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Modified Duration

Measures the percentage price change for a 1% yield change.

Modified duration measures interest rate sensitivity: it estimates how much a bond's price changes when yields move. A duration of 5.0 means a 1% yield increase causes roughly a 5% price drop. This is a first-order (linear) approximation — it works well for small yield changes but becomes less accurate for large moves (where convexity matters). For example, if a bond has modified duration of 7.2 and yields rise 0.5%, expect price to fall about 3.6% (7.2 × 0.5%). Textbooks often derive modified duration from Macaulay duration as MacDur / (1 + y/m). In practice, Strata computes it numerically using symmetric finite difference: the bond is repriced at yield ± 1bp and the slope of the price-yield curve is estimated from the two prices. This numerical approach handles irregular cash flows, odd first coupons, and day-count conventions that the closed-form formula cannot.

Formula
ModDur=P+P2Δy  P0\text{ModDur} = -\,\frac{P_{+} - P_{-}}{2\,\Delta y\;P_{0}}
Where
P+P_{+}=Dirty price at yield + 1bp
PP_{-}=Dirty price at yield − 1bp
Δy\Delta y=Yield bump (0.0001)
P0P_{0}=Dirty price at current yield
Variables
D_{mod}Modified duration (years)
PCurrent dirty price
P_{+1bp}Price at yield + 1bp
P_{-1bp}Price at yield - 1bp
Assumptions
  • Symmetric 1bp yield shock for finite difference
  • Assumes parallel shift in yield curve
  • Does not capture convexity effects
vs. Industry Tools
Excel MDURATION()Uses analytical formula; small differences possible
Bloomberg DURGenerally matches for standard fixed-rate bonds