Key Rate Duration — Claude Prompts for Yield Curve Risk

The Limits of Parallel Duration and Why KRD Matters

Effective duration is one of fixed income's most useful tools — but it rests on an assumption that almost never holds in practice: that the entire yield curve shifts up or down by the same amount simultaneously. Real yield curve moves are almost never parallel. The Fed hiking cycle flattens the curve (front end up, long end barely moves). A flight to quality steepens it (long end rallies, short end lags). A supply shock cheapens the 10Y or 30Y without affecting the front end. A duration-neutral portfolio (matching the benchmark's effective duration) can still generate significant tracking error when the curve twists rather than shifts.

Key rate duration (KRD) — also called partial duration or bucket duration — is the solution. It measures price sensitivity to shifts at individual tenor points, allowing portfolio managers to see their full curve exposure bucket-by-bucket, match it to a benchmark, and hedge residual mismatches with targeted instruments. This article works through the mechanics and the portfolio applications with a real 6-bond portfolio and specific Claude prompts.

KRD Mechanics: The Formula and Intuition

Key rate duration at tenor k measures the price change from a 1bp shift at that specific tenor, with all other spot rates held constant. The calculation method mirrors effective duration but uses a localized yield shift rather than a parallel one.

Formula: KRD_k = (P_k− − P_k+) / (2 × P × 0.0001)

Where P_k− = bond price when spot rate at tenor k shifts down 1bp, P_k+ = price when spot rate at tenor k shifts up 1bp, P = current price, and the denominator uses 0.0001 (1bp in decimal).

The shift is implemented with linear interpolation — a 1bp shift at the 5Y tenor affects spot rates between 3Y and 7Y proportionally, peaking at the 5Y point and tapering to zero at the neighboring bucket boundaries. This triangular interpolation scheme ensures the KRD at each tenor captures only the local rate sensitivity without double-counting.

Key property: Σ_k KRD_k = Effective Duration

This identity confirms that effective duration is simply the sum of all localized sensitivities — a parallel shift is equivalent to simultaneously shifting every tenor point by 1bp.

• "Explain key rate duration calculation for a 10-year 4% semi-annual coupon Treasury bond (price $97.20, YTM=4.45%, effective duration=8.35). Given the following spot rate curve (annual): 2Y=4.85%, 3Y=4.78%, 5Y=4.65%, 7Y=4.55%, 10Y=4.45%, 20Y=4.50%, 30Y=4.60%: (1) describe the triangular interpolation scheme for a 1bp shift at the 10Y tenor; (2) show why this bond's KRD is concentrated at the 10Y bucket (KRD10Y≈8.20) with small residual KRDs at the 7Y and 20Y buckets; (3) confirm that the sum of all KRDs approximates effective duration 8.35; (4) contrast with a 5Y Treasury — where would its KRD mass be concentrated?"

Standard Bloomberg KRD Buckets and Conventions

Bloomberg's DURA <GO> function reports KRDs at 10 standard tenor points for US fixed income: 3M, 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 20Y, 30Y. These align with on-the-run Treasury maturities and the most liquid parts of the yield curve.

Practical conventions that matter for CFA Level 3 and professional portfolio management:

• Cash allocation: The 3M and 6M buckets capture money market exposure. A portfolio with large cash holdings has significant 3M KRD relative to the benchmark — technically a duration underweight at the very front of the curve.
• Interpolation for off-the-run maturities: A 15Y bond gets its KRD mass split between the 10Y and 20Y buckets based on linear interpolation. A 15Y bond has approximately equal KRDs at 10Y and 20Y if the cash flows are concentrated at maturity.
• Amortizing securities: MBS, ABS, and CMBS with scheduled and unscheduled principal payments have their KRD mass spread across many buckets reflecting principal payment timing. This is why MBS duration management requires a full KRD profile rather than a single duration number.
• Negative KRD: Some structured products and derivatives can have negative KRD at specific tenors — for example, an inverse floater or a principal-only (PO) MBS strip has negative KRD at the prepayment-sensitive tenor points.

• "Generate a full KRD profile for each of the following bonds across Bloomberg's standard tenor buckets (3M, 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 20Y, 30Y): (A) 5-year Treasury note, 4.25% coupon, price $99.50; (B) 10-year Treasury note, 4.00% coupon, price $97.20; (C) 30-year Treasury bond, 4.375% coupon, price $96.80; (D) 2-year Treasury note, 4.75% coupon, price $100.05. For each, estimate KRD at each tenor bucket (use zero at non-maturity tenors, and interpolate for the two adjacent buckets to the maturity). Verify that each bond's KRD sum ≈ its effective duration."

Portfolio KRD Aggregation: Barbell vs Bullet

Portfolio KRD is the market-value-weighted sum of individual bond KRDs at each tenor bucket. This is where the real power of KRD emerges — you can see exactly where the portfolio's rate sensitivity lives relative to the benchmark.

Barbell vs Bullet — same effective duration, completely different KRD profile:

• Bullet portfolio (100% in 10Y Treasuries, effective duration=8.35): KRD10Y=8.35, all other KRDs ≈ 0
• Barbell portfolio (50% in 2Y + 50% in 30Y, targeting same duration):
• 50% in 2Y (effective duration 1.91): contributes 0.5 × 1.91 = 0.955 to portfolio duration at 2Y bucket
• 50% in 30Y (effective duration 18.50): contributes 0.5 × 18.50 = 9.25 to portfolio duration at 30Y bucket
• Total portfolio effective duration = 0.955 + 9.25 = 10.20 — not the same as bullet 8.35. To match, adjust weights.
• To match duration 8.35: solve 1.91w + 18.50(1-w) = 8.35 → w = 62.2% in 2Y, 37.8% in 30Y
• Barbell KRD profile: KRD2Y=1.19, KRD30Y=6.99, KRD10Y≈0 — completely opposite from bullet

In a yield curve steepening (30Y sells off, 2Y unchanged), the barbell underperforms the bullet despite identical total duration. This is the shaping risk that parallel duration ignores.

• "Build and compare KRD profiles for the following two portfolios, both targeting effective duration of 7.5 years: Portfolio A (Bullet): 100% in 7Y Treasury (4.55% coupon, price $99.30, effective duration=6.78) — actually use 100% in a 10Y Treasury (ModD=8.35) weighted to achieve duration 7.5. Portfolio B (Barbell): mix of 2Y Treasury (ModD=1.91) and 30Y Treasury (ModD=17.80) weighted to achieve the same portfolio effective duration 7.5. (1) Calculate the weight in each leg of the barbell; (2) build the KRD profile table for each portfolio at the 2Y, 5Y, 7Y, 10Y, 20Y, and 30Y tenor buckets; (3) calculate P&L for each portfolio if the yield curve steepens with 2Y unchanged but 30Y rises 30bps; (4) calculate P&L for each portfolio on a parallel +50bp shift."

Using KRDs to Match a Benchmark Index

Index-relative fixed income management (e.g., managing against the Bloomberg US Aggregate Bond Index) requires matching not just the benchmark's duration but its full KRD profile. Significant KRD mismatch at any tenor contributes to tracking error even when total duration is matched.

Bloomberg US Aggregate approximate KRD profile (illustrative 2026 levels):

• KRD2Y ≈ 0.80, KRD3Y ≈ 0.65, KRD5Y ≈ 1.20, KRD7Y ≈ 0.90, KRD10Y ≈ 1.80, KRD20Y ≈ 0.55, KRD30Y ≈ 0.60
• Sum ≈ 6.50 ≈ benchmark effective duration 6.40 ✓

A portfolio manager who overweights 10Y sector bonds (say, KRD10Y = 2.80 vs benchmark 1.80) has a KRD10Y mismatch of +1.00. With $500M in assets, that is $500M × 1.00 × 0.0001 = $50,000 in annual DV01 per bp move in the 10Y rate not shared with the benchmark. If the manager is right about the 10Y (rates fall there), this is a source of excess return. If wrong (10Y sells off), it generates tracking error loss.

• "A $500M fixed income portfolio tracks the Bloomberg US Aggregate Bond Index (effective duration 6.40, KRD profile: KRD2Y=0.80, KRD5Y=1.20, KRD10Y=1.80, KRD30Y=0.60). The portfolio's current KRD profile is: KRD2Y=0.70, KRD5Y=0.90, KRD10Y=2.40, KRD30Y=0.80. (1) Calculate the KRD mismatch at each tenor bucket; (2) express the mismatch as dollar DV01 at each tenor (KRD mismatch × portfolio AUM × 0.0001); (3) identify the largest active bet (tenor with highest absolute DV01 mismatch); (4) describe two specific trades that would reduce the 10Y KRD mismatch while approximately preserving the 30Y KRD position."

Hedging Non-Parallel Risk with Treasury Futures

Once KRD mismatches are identified, portfolio managers hedge specific tenor buckets using the most liquid instruments: US Treasury futures (2Y, 5Y, 10Y, Ultra 10Y, 30Y, Ultra Bond). Each futures contract has a known DV01 that can be looked up from the exchange or Bloomberg.

Approximate DV01 per contract (current rates, illustrative):

• 2Y T-Note futures: ~$37/contract per bp
• 5Y T-Note futures: ~$44/contract per bp
• 10Y T-Note futures: ~$64/contract per bp
• Ultra 10Y T-Note futures: ~$82/contract per bp
• 30Y T-Bond futures: ~$140/contract per bp
• Ultra T-Bond (30Y+ long end): ~$185/contract per bp

Hedging calculation: To neutralize a +$50,000 DV01 mismatch at the 10Y tenor (portfolio is $50,000 longer than benchmark at 10Y):

• Contracts needed = $50,000 / $64 per contract = 781 contracts short of 10Y T-Note futures
• This eliminates the 10Y KRD mismatch without affecting other tenor exposures

• "A portfolio has the following KRD mismatches vs its benchmark (portfolio KRD minus benchmark KRD, × $300M portfolio value × 0.0001 = dollar DV01 mismatch): 2Y bucket: +$12,000; 5Y bucket: −$8,000; 10Y bucket: +$35,000; 30Y bucket: −$15,000. Using these futures DV01s per contract: 2Y=$37, 5Y=$44, 10Y=$64, 30Y=$140: (1) Calculate the number of contracts to buy/short for each tenor bucket to fully neutralize all four KRD mismatches; (2) confirm that the 10Y hedge does not affect the 30Y KRD mismatch (explain why futures at different tenors are independent); (3) estimate total margin required if initial margin is approximately $2,500 per futures contract; (4) describe an alternative to using futures: using an interest rate swap to reduce the 10Y KRD mismatch."

KRD and Yield Curve Factor Models

The three canonical yield curve risk factors — level, slope, and curvature — map directly onto combinations of KRD exposures. Understanding this linkage allows portfolio managers to express views as factor bets rather than security-by-security decisions.

Factor decomposition:

• Level factor (parallel shift): All tenor points shift by 1bp. Portfolio P&L from a parallel +1bp shift = −$1 × (sum of all dollar KRDs) = −portfolio dollar effective duration. A portfolio long the level factor is short effective duration vs benchmark.
• Slope factor (2Y vs 30Y twist): 2Y rises 1bp, 30Y falls 1bp (steepening). P&L = +(KRD30Y − KRD2Y) per bp of steepening, scaled by dollar sensitivity. Long the slope factor = long 30Y KRD relative to 2Y KRD = benefits from steepening.
• Curvature factor (butterfly / belly): 10Y rises 1bp, 2Y and 30Y unchanged (belly cheapens). P&L = −KRD10Y × dollar factor. Short the curvature factor = long 10Y KRD = the 10Y sells off is painful; long the factor = short 10Y KRD, benefits from 10Y cheapening relative to wings.

• "Decompose the following portfolio's KRD profile into level, slope, and curvature factor exposures relative to benchmark. Portfolio (P) vs Benchmark (B) KRD mismatches: KRD2Y: P=0.70 vs B=0.80, mismatch=−0.10; KRD5Y: P=0.90 vs B=1.20, mismatch=−0.30; KRD10Y: P=2.40 vs B=1.80, mismatch=+0.60; KRD30Y: P=0.80 vs B=0.60, mismatch=+0.20. Portfolio AUM=$500M. (1) Is the portfolio long or short the level factor (total KRD mismatch)? (2) Is the portfolio long or short the slope factor? Express as 30Y KRD mismatch minus 2Y KRD mismatch in dollar DV01. (3) Is the portfolio long or short the curvature factor (belly KRD mismatch vs wings)? (4) Which market environment (parallel sell-off, bear flattening, or belly cheapening) is most harmful to this portfolio?"

CFA Level 3 Application: KRD in an Index-Relative Mandate

CFA Level 3 fixed income questions frequently test KRD in the context of a manager running a portfolio against a benchmark index — typically the Bloomberg US Aggregate or a custom liability-matching benchmark. The exam scenario: a manager has a view on the yield curve slope (expecting steepening or flattening) and wants to express that view while keeping total duration close to the benchmark. This is precisely the scenario where KRD is the essential tool — effective duration tells you nothing about the steepener/flattener bet.

A manager who is bullish on the long end (expects 30Y to rally more than 2Y) wants to be: long 30Y KRD versus benchmark, potentially short 2Y KRD versus benchmark, with total effective duration unchanged. In a $400M portfolio against a benchmark with KRD30Y=0.60 and KRD2Y=0.80:

• Bull steepener position: increase KRD30Y to 0.90 (+0.30 vs benchmark), decrease KRD2Y to 0.50 (−0.30 vs benchmark)
• Net effective duration change: approximately zero (gains and losses in duration at tail tenors roughly offset)
• Dollar DV01 bet at 30Y bucket: +0.30 × $400M × 0.0001 = +$12,000 per bp
• Dollar DV01 bet at 2Y bucket: −0.30 × $400M × 0.0001 = −$12,000 per bp
• Profit if 2Y rises 20bps while 30Y falls 20bps (steepening): (+$12,000 + $12,000) × 20bps = +$480,000

• "A $400M fixed income fund tracks the Bloomberg US Aggregate (effective duration=6.40). The manager wants to express a bull steepener view (expects 2Y yields to rise and 30Y yields to fall by similar amounts) without changing total effective duration. Benchmark KRDs: KRD2Y=0.80, KRD5Y=1.20, KRD10Y=1.80, KRD30Y=0.60. (1) Design a KRD overlay that increases the 30Y KRD by +0.35 and decreases the 2Y KRD by −0.30 while keeping total duration approximately unchanged; (2) calculate the number of 30Y T-Bond futures to buy (long) and 2Y T-Note futures to short to implement this KRD overlay, using DV01/contract: 2Y=$37, 30Y=$140; (3) calculate P&L if over the next 3 months the 2Y yield rises 30bps and 30Y yield falls 20bps; (4) what is the breakeven scenario where the steepener produces zero P&L?"

KRD for Non-Government Securities: Corporates and MBS

For corporate bonds, the KRD methodology applies to the interest rate component of risk. But corporate bonds have two sources of price risk: (1) interest rate risk (captured by KRD, using the Treasury or swap curve as reference) and (2) credit spread risk (captured by spread duration). These are additive: total price sensitivity = rate sensitivity (via KRD) + spread sensitivity (via spread duration).

For agency MBS, the KRD picture is complicated by prepayment optionality. When rates fall, homeowners prepay faster, shortening the MBS's effective maturity and shifting the KRD mass toward shorter tenors. This is the negative convexity and KRD extension risk inherent in MBS. A standard 30Y MBS at a discount (below par) has effectively shorter KRD because prepayment expectations are low; a premium MBS (above par) has even shorter KRD as prepayment is likely. OAD (option-adjusted duration) captures this dynamic — it is effectively the expected KRD across interest rate scenarios.

• "A portfolio holds these six bonds and wants to calculate its full KRD profile at tenor buckets 2Y, 5Y, 10Y, and 30Y: (1) $50M 2Y Treasury, 4.75% coupon, KRDs: 2Y=1.90; (2) $40M 5Y IG corporate (A-rated, Z+80bps), 4.90% coupon, KRDs: 5Y=4.45; (3) $60M 10Y Treasury, 4.00% coupon, KRDs: 10Y=8.35; (4) $30M 10Y BBB corporate (Z+145bps), 5.50% coupon, KRDs: 10Y=8.10; (5) $20M 30Y Treasury, 4.375% coupon, KRDs: 30Y=17.80; (6) $25M FNMA 30Y MBS (OAD=5.0), KRDs split: 5Y=1.5, 10Y=2.5, 20Y=1.0. Calculate the portfolio dollar DV01 at each of the four tenor buckets and the total portfolio DV01. Identify which single position contributes most to the 10Y bucket."

Frequently Asked Questions

How is key rate duration reported in Bloomberg?

Bloomberg reports KRDs via the DURA function (Duration Analysis) and on the PORT (Portfolio Analytics) screen. For individual bonds, enter the CUSIP or ticker, type DURA <GO>, and navigate to the KRD section. Bloomberg uses the 10-tenor standard grid (3M through 30Y). For portfolio-level KRD, the Bloomberg PORT screen aggregates across all positions and allows comparison against a benchmark index (e.g., Bloomberg US Aggregate, Bloomberg US Corporate). The KRD mismatch view in PORT is the most direct tool for identifying which tenor buckets carry active duration risk relative to the benchmark. See fixed income analysis with AI for integrating Bloomberg KRD data into Claude workflows.

Is key rate duration the same as bucket duration?

Yes — key rate duration and bucket duration are the same concept. The terminology varies by firm and system. Bloomberg calls it KRD. Some risk systems call it partial DV01 or bucket DV01. BlackRock's Aladdin reports it as partial duration. The calculation methodology is consistent across systems (1bp shift at a tenor point, price change normalized by price), though the tenor bucketing grid and interpolation scheme can vary slightly — which is why KRD comparisons between systems sometimes produce small differences for bonds near bucket boundaries.

Can a portfolio's KRD at a specific tenor be negative?

Yes, for derivative-heavy portfolios or portfolios with interest rate overlay positions. A portfolio that is short Treasury futures at the 5Y tenor will have a negative KRD5Y — a 1bp rise at the 5Y point increases the portfolio value (the futures short gains). Portfolios with receive-fixed swaps also have positive rate-sensitivity KRD (benefit from rate falls). Pay-fixed swaps contribute negative KRD (benefit from rate rises). When computing portfolio KRD including derivatives, the algebraic sum includes both long and short exposures at each tenor point. This is why a derivatives overlay can be used to precisely target any KRD profile — long or short — at any specific tenor.

How does KRD help with fixed income index replication?

An indexed fixed income portfolio aims