Key rate duration

Two portfolios can share exactly the same overall duration and behave in opposite ways when the curve deforms. One concentrates its cash flows at ten years, the other spreads them between two and thirty. Facing a parallel move they react identically; facing a steepening, one gains and the other loses. Key rate duration measures that difference by computing the sensitivity of value to a move in a single segment of the curve, the others held fixed, for a series of reference points, typically two, five, ten, twenty and thirty years. The sum of the partial durations returns the overall duration, but their profile says what the sum conceals. The use is twofold. In hedging, it allows a position that neutralizes each segment rather than the average level alone, which is indispensable for a very long annuity liability set against intermediate maturity assets. In risk measurement, it reveals an exposure that the observed deformation of curves, rarely parallel in fact, makes more real every year.

Life insurer balance sheet as of December 31, 2025, overall asset and liability duration both equal to 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; at thirty years, assets at 0.9 and liabilities at 3.4. A thirty basis point flattening between five and thirty years then costs some fifteen million euros to a balance sheet that is officially matched.

key rate duration, sensibilité par segment, duration partielle, profil de sensibilité