Key-rate duration and yield-curve risk guide

In plain language — Saying “duration is five” often imagines that all rates move together. Key-rate duration divides the curve into regions and asks what happens if, for example, the two-year node moves but the ten-year node does not.

Key-rate duration (KRD) is a local price sensitivity to a shock at one point or segment of a curve, while other nodes remain fixed under a stated interpolation rule. A set of KRDs forms a profile and exposes short-, medium- and long-term positions that one total duration can offset or conceal.

From one duration to curve nodes

Two portfolios can have the same aggregate duration. One may concentrate cash flows around five years; another may combine positive exposure at two and ten years. They appear similar under a parallel shift but respond differently to a twist or curvature change.

For node i, a central finite-difference estimate is:

KRDᵢ ≈ (Pᵢ,− − Pᵢ,+) / (2 × P₀ × Δyᵢ)

Pᵢ,− and Pᵢ,+ are revalued prices after downward and upward node shocks; P₀ is initial price and Δyᵢ the positive bump size. For small moves:

ΔP / P ≈ −Σ KRDᵢ × Δyᵢ

The result depends on the curve being shocked—government, zero, swap, discounting or another term structure—and on nodes, interpolation, bump size, repricing and option treatment.

Curve shapes without slogans

A steepening increases the yield difference between stated long and short nodes; a flattening reduces it. Those words do not specify which points move or their absolute direction. A bear steepener can involve larger rises at the long end, while a bull steepener can involve larger declines at the short end. Displaying basis-point shocks by maturity removes ambiguity.

Curve shape is a snapshot. KRD describes portfolio response; it does not estimate the probability of a curve shape occurring.

Operational workflow

Start with reconciled positions and cash flows. Build a base curve from documented instruments, conventions and algorithms. Choose economically meaningful nodes—perhaps 2, 5, 10 and 30 years—without assuming that set fits every book. Perturb each node, rebuild intermediate points and fully reprice the portfolio.

KRD can be converted into key-rate DV01 by applying full value and one basis point. Aggregation preserves signs and currency. A total near zero does not remove gross exposure: opposite sensitivities at different nodes can lose together under a twist.

A node hedge uses instruments with compatible profiles but introduces basis, credit, liquidity, convexity and execution costs. “Duration neutral” is not “free of rate risk.”

Model limits

Large shocks require convexity and full repricing. Callable and mortgage-backed cash flows change, so effective KRD depends on exercise or prepayment models. In credit bonds, risk-free rates and spreads may move together: separating them is an attribution choice rather than a causal law.

Estimates also change as maturity shortens, coupons enter the horizon and curves are recalibrated. Data version and timestamp are part of the measure.

Common error — Cancelling signs until aggregate duration looks harmless. Preserve node profiles, gross sensitivities and multi-node scenarios.

Questions this page answers

Which curve moves? Where are the nodes? How are shocks interpolated? Is the result percentage or monetary? Are cash flows fixed? What gross exposure remains behind the total?