FRM Exam Part I · Applying Duration, Convexity, and DV01

Limitations of Duration and Key Rate Measures Explained

Updated 11 October 2026 · Fact-checked

Duration measures a bond's price sensitivity to a small, parallel shift in yields. It fails when the curve twists, when convexity matters, or when cash flows change with rates. Key rate duration fixes the first problem by shifting one point on the curve at a time. Under a parallel shift, key rate exposures sum approximately to total effective duration.

Understand Limitations of Duration and Key Rate Measures

Duration gives one number: the approximate percentage price change for a small change in yield. DV01 turns the same idea into a currency amount per 1 basis point. Both rest on a single yield or a single shift applied to the whole curve.

That is the main weakness. Duration and DV01 assume a parallel shift: every spot rate moves by the same amount. Real curves steepen, flatten and twist. Two portfolios can have the same duration and still react very differently, because one holds cash flows near 2 years and the other holds them near 10 and 30 years.

Duration has other limits. It is a first-order, linear approximation, so it is less accurate for large yield moves. Convexity corrects part of this. It also assumes cash flows do not change when rates change. For bonds with embedded options or mortgage prepayments, you need effective duration, which reprices the bond under up and down shifts. Duration also says nothing about spread, credit or liquidity risk unless you measure those separately.

Key rate duration (KRD) is the curve-risk extension. Pick key maturities, for example 2, 5, 10 and 30 years. Shift one key rate by a small amount, let nearby rates adjust by interpolation, hold the others fixed, and reprice. The result is the exposure to that part of the curve. KR01 is the same exposure in currency per 1 bp.

The key rate exposures add up to the total. If you shift all key rates by the same amount, you get a parallel shift. So the sum of KRDs is approximately effective duration, and the sum of KR01s is approximately DV01. KRDs show where the risk sits, which total duration cannot do.

Key formulas to remember

Duration price approximation: ΔP ÷ P ≈ −D × Δy; D is modified (or effective) duration. Valid for small, parallel yield changes.
DV01: DV01 ≈ D × P × 0.0001; The absolute price change in currency for a 1 bp yield move, i.e. −ΔP for a 1 bp rise. Quote DV01 as a positive number for a long bond position.
Duration with convexity: ΔP ÷ P ≈ −D × Δy + ½ × C × (Δy)²; Adds a second-order term. Convexity helps for large moves but still assumes a parallel shift.
Key rate duration: KRD_i = −(1 ÷ P) × (ΔP_i ÷ Δy_i); ΔP_i is the price change when only key rate i moves by Δy_i. Other key rates stay fixed.
KR01: KR01_i = −(ΔP_i for a +1 bp rise in key rate i); Currency version of KRD, positive for a long bond because it is the loss from a rate rise. KR01_i ≈ KRD_i × P × 0.0001.
Sum of key rate exposures: Σ KRD_i ≈ effective duration; Σ KR01_i ≈ DV01; Holds when the key rate shifts together make up a parallel shift.
P&L from a non-parallel move: ΔP ≈ −Σ (KR01_i × Δy_i), with Δy_i in bp; Use the KR01 of each bucket with that bucket's own yield change, then add. KR01 is the loss per 1 bp rise, so the sign is flipped once.

How to solve Limitations of Duration and Key Rate Measures questions

Use this approach for any question on duration limits or key rate measures.

1Read what moves: is the yield change parallel, or does each maturity move by a different amount?
2If parallel and small, use duration or DV01. Add convexity if the move is large.
3If non-parallel, list the key rate exposures (KRD or KR01) and the yield change for each key rate.
4Check units: KRD is a percentage sensitivity per unit of yield. KR01 is currency per 1 bp. Convert bp to decimals when using KRD.
5Multiply each exposure by its own yield change, add them, and apply the sign: price falls when yields rise.
6For KRD, multiply the percentage change by portfolio value to get the currency P&L.
7Sanity check: with all shifts equal, the answer should match total duration or DV01.
8For conceptual questions, name the limitation (parallel shift, linearity, fixed cash flows) and the fix (KRD, convexity, effective duration).

Quickest way: Bucket-by-bucket P&L

When to use it: When you are given KRDs or KR01s and a scenario with different yield moves at different maturities.

Write each bucket's exposure beside its shift in bp.
For KR01 in currency per bp: multiply directly by the bp move. For KRD: multiply by the decimal move and by portfolio value.
Add the bucket results with signs (yield up = loss for a positive exposure).
Flip the sign once at the end, not in every line.
Eliminate options that treat the shift as parallel or use total duration.

