Key rate duration

Textbook case: a life insurer's balance sheet as of December 31, 2025, with asset and liability duration both at 9.8 years, hence matched at first order. The partial durations tell another story: at five years, assets are sensitive at 3.1 and liabilities at 1.2, while at thirty years assets sit at 0.9 and liabilities at 3.4. A flattening between five and thirty years makes this officially matched balance sheet lose money. Key rate duration measures the sensitivity of value to a move in a single segment of the curve, the others held fixed, across a grid of reference points, typically two, five, ten, twenty and thirty years. The partial durations add up to the overall duration, but their profile shows what the sum hides. Two portfolios with the same duration react the same way to a parallel shock and in opposite ways to a steepening. In hedging, a very long annuity liability set against intermediate maturity assets forces you to neutralize each segment, and no longer the average level alone. In risk measurement, the tool matters all the more because curves rarely move in parallel.