Key-Rate Duration: How to Read Yield-Curve Risk

Modified or effective duration is useful for estimating a price response to a small, broadly parallel yield move. But market curves do not always shift in parallel: short, intermediate, and long rates can move by different amounts or in opposite directions. A single duration cannot show where a portfolio’s cash flows are most exposed along the curve.

CFA Institute treats level, slope, and curvature as distinct yield-curve movements. Key-rate duration (KRD) adds a maturity-by-maturity view: it estimates the price sensitivity associated with a change around one chosen benchmark maturity while the rest of the curve follows a defined shock shape. See the CFA Institute overview of curve-based fixed-income risk measures.

A key rate, or partial, duration measures sensitivity to the benchmark yield at a specific maturity point or segment. A system might report exposures around 2, 5, 10, and 30 years. Those nodes are a model’s chosen grid, not a universal set of market rates. For each node, the measure asks how the instrument’s value changes when that part of the benchmark curve is shocked under the system’s convention.

Modified duration usually relates price to a bond’s own yield-to-maturity. Effective duration relates price to a shift in a benchmark curve and can accommodate cash flows that change with rates. KRD refines curve sensitivity by separating selected maturities. The measures answer related but different questions; a KRD bucket is not the same thing as a separate bond maturing at that tenor.

Start with a base value, (P_0). For one selected maturity, create an up-shocked and a down-shocked benchmark curve using a small yield bump (h), then reprice the instrument under both curves. A common central-difference estimate is:

KRD_i ≈ (P_down − P_up) ÷ (2 × P_0 × h)

Here, (P_{down}) is the value after the selected key-rate shock moves down by (h), and (P_{up}) is the value after it moves up by (h). Express (h) as a decimal: 1 basis point is 0.0001. In practice, the shock is localized using the curve model’s interpolation or neighboring-node rules. The exact result therefore depends on the bump size, curve construction, pricing model, and treatment of embedded options. The CFA Institute’s yield-curve strategy reading discusses KRD as a way to quantify exposure along the curve.

Assume, for teaching only, a $1,000,000 portfolio has KRD contributions of 0.8 at 2 years, 1.5 at 5 years, 2.7 at 10 years, and 1.0 at 30 years. Under the same valuation and shock conventions, those weighted contributions sum to an effective duration of 6.0 years for a parallel move.

If the modeled 10-year key-rate component rises by 5 basis points while the other components do not move, the first-order estimate is −$1,000,000 × 2.7 × 0.0005 = −$1,350. A parallel rise of 5 basis points across the same four components gives an approximate change of −$1,000,000 × 6.0 × 0.0005 = −$3,000. These are hypothetical duration-only estimates; they omit convexity, transaction costs, credit-spread changes, and any cash-flow changes.

The sum relationship holds when the KRDs are weighted consistently and their curve shocks combine to the same parallel shift used for effective duration. Different node sets, interpolation rules, or valuation conventions can make reported measures differ. Treat the example as a model-based sensitivity calculation, not a market quote or expected loss.

A KRD vector shows where the portfolio has more or less benchmark-rate sensitivity. In a steepener scenario, long rates rise more than short rates; in a flattener, the short end rises relative to the long end. A twist or butterfly-like move may concentrate changes in the middle of the curve. Apply the scenario’s yield change at each modeled key rate to the corresponding KRD contribution to estimate a first-order price effect.

For example, two portfolios can each have a total effective duration near six years, but one can concentrate more sensitivity at 5 years and the other at 30 years. A parallel move may look similar in a duration-only comparison, while a 5-year or 30-year shock can produce very different estimated changes. The CFA Institute’s yield-curve strategies material describes using key-rate durations to examine slope and curve-shape exposure.

KRD depends on how the curve is represented. Systems may choose different tenor nodes, interpolate between them differently, or use different bump magnitudes and repricing conventions. Market value weights, settlement assumptions, discount curves, and the treatment of optional cash flows also matter. A KRD report is meaningful only alongside its curve, node, shock, and valuation definitions.

When comparing a portfolio with a benchmark, use the same conventions for both. A difference between the two KRD vectors can reveal active exposure by maturity, but it does not say whether that exposure will earn a return. The CME Group case study on adjusting key-rate duration illustrates that managers can alter targeted curve exposures with cash securities or derivatives; implementation still carries market, basis, collateral, and transaction risks.

KRD is a local, first-order sensitivity. Larger yield moves can make convexity material, and a bond with a call, prepayment option, or other rate-dependent cash flows may change its effective KRD as rates move. A benchmark-curve KRD also does not automatically capture a change in the issuer’s credit spread, a swap-spread basis, liquidity, currency, or funding cost.

A curve shock is a scenario input, not a prediction. If short and long rates move together differently from the model’s localized bump, the realized result can differ. For portfolios with embedded options or material spread exposure, add appropriate convexity, spread-duration, basis, and scenario analysis rather than treating the KRD table as a complete risk report.

Read the reported nodes and conventions first. Check whether the figures are per-bond sensitivities or portfolio-weighted contributions, whether they use market values, and whether the units are years or currency per basis point. Then compare the KRD vector with total effective duration, convexity, and the benchmark’s corresponding exposures. Translate a specific curve scenario into a change at each node before estimating the first-order effect.

KRD is most useful when it answers a concrete question, such as which maturities explain a portfolio’s exposure to a 5-year selloff or how its curve profile differs from a benchmark. It does not identify a “best” maturity or guarantee that a hedge will offset realized losses. For related concepts, see bond duration and convexity and Treasury futures DV01.