CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures

Key Rate Duration and Yield Curve Exposure

Updated 7 October 2026 · Fact-checked

Key rate duration measures how much a bond or portfolio's value changes when one point on the yield curve, such as the 5-year rate, moves by a small amount while other points stay fixed. Compute it as (PV₋ − PV₊) ÷ (2 × PV₀ × Δy). Use it to see exposure to nonparallel curve shifts.

Understand Key Rate Duration and Yield Curve Exposure

Effective duration gives you one number. It tells you the price change for a parallel shift of the whole yield curve. Real curves rarely move that way. Short rates may fall while long rates rise, or the curve may twist around the 10-year point. One number cannot show which part of the curve hurts you.

Key rate duration (also called partial duration) fixes this. You pick a few maturity points on the curve, called key rates, such as 2, 5, 10 and 30 years. You shift one key rate by a small amount, hold the others constant, and see how the value changes. The result is the sensitivity to that one maturity.

A bond is exposed mainly to the key rates near its cash flows. A 5-year zero-coupon bond has almost all its key rate duration at the 5-year point. A coupon bond spreads its exposure across several points, with the biggest share where its final, largest cash flow falls.

If you shift all key rates by the same amount, you get a parallel shift. So the key rate durations add up to approximately the bond's effective duration. A portfolio's key rate duration at each point is the market-value-weighted average of its holdings' key rate durations.

The main use is comparing a portfolio with its benchmark. If the two have the same total duration but different key rate durations, the portfolio is making a bet on the shape of the curve. The difference at each point is the active key rate duration. It shows where you gain or lose if the curve changes shape.

Key formulas to remember

Key rate duration: KRD_k = (PV₋ − PV₊) ÷ (2 × PV₀ × Δy_k); PV₋ and PV₊ are values after the k-th key rate falls and rises by Δy_k, with all other key rates unchanged. Δy_k is in decimals (10 bp = 0.0010).
Price change from one key rate: %ΔPV ≈ −KRD_k × Δy_k; For several key rate changes, add the individual effects: %ΔPV ≈ −Σ(KRD_k × Δy_k). This is a first-order estimate and ignores convexity.
Sum of key rate durations: Σ KRD_k ≈ effective duration; Holds when all key rates shift by the same amount (a parallel shift).
Portfolio key rate duration: KRD_p,k = Σ (w_i × KRD_i,k); w_i is the market value weight of bond i. Use market value weights, not par weights.
Active key rate duration: Active KRD_k = KRD_portfolio,k − KRD_benchmark,k; A positive value means the portfolio gains more than the benchmark if that key rate falls, and loses more if it rises.

How to solve Key Rate Duration and Yield Curve Exposure questions

Use this order for any key rate duration question. It works for calculation items and for interpretation items.

1Identify what is moving. Note which key rate changes and which stay unchanged. A question about one maturity point is a key rate question, not an effective duration question.
2If you must compute KRD, list PV₀, PV₋ and PV₊ and confirm the shift size Δy for that key rate only.
3Apply KRD = (PV₋ − PV₊) ÷ (2 × PV₀ × Δy). Convert basis points to decimals first.
4To estimate a price change, multiply: %ΔPV ≈ −KRD × Δy. Fall in yield gives a gain. Rise in yield gives a loss.
5For portfolios, weight each holding's KRD by market value, then compare with the benchmark to get active KRD at each key rate.
6For a nonparallel shift, multiply each key rate's duration by its own yield change and add the results.
7Check your answer for sign and size. Does the total look sensible against the effective duration?

Quickest way: Active KRD times yield change

When to use it: Use this when a question gives portfolio and benchmark key rate durations and a scenario in which one or two key rates move.

Subtract benchmark KRD from portfolio KRD at each key rate that moves.
Multiply each difference by the yield change at that point, and flip the sign: relative return ≈ −active KRD × Δy.
Ignore key rates that do not move. Their contribution is zero.
Eliminate options with the wrong sign first. Then check that the size matches the active KRD, not the portfolio KRD.

