BMGT343 Chapter 11 Managing Bond Portfolios Interest Rate Risk Interest Rate Sensitivity as interest rates rise and fall bondholders experience capital gains and loss in a competitive market all securities must offer investors fair expected rates of return bond prices decrease when yields rise and the price is convex meaning that decreases in yields have bigger impacts on price than increase in yields of equal magnitude o o o o o o bond prices and yields are inversely related as yields increase bond prices fall as yields fall bond prices rise an increase in a bond s YTM results in a smaller price change than decrease in yield of equal magnitude prices of long term bonds tend to be more sensitive to interest rate changed than prices of short term bonds if rates increase the bond is less valuable as its cash flows are discounted at a now higher rate the sensitivity of bonds prices to changes in yields increases at a decreasing rate as maturity increase Interest rate risk is less than proportional to bond maturity interest rate risk is inversely related to the bond s coupon rate Prices of low coupon bonds are more sensitive to change in interest rates than prices of high coupon bonds the sensitivity of a bond s price to a change in its yield are inversely related to the yield to maturity at which the bond is currently selling at a higher yield a higher fraction of the bond s value is due to its earlier payments which have lower effective maturity and interest rate sensitivity The overall sensitivity of the bond price to change in yields is thus lower Duration Macauly s duration a measure of the effective maturity of a bond defined as the weighted average of the times until each payment with weights proportional to the PV of the payment Weight PV bond price o Wt CFt 1 i t bond price D t x Wt Duration is a simple summary measure of the effective average maturity of the portfolio It is an essential tool in immunizing portfolios from interest rate risk Duration is a measure of interest rate sensitivity of a bond portfolio When interest rates change the percentage change in a bond s price is proportional to its duration o P P D x 1 y 1 y Modified duration macauly s duration divided by 1 YTM measures interest rate sensitivity of bond o P P D x y o Percentage change in bond price is the product of modified duration D and the change in bond s YTM y What Determines Duration duration allows us to quantify sensitivity which greatly enhances our ability to formulate investment strategies o Rule 1 the duration of a zero coupon bond equals its time to maturity o Rule 2 With time to maturity and YTM held constant a bond s duration and interest rate sensitivity are higher when the coupon rate is lower o Rule 3 With the coupon rate held constant a bond s duration and interest rate sensitivity generally increase with time to maturity Duration always increases with maturity for bonds selling at par or at premium to par o Rule 4 With other factors held constant the duration and interest rate sensitivity of a coupon bond are higher when the bond s YTM is lower o Rule 5 the duration of a perpetuity is 1 y y Passive Bond Management the net worth of a firm and its ability to meet future obligations fluctuate with interest rates immunization strategy to shield net worth from interest rate movements o when interest rates increase unexpectedly banks can suffer serious decreases in net worth their assets fall in value by o o o o o more than their liabilities funds should match interest rate exposure of assets and liabilities so that the value of assets will track the value of liabilities whether rates rise or fall the financial manager may want to immunize the fund against interest rate volatility at a higher interest rate reinvested coupons will grow at a faster rate offsetting capital loss fixed income investors face two offsetting types of interest rate risk price risk and reinvestment rate risk for a horizon equal to the portfolio s duration price and reinvestment risk exactly cancel out and the obligation is immunized as interest rates and asset durations continually change managers must rebalance the portfolio of fixed income assets to realign its duration with the duration of the obligation immunization is a passive strategy only in the sense that it does not involve attempts to identify undervalued securities Immunization managers still actively update and monitor their positions Cash Flow Matching and Dedication cash flow matching matching cash flows from a fixed income portfolio with those of an obligation o CF matching automatically immunizes a portfolio from interest rate movements because the CF from the bond and the obligation exactly offset each other Dedication strategy refers to multiperiod cash flow matching o The manger selects either zero coupon or coupon bonds that provide total cash flows that match a series of obligations in each period o The advantage of dedication is that it is a once and for all approach to eliminating interest rate risk Convexity the percentage change in the value of a bond approximately equals the product of modified duration times the change in the bond s yield o P P D x y o The percentage change in price change is directly proportional to the change in the bond s yield Duration approximation the straight line always understates the value of the bonds it underestimates the increase in bond price when yield falls it overestimates the decline in price when yield rises o o we can quantify the rate of change of the slope of the price yield curve expressed as a fraction of the bond price o P P D x y convexity x y 2 Convexity is generally considered a desirable trait bonds with greater curvature gain more in price when yields fall than they lose when yields rise Investors will pay more and accept lower yields on bonds with greater convexity Active Bond Management 1 substitution swap exchange of one bond for a bond with similar attributed but more attractively price a would be motivated by the belief that the market has temporarily mispriced the two bonds with a discrepancy representing a profit opportunity 2 intermarket spread swap switching from one segment of the bond market to another a pursued when an investor believes the spread between two sectors of the bond market is temporarily out of line 3 rate anticipation swap a switch made in response to forecasts of interest rate changes investors who believe rates will swap into bonds of longer duration 4 pure yield