So far in this reading, we focused on how to use duration and convexity to measure the price change given a change in YTM. Now, we will look at what causes the YTM to change.
Example 19: Calculating modified duration
Consider a 4-year, 9% coupon paying semi-annual bond with a YTM of 9%. The duration of the bond is 6.89 periods. Calculate the modified duration.
For a one percent change in the annual YTM, the percentage change in the bond price is 3.297%.
Example 20: Calculating the change in the credit spread on a corporate bond
The (flat) price on a fixed-rate corporate bond falls one day from 96.55 to 95.40 per 100 of par value because of poor earnings and an unexpected ratings downgrade of the issuer. The (annual) modified duration for the bond is 5.32. What is the estimated change in the credit spread on the corporate bond, assuming benchmark yields are unchanged?
Given that the price falls from 96.55 to 95.40, the percentage price decrease is 1.191%.
-1.191% ≈ -5.32 × ∆Yield,
Given an annual modified duration of 5.32, the change in the yield-to-maturity is 22.39 bps.