Key-Rate Duration: Measuring Yield Curve Shape Risk

Key Takeaways

• Key-rate durations sum approximately to effective duration but reveal exposure at each maturity anchor point.
• A 10-year bullet has nearly all its key-rate duration at the 10-year anchor; a barbell has exposure at both ends.
• Portfolio managers use key-rate durations to hedge specific curve segments without disturbing overall duration.
• Key-rate durations depend on the benchmark curve used; Treasury and swap curve KRDs are not interchangeable.

What It Is

Effective duration gives you one number for a parallel shift of the whole yield curve. Key-rate duration splits that single number into several, one per anchor maturity on the curve. Standard anchor points are 3-month, 2-year, 5-year, 10-year, and 30-year, though the exact set depends on the benchmark curve.

A 10-year Treasury note, for instance, might have a key-rate duration of almost 9 at the 10-year point and near zero everywhere else. A barbell portfolio made of 2-year and 30-year bonds will have meaningful key-rate durations at both ends and almost nothing in the middle. The sum of the key-rate durations across all anchor points approximately equals the effective duration.

The Intuition

The yield curve does not usually move in parallel. Short rates can jump while the long end sits still, or the belly can bulge and cheapen versus the wings. Effective duration cannot see any of that. To a parallel-shift metric, a 10-year bullet and a 2/30 barbell with the same effective duration look identical, even though they react completely differently to a steepener or a flattener.

Key-rate duration pulls those differences into view. It lets a portfolio manager ask questions like: "If only the 5-year yield rises 25 basis points, how much does my portfolio lose?" The answer is the 5-year key-rate duration multiplied by that shock.

This matters whenever your view on rates is shape-specific rather than level-specific. Betting on a flatter curve, hedging a pension liability that sits at a specific maturity, or neutralizing one part of the curve without neutralizing the rest all require key-rate numbers.

How It Works

For each anchor maturity i, shock only that point on the zero-coupon curve by a small amount, hold every other anchor fixed, and reprice the bond.

KRD_i = (PV- - PV+) / (2 x PV0 x dCurve_i)

Where:

PV0       = current bond price
PV-       = price after the i-th anchor shifts DOWN by dCurve_i
PV+       = price after the i-th anchor shifts UP by dCurve_i
dCurve_i  = size of the shock at anchor i, in decimal

Between the shocked anchor and its neighbors, the change in yields is usually interpolated linearly so the curve stays continuous. Outside the nearest neighbors it stays flat at zero.

The total price change estimate under an arbitrary non-parallel shift is the sum across anchors:

dP / P = - sum( KRD_i x dy_i )

Plug in the specific basis-point move at each anchor and you get a scenario-level estimate.

Worked Example

Consider a portfolio with these key-rate durations, computed at the standard anchor points:

• 2-year KRD: 1.2
• 5-year KRD: 2.0
• 10-year KRD: 4.5
• 30-year KRD: 0.8

Effective duration is the sum, roughly 8.5.

Scenario: a steepener where the 2-year yield falls 25 bps and the 30-year yield rises 25 bps, with the 5-year and 10-year unchanged.

dP / P = -(1.2 x -0.0025) - (2.0 x 0) - (4.5 x 0) - (0.8 x 0.0025)
       =  0.0030 - 0 - 0 - 0.0020
       =  0.0010  (or +0.10 percent)

The two effects nearly offset because the portfolio is fairly balanced. A 10-year bullet with the same 8.5 effective duration would be unchanged under the same scenario (its 2-year and 30-year KRDs are near zero), showing how the two portfolios look identical to effective duration but behave differently under a curve twist.

Common Mistakes

1. Assuming the sum of KRDs always equals effective duration exactly. It is a close approximation, not an identity. Small differences come from the interpolation rule and the fact that shocking anchors one at a time and adding is not the same as shocking them simultaneously.

2. Using too few anchor points. A three-anchor setup (short, mid, long) may hide exposure to the belly or to the very short end. Standard institutional practice uses five or six anchors at minimum.

3. Mixing benchmark curves. Key-rate durations against the Treasury curve and against the swap curve are not interchangeable. Be explicit about which curve the shocks apply to.

4. Ignoring convexity. Key-rate duration is still a linear approximation. For large curve moves, add a second-order term or use full repricing. The same convexity caveats from effective duration apply here.

Frequently Asked Questions

How many key-rate anchor points should I use? Standard institutional practice uses five to seven anchors, typically the 3-month, 2-year, 5-year, 10-year, and 30-year points on the curve. Some desks add the 1-year, 7-year, or 20-year. Fewer anchors miss important exposure; too many anchor points become redundant and add noise without improving precision.

Can two portfolios have the same effective duration but different key-rate profiles? Yes, and this is exactly the point of key-rate duration. A 10-year bullet and a 2/30 barbell can be constructed with identical effective durations. Their key-rate profiles differ entirely: the bullet has nearly all exposure at the 10-year anchor while the barbell has exposure split between the 2-year and 30-year anchors. Under a yield curve twist, they perform very differently.

How is key-rate duration used in liability-driven investing? Pension funds and insurers need to match the key-rate duration profile of their bond portfolio to the key-rate profile of their liabilities, not just total effective duration. Matching only total duration leaves the portfolio exposed to curve twists that push asset and liability values in different directions even though both have the same parallel-shift sensitivity.

What is the relationship between key-rate duration and the 2s10s spread trade? A position structured to benefit from a widening 2s10s spread (curve steepener) is long 10-year key-rate duration and short 2-year key-rate duration. Key-rate duration quantifies the exact exposure at each anchor, letting traders size the hedge precisely for the expected curve move rather than relying on rough estimates.

Does key-rate duration work for corporate bonds? Yes, but the benchmark curve matters. Corporate bond key-rate durations are typically computed against Treasury or swap curves, and the spread component adds credit sensitivity that key-rate duration does not capture. In practice, portfolio managers compute both the rate key-rate durations and track credit spread sensitivity separately.

Sources

1. CFA Institute. "Yield Curve Strategies." https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/yield-curve-strategies
2. AnalystPrep. "Key Rate Duration Explained." https://analystprep.com/cfa-level-1-exam/fixed-income/key-rate-duration/
3. Corporate Finance Institute. "Key Rate Duration." https://corporatefinanceinstitute.com/resources/fixed-income/key-rate-duration/
4. MathWorks. "Bond Prices and Yield Curve Nonparallel Shifts." https://www.mathworks.com/help/finance/bond-prices-and-yield-curve-nonparallel-shifts.html

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.