对外经济贸易大学投资学课件9

《对外经济贸易大学投资学课件9》由会员分享，可在线阅读，更多相关《对外经济贸易大学投资学课件9（24页珍藏版）》请在装配图网上搜索。

1、Lecture 9 Managing Bond Portfolio nInverse relationship between price and yieldnAn increase in a bonds yield to maturity results in a smaller price decline than the gain associated with a decrease in yieldnLong-term bonds tend to be more price sensitive than short-term bondsBond Pricing Relationship

2、snAs maturity increases,price sensitivity increases at a decreasing ratenPrice sensitivity is inversely related to a bonds coupon ratenPrice sensitivity is inversely related to the yield to maturity at which the bond is sellingBond Pricing Relationships(contd)Figure 16.1 Change in Bond Price as a Fu

3、nction of Change in Yield to MaturitynA measure of the effective maturity of a bondnThe weighted average of the times until each payment is received,with the weights proportional to the present value of the paymentnDuration is the slope of the price-yield curve expressed as a fraction of the bond pr

4、icenDuration can be used to measure the sensitivity of bond price changes to yield changesDurationpriceytCFDTttt/)1(1 Duration:CalculationY:discount rateCFt:cash flow on year tDuration calculation examplenTwo year bond,coupon rate 6%,yield to maturity 8%,par value$1,000,compute the durationCompute t

5、he bond price first 60/(1+8%)+1060/(1+8)2=964.33Compute the duration1*60/(1+8%)+2*1060/(1+8)2/964.33=1.94Rules for DurationRule 1 The duration of a zero-coupon bond equals its time to maturityRule 2 Holding maturity constant,a bonds duration is higher when the coupon rate is lowerRule 3 Holding the

6、coupon rate constant,a bonds duration generally increases with its time to maturityRule 4 Holding other factors constant,the duration of a coupon bond is higher when the bonds yield to maturity is lowerPrice change is proportional to durationP/P=-D x(1+y)/(1+y)D*=modified durationD*=D/(1+y)P/P=-D*x

7、yDuration/Price RelationshipDuration/price relationship-examplen30 year bond,coupon rate 8%,yield to maturity 9%,current price$897.26,modified duration is 11.37 years,if yield to maturity increases to 9.1%,what is the price changes?P=-D*x(y)*P =-11.37*897.26*(9.1%-9%)=-9.36Price decreases$9.36Rules

8、for DurationRule 1 The duration of a zero-coupon bond equals its time to maturityRule 2 Holding maturity constant,a bonds duration is higher when the coupon rate is lowerRule 3 Holding the coupon rate constant,a bonds duration generally increases with its time to maturityRule 4 Holding other factors

9、 constant,the duration of a coupon bond is higher when the bonds yield to maturity is lowerRules 5 The duration of a level perpetuity is equal to:(1+y)/yFigure 16.2 Bond Duration versus Bond MaturityConvexitynThe actual relationship between bond price and yields is not linear,duration rule is a good

10、 approximation for small changes in bond yieldnWhen yield change is big,need to consider convexitynConvexity measures the curvature of the price-yield curve,it is the second derivative(the rate of change of he slope)of the price-yield curve divided by the bond priceYieldPriceDurationPricing Error fr

11、om convexityDuration and ConvexityCorrection for ConvexityntttttyCFyPConvexity122)()1()1(1Correction for Convexity:)(21*2yConveixityyDPP Convexity-examplen30 year bond,par value$1,000,coupon rate 8%,yield to maturity 8%,suppose the bond pay coupon annually.if yield increase from 8%to 10%,compute the

12、 price change a)using duration only;b)using duration and convexityConvexity-example16.121000/30%)81(1080*30.2%)81(80*2%)81(80*1 DModified duration=12.16/(1+8%)=11.26Price change based on duration onlyP=-D*x(y)*P=-11.26*0.02*1000=-225.2Price decreases$225.2Convexity-examplenCompute convexity78.247100

13、0/30%)81(1080*31*30.2%)81(80*3*2%)81(80*2*1 CPrice change based on duration and convexity)(21*2yConveixityyDPP 7.182*08.102.0*78.247*2102.0*26.1122 PPPrice decreases$182.7,big difference because the yield change is largeRules for ConvexityRule 1 Holding maturity constant,a bonds convexity is higher

14、when the coupon rate is lowerRule 2 Holding the coupon rate constant,a bonds convexity generally increases with its time to maturityRule 3 Holding other factors constant,the convexity of a coupon bond is higher when the bonds yield to maturity is lowerImmunization of interest rate risknNet worth imm

15、unizationDuration of assets=Duration of liabilitiesNet Present Value of asset=Net Present Value of LiabilityAssume interest can be reinvested at current interest rateImmunization of interest rate risk-examplenSuppose a firm has a single payment of$1,931 in 10 years,r=10%,if interest rate increase,th

16、e value of the firms asset will drop,the firm may not have enough fund to pay the obligation,how can the firm immunize from interest rate risk?Example(Cont)nPV of the liability(1931*(1+10%)-10)=745nDuration of single payment liability equal to time to maturity,10 yearsnTo immunize,the firm search se

17、curities that have duration of 10 years and net present value no less than 745nA 20 year bond,par value$1,000,coupon rate 7%,has a duration of 10 years and NPV of 745,the firm purchase this bond to immunize interest rate risk of its liabilityEffect of Interest Rate changes on terminal values in year

18、 10Rates stay at 10%Rates fall to 4%Rates rise to 16%Accumulated value of interest payments received and reinvested70*1.10970*1.04970*1.16970*170*170*1Total=1115Total=842Total=1492Market value in the 10th year8161243565Grand total193120852057Total Liability 1931193119311931Net Surplus0154126Immunization and portfolio rebalancenWhen interest rate fall,the value of your liability increase,however,the value of your asset also increase nWhen interest rate increase,the value of your asset fall,however,the value of your liability also fallnThat is how immunization works nNeed dynamic rebalancing