Chapter 11 Managing Bond Portfolios I Interest Rate Risk a Interest Rate Sensitivity i Bond prices and Yields are inversely related ii An increase in a bonds YTM resukts in a smaller price change than a decrease in YTM of equal magnitude iii Prices of longer bonds are more sensitive to interests rate changes than prices of short term bonds iv The sensitivity of bond prices to change in yields increases at a decreasing rate as maturity increases 1 Interest rate risk is less that proportional to bond maturity v Interest rate is risk is inversely related to the bonds coupon rate 1 Prices of lower coupon bonds are more sensitive to changes in interest rates than prices of higher coupon bonds vi Sensitivy of a bonds price to a change in its yields is inversely rekated to the yield to maturity at which the bond is currently selling b Duration measure of the effective maturity of a bond defined as the weighted average of the times until payment woth weights proportional to the present value of the payment i Wt CFt 1 y t Bond Price t time 1 wt weight 2 CFt Cash flow of time t 3 4 y yield to maturity 5 Numerator is the peresrnt value of cash flow of time t 6 Denominator is present value of all payments forthcoming from the bond 7 Weights sum to 1 ii D t wt 1 D Duration iii Importance of the portfolio 1 simple summary measure of the effective average maturity 2 way to immunize portfolio from interest rate risk 3 measure of interest rate sensitivity of a bond iv Bonds price volatility is proportional to its duration v D D 1 y 1 D Modified Duration a Measures interest rate sensitivity of bonds c Determinates of Duration i Duration of a 0 Coupon Bond is equal to its time to maturity ii With Time to Maturity and YTM held constant a bonds duration and interest rate sensitivity are higher when the coupon rate is lower iii With Coupon rate held constant a bonds duration and interest rate sensitivity generally increase with time to maturity Duration always increases with maturity for bond selling at par or at premium to par iv With other factors held constant the duration and interest rate sensitivity of a coupon bond are higher when the bonds yield to maturity is lower v Duration of a Perpetuity 1 y y II Passove Bond Management a Immunization a strategy to shield net worth from interest rate movement i Horizon equal to the portfolios duration price risk and reinvestment risk exactly cancel out b Cash Flow Matching with that of an obligation matching cash flow from a fixed income portfolio i Dedication Strategy refers to multiple cash flow matching III Convexity a The curvature of the price of price yield relationship of a bond
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