If there is a change in a bond’s YTM, there will be a corresponding change in the price of a bond. The change in the price can be explained as the product of two factors:
The percentage change in the price of a bond for a given change in yield can also be determined using this equation:
Example 17: Ranking bonds in terms of interest rate risk
A fixed-income analyst is asked to rank three bonds in terms of interest rate risk. The increases in the yields-to-maturity represent the “worst case” for the scenario being considered.
The modified duration and convexity statistics are annualized. ∆Yield is the increase in the annual yield-to-maturity. Rank the bonds in terms of interest rate risk.
Calculate the estimated price change for each bond:
The duration effect is -3.65 × 0.005 = -1.825%.
The convexity effect is 0.5 × 14.8 × 0.005^2= 0.0185%.
The expected change in bond price is -1.825% + 0.0185% = -1.8065%.
The duration effect is -5.75 × 0.0025 = -1.4375%.
The convexity effect is 0.5 × 38.7 × 0.0025^2= 0.0121%.
The expected change in bond price is -1.4375% + 0.0121% = -1.4254%.
The duration effect is -12.28 × 0.0015 = -1.842%.
The convexity effect is 0.5 × 146 × 0.0015^2= 0.0164%.
The expected change in bond price is -1.842% + 0.0164% = -1.8256%.
Bond C has the highest degree of interest rate risk (a potential loss of 1.8256%), followed by Bond A (a potential loss of 1.8065%) and Bond B (a potential loss of 1.4254%).