FRM Glossary · Part I · Valuation

Duration (Macaulay / Modified)

The weighted-average time to a bond's cash flows (Macaulay) and the percentage price sensitivity to a 1% yield change (Modified).

In more detail

Macaulay duration is the cash-flow-weighted average time-to-payment. Modified duration = Macaulay / (1 + y/k) where k is compounding frequency per year. For a small parallel yield shift Δy, the bond price changes by approximately −MD × Δy. Convexity captures the second-order (curvature) effect for larger yield moves.