Fixed Income · Core
Modified Duration
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
Definition
ModD = −(1/P) dP/dy = MacD / (1+y/k). A ModD of 8 means about −8% price for +100bp yields (before convexity). DV01 is the dollar version on a 1bp move.
Why it matters
This is what you hedge. Key-rate durations break the parallel-shift lie.
Case
A 10-year at ModD 8.5 loses ~8.5% on a 100bp backup, less on the way down because of convexity. The first print is the duration; the second is the convexity smile.
How to read it
Parallel shift is a toy. Use KRDs and a curve scenario. Then add spread duration for credit.
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