A sensitivity, not a countdown
Macaulay duration is the present-value-weighted timing of a bond’s cash flows. Modified duration converts that idea into a local measure of price sensitivity to yield. For a small yield change, percentage price change is approximately minus modified duration multiplied by the yield change expressed as a decimal.
A simple calculation
A modified duration of 4.5 suggests that a 0.50 percentage point rise in yield would reduce price by roughly 2.25%, all else equal. The input is 0.005, not 0.50. This is a first-order approximation: it is most useful for relatively small yield changes around the starting point.
What the number leaves out
Price–yield relationships are curved, which is why convexity can improve the estimate for a conventional option-free bond. A single duration also does not describe every change in the yield curve. For larger moves, non-parallel curve shifts or instruments with embedded options, use a model appropriate to the cash flows and compare the approximation with full repricing.
A learning example, not a market recommendation. Work through the assumptions before applying any model.
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