Common mistakes in Key Rate Duration and Yield Curve Exposure

Forgetting the 2 in the denominator
Candidates mix this formula with the one-sided duration idea and divide by only PV₀ × Δy.
Fix: The 2 appears because you use both a down shift and an up shift. The price difference spans a 2 × Δy range. Always write (PV₋ − PV₊) ÷ (2 × PV₀ × Δy).
Using basis points as whole numbers
The shift is quoted as 10 bp and gets typed as 10 instead of 0.0010.
Fix: Convert basis points to decimals before calculating. 1 bp = 0.0001.
Treating key rate duration as a parallel-shift measure
It is named duration, so candidates assume the whole curve moves.
Fix: Key rate duration isolates one maturity point. Only the sum of key rate durations approximates the parallel-shift measure, effective duration.
Using portfolio KRD instead of active KRD when judging relative performance
The benchmark is ignored, so both portfolio and benchmark exposure get counted.
Fix: For performance relative to the benchmark, use portfolio KRD minus benchmark KRD at each key rate.
Getting the sign wrong
Candidates forget that prices move opposite to yields.
Fix: Write the formula with its minus sign. A fall in the key rate with positive KRD gives a gain.
Assuming equal total duration means equal risk
A portfolio and benchmark can match on effective duration yet have very different exposures at individual maturities, so a single number hides the difference.
Fix: Matching total duration only protects against a parallel shift. Compare key rate durations to check exposure to steepening, flattening or twists.

Worked examples

Example 1

A bond has a price of 100.00. If only the 5-year key rate falls by 10 bps, its price rises to 100.20. If only the 5-year key rate rises by 10 bps, its price falls to 99.80. The 5-year key rate duration is closest to: A. 0.40, B. 2.00, C. 4.00.

Show the solution

PV₀ = 100.00, PV₋ = 100.20, PV₊ = 99.80, Δy = 0.0010.
Numerator: PV₋ − PV₊ = 100.20 − 99.80 = 0.40.
Denominator: 2 × 100.00 × 0.0010 = 0.20.
KRD = 0.40 ÷ 0.20 = 2.00.
Option A is just the price difference (0.40) with no division at all. Option C results from dividing by PV₀ × Δy = 100.00 × 0.0010 = 0.10 and omitting the 2 (0.40 ÷ 0.10 = 4.00).

Answer: B. The 5-year key rate duration is 2.00.

Example 2

A portfolio and its benchmark both have an effective duration of 6.0. Key rate durations at 2, 5, 10 and 30 years are: portfolio 0.5, 1.5, 3.0, 1.0 and benchmark 0.8, 1.7, 2.0, 1.5. Only the 10-year key rate falls by 40 bps. The estimated return of the portfolio relative to the benchmark is closest to: A. −0.40%, B. 0.40%, C. 1.20%.

Show the solution

Check totals: portfolio 0.5 + 1.5 + 3.0 + 1.0 = 6.0. Benchmark 0.8 + 1.7 + 2.0 + 1.5 = 6.0. Total duration is the same, so the difference lies in curve shape.
Active KRD at 10 years = 3.0 − 2.0 = +1.0.
Only the 10-year rate moves, so other key rates contribute zero.
Relative return ≈ −active KRD × Δy = −1.0 × (−0.40%) = +0.40%.
Option C uses the portfolio KRD of 3.0 (3.0 × 0.40% = 1.20%), which ignores the benchmark. Option A has the wrong sign.

Answer: B. The portfolio outperforms the benchmark by about 0.40%.

Exam tips

Expect a question that gives key rate durations and a nonparallel scenario. Multiply each key rate's duration by its own yield change, then add.
When two portfolios have the same effective duration, the question is usually testing whether you see the difference in curve exposure.
Check the sign first. Eliminating the option with the wrong sign often leaves two choices.
Remember the sum rule: key rate durations add to roughly effective duration for a parallel shift. Use it to sanity-check your numbers.
On a calculator, enter 10 bp as 0.0010 and use the memory keys to store the denominator, so you avoid rounding errors.

Practice questions from Curve-Based and Empirical Fixed-Income Risk Measures

Key Rate Duration and Yield Curve Exposure in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Key Rate Duration and Yield Curve Exposure: frequently asked questions

What is the difference between key rate duration and effective duration?

Effective duration measures price sensitivity to a parallel shift of the whole curve. Key rate duration measures sensitivity to a change at one maturity point only. The key rate durations sum to approximately the effective duration.

How do I use key rate duration for a portfolio?

Compute the market-value-weighted average of each holding's key rate duration at every key rate. Compare it with the benchmark to find active key rate durations. These show where the portfolio gains or loses if the curve steepens, flattens or twists.

Why does a zero-coupon bond have a single key rate duration?

A zero-coupon bond has only one cash flow, at maturity. Its value depends almost entirely on the rate at that maturity. So its exposure sits at that key rate.

Does key rate duration include convexity?

No. It is a first-order estimate, like duration. For large yield changes the estimate becomes less accurate because convexity is ignored.