# Figure 11.1 Change in Bond Prices as a Function of Change in ...

Managing Bond Portfolios Bodie, Kane, and Marcus Essentials of Investments, 9th Edition McGraw-Hill/Irwin 11 Copyright 2013 by The McGraw-Hill Companies, Inc. All rights reserved. 11.1 Interest Rate Risk

Interest Rate Sensitivity Bond prices and yields are inversely related Increase in bonds yield to maturity results in smaller price change than yield decrease of equal magnitude Long-term bond prices more sensitive to interest rate changes than short-term bonds As maturity increases, sensitivity of bond prices to changes in yields increases at decreasing rate 11-2

11.1 Interest Rate Risk Interest Rate Sensitivity As maturity increases, sensitivity of bond prices to changes in yields increases at decreasing rate Interest rate risk is inversely related to bonds coupon rate; low-coupon bonds are more sensitive to interest rates Sensitivity of bonds price-to-yield change is inversely related to current yield to maturity

11-3 Figure 11.1 Change in Bond Prices as a Function of Change in Yield to Maturity 11-4 Table 11.1 Annual Coupon Prices Prices of 8% annual coupon bonds *Equals value of bond at a 9% yield to maturity minus value of bond at (the original) 8% yield, divided by the value at 8% yield.

11-5 Table 11.2 Zero-Coupon Bond Prices Prices of zero-coupon bonds *Equals value of bond at a 9% yield to maturity minus value of bond at (the original) 8% yield, divided by the value at 8% yield. 11-6 11.1 Interest Rate Risk

11-7 Spreadsheet 11.1 Calculation of Duration of Two Bonds 11-8 11.1 Interest Rate Risk 11-9 Spreadsheet 11.2 Computing Duration

11-10 11.1 Interest Rate Risk What Determines Duration? Zero-coupon bonds duration is time to maturity Time/yield to maturity constant, bonds duration and interest-rate sensitivity higher when coupon price lower Coupon rate constant, bonds duration and interest-rate sensitivity generally increase with

time to maturity; duration always increases with maturity for bonds at or above par 11-11 11.1 Interest Rate Risk 11-12 Figure 11.2 Duration as Function of Maturity 11-13

Table 11.3 Annual Coupon Bond Duration Durations of annual coupon bonds (initial bond yield = 6%) Coupon Rates (% per year) Years to Maturity 4% 6% 8%

10% 1 1.000 1.000 1.000 1.000

5 4.611 4.465 4.342 4.237 10 8.281

7.802 7.445 7.169 20 13.216 12.158

11.495 11.041 Infinite (perpetuity) 17.667 17.667 17.667

17.667 11-14

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