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Bond Duration

A bond's price sensitivity to interest-rate changes.

Macaulay duration is the cash-flow-weighted average time to receive a bond's payments; modified duration converts it into a % price change per 1% rate move. Longer-duration bonds are far more rate-sensitive — the core of fixed-income risk.

D_mac = Σ (t · PV_t) / Price
D_mod = D_mac / (1 + y)

import numpy as np
t = np.arange(1, n + 1)
pv = cash_flows / (1 + y)**t
macaulay = (t * pv).sum() / pv.sum()
mod_duration = macaulay / (1 + y)