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Interest Rate Risk and Yield Curve

Duration

Macaulay duration is the weighted average time to receive a bond's cash flows. Modified duration converts that into a price sensitivity, and it is the number traders use:

ΔPP≈−Dmod×Δy\frac{\Delta P}{P} \approx -D_{\text{mod}} \times \Delta y

A bond with modified duration 7 falls about 7% in price when yields rise 1%. That is the entire practical content: duration is the beta of fixed income, and it is a hedge ratio.

DV01 (dollar value of a basis point) is the same idea in currency: the P&L change per 0.01% move in yields. Desks manage risk in DV01 because it aggregates across bonds with different prices and maturities.

What raises duration: longer maturity, lower coupon (more value in the distant principal payment), and lower yield. A zero-coupon bond has duration exactly equal to its maturity, since there is only one cash flow.

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