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Duration & Convexity

How bond prices respond to rate moves — the first- and second-order sensitivities every ALM desk watches.

Duration measures the price sensitivity of a fixed-income instrument to a change in interest rates. Modified duration of 5 means roughly a 5% price decline for a +100bp move in yield (and a 5% gain for −100bp).

It is a first-order approximation: the price/yield relationship is a curve, not a line.

Convexity

Convexity is the second-order term — it captures the curvature duration misses. Positive convexity means prices rise more when rates fall than they drop when rates rise by the same amount: a favorable asymmetry. Callable bonds and MBS can exhibit negative convexity, where prepayment behavior works against the holder as rates fall.

Why it matters for a balance sheet

  • Asset/liability duration mismatch is the core interest-rate exposure of a bank or credit union. If asset duration exceeds liability duration, a rate rise erodes economic value of equity (EVE).
  • Duration of equity = (D_assets × Assets − D_liabilities × Liabilities) / Equity. ALM committees target a band around it.

How PhxIQ relates

The treasury curve on the dashboard (2/5/10/30Y) is the backbone of any duration estimate. A steepening or flattening changes the marginal cost of extending duration — watch the 2s10s and 10s3m spreads.