Common mistakes in Limitations of Duration and Key Rate Measures

Applying total duration to a curve steepener or flattener
Duration is taught first, so it becomes the default tool.
Fix: If the scenario gives different moves by maturity, use key rate exposures bucket by bucket.
Assuming equal duration means equal risk
One number looks like a full risk summary.
Fix: Two portfolios with the same duration can have very different KRDs. Compare their exposure by bucket.
Mixing KRD and KR01 units
Both measure key rate risk but one is a percentage per unit of yield and the other is currency per bp.
Fix: KRD × decimal yield change × value, or KR01 × bp change. Never mix them.
Thinking the sum of KR01s always equals DV01 exactly
The sum rule is taught as an identity.
Fix: It holds approximately, when the key rate shifts together form a parallel shift. Say 'approximately'.
Believing key rate duration removes all limits of duration
KRD sounds like a complete fix.
Fix: KRD handles non-parallel moves. It is still a linear measure, so large moves need convexity, and options need effective duration.
Getting the sign wrong when the curve flattens
A flattening can mean short yields rise and long yields fall, which is easy to mix up.
Fix: Write each bucket's yield change with its sign first, then compute −KR01 × Δy for each bucket.

Worked examples

Example 1

A USD bond portfolio is worth $50 million. Its key rate durations are 2-year 0.40, 5-year 1.50, 10-year 3.10 and 30-year 0.60. The curve steepens: the 2-year yield falls 20 bp, the 5-year falls 10 bp, the 10-year is unchanged and the 30-year rises 30 bp. Estimate the percentage and dollar P&L, and compare it with a parallel +10 bp shift.

Show the solution

Total duration ≈ 0.40 + 1.50 + 3.10 + 0.60 = 5.60.
Percentage change ≈ −Σ KRD_i × Δy_i.
2-year: 0.40 × (−0.0020) = −0.0008.
5-year: 1.50 × (−0.0010) = −0.0015.
10-year: 3.10 × 0 = 0.
30-year: 0.60 × 0.0030 = +0.0018.
Sum = −0.0008 − 0.0015 + 0 + 0.0018 = −0.0005.
Percentage change = −(−0.0005) = +0.0005, or +0.05%.
Dollar P&L = $50,000,000 × 0.0005 = +$25,000.
Parallel +10 bp: −5.60 × 0.0010 = −0.56%, a loss of $280,000. Total duration, which assumes one parallel shift, cannot capture the small gain from the steepener and would give a misleading answer.

Answer: About +0.05%, or a gain of $25,000. A parallel +10 bp shift would cost about 0.56%, or $280,000.

Example 2

A trader is long a 2-year position with KR01 of $4,000 and short a 10-year position with KR01 of −$4,000 (KR01 is the loss for a 1 bp rise in that key rate, so it is positive for a long position and negative for a short one). Find the portfolio DV01 and the P&L if the curve flattens, with the 2-year yield up 10 bp and the 10-year yield down 10 bp.

Show the solution

DV01 ≈ Σ KR01 = 4,000 + (−4,000) = 0.
Under a parallel move the portfolio looks hedged.
Because KR01 is a loss per bp of rise, P&L ≈ −Σ KR01_i × Δy_i, with Δy in bp.
2-year: KR01 × Δy = 4,000 × (+10) = +40,000.
10-year: KR01 × Δy = (−4,000) × (−10) = +40,000.
Σ KR01_i × Δy_i = 40,000 + 40,000 = 80,000.
P&L = −80,000.
Check by position: the long 2-year loses 4,000 × 10 = $40,000 as yields rise. The short 10-year (KR01 of −4,000) loses 4,000 × 10 = $40,000 as yields fall. Total loss = $80,000.

Answer: Portfolio DV01 is about $0, but the flattening produces a P&L of −$80,000, a loss of $80,000. DV01 hides this curve risk.

Exam tips

If a question describes a twist, steepening or flattening, expect the answer to need key rate exposures, not total duration.
Know the sum rule: ΣKRD ≈ effective duration and ΣKR01 ≈ DV01. It is a quick check on your own numbers.
For limitation questions, list three issues: parallel shift, linear approximation, and cash flows that depend on rates.
Check sign and units on every line. Most lost marks here are sign errors or mixing bp and decimals.
A zero or small DV01 does not mean low risk. Look at the bucket exposures.

Practice questions from Applying Duration, Convexity, and DV01

Limitations of Duration and Key Rate Measures in other exams

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

Limitations of Duration and Key Rate Measures: frequently asked questions

What is the main limitation of duration as a risk measure?

It assumes a small, parallel shift in the yield curve. Real curves steepen, flatten and twist. It is also a linear approximation and assumes cash flows do not change with rates.

What is the difference between key rate 01 and DV01?

DV01 is the price change for a 1 bp parallel shift of the whole curve. KR01 is the price change for a 1 bp move at one key maturity only. The KR01s add up to approximately the DV01.

How is key rate duration calculated?

Shift one key rate by a small amount, hold the other key rates fixed, and reprice the portfolio. Then compute −(1 ÷ P) × (ΔP ÷ Δy). Repeat for each key maturity.

Does key rate duration replace convexity?

No. Key rate duration addresses non-parallel moves. It is still a first-order measure, so for large yield changes you still need convexity, and for bonds with options you need effective duration.