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Unformatted text preview: FIN 401 Principles of Investments and Security Markets Chapter 11: Managing Bond Portfolios 2 Interest Rate Risk There is an inverse relationship between bond prices and yields high yields imply low prices . This relationship becomes fundamental when considering that interest rates fluctuate substantially. The capital gains or losses that result from these interest rate movements, make investment risky. This is true even if the coupon and principal payments are guaranteed. 3 Interest Rate Sensitivity Not symmetric relationship : An increase in a bonds yield to maturity results in smaller price decline than the price gain associated with a decrease of equal magnitude in yield; For a 1year zero coupon bond P = 1000/(1+Y): Yield 10% 15% 20% Price 909.09 869.57 833.33 Change in Price 39.5236.24 Prices of longterm bonds tend to be more sensitive to interest rate changes than prices of shortterm bonds; Increase Decrease 4 Interest Rate Sensitivity As maturity increases, price sensitivity to yield changes increases at a decreasing rate; But it is not proportional. For example, a 2 yr bond is more sensitive to interest rate changes than a 1 yr bond, but less than twice as sensitive. Interest rate risk is inversely related to the bonds coupon rate; Higher coupon means investor gets more money sooner Bond prices are more sensitive to changes in yields when the bond is selling at a lower initial yield to maturity. Changes from lower initial YTM represent greater proportional changes than changes from higher initial YTM. 5 Changes in Bond Prices % Change in Bond Price Change in Yield to Maturity A B C D Bond A: Coupon: 11% Maturity: 5 years Initial YTM: 9% Bond B: Coupon: 11% Maturity: 30 years Initial YTM:9% Bond C: Coupon: 4% Maturity: 30 years Initial YTM: 9% Bond D: Coupon: 4% Maturity: 30 years Initial YTM: 6% 6 Coupon Rate and Interest Rate Sensitivity Example 1: Prices of 8% Coupon Bond (semiannual payments) Yield to Maturity T = 1 Year T = 10 Years T = 20 Years 8% 1,000 1,000 1,000 9% 990.64 934.96 907.99 Change in Price 0.94% 6.50% 9.20% Example 2: Prices of ZeroCoupon Bond (semiannual compounding) Yield to Maturity T = 1 Year T = 10 Years T = 20 Years 8% 924.56 456.39 208.29 9% 915.73 414.64 171.93 Change in Price 0.96% 9.15% 17.46% 7 Duration Measure Interest Rate Sensitivity Look at the effective maturity of a bond. Investors can do so by looking at the promised cash flows; these provide a summary statistic of the effective maturity. Concept of duration: the weighted average of the times to each coupon or principal payment made by the bond. 8 Duration The cash flow weights are related to the importance of every single payment to the value of the bond....
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 Spring '08
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