estimated over $60 trillion today Hedging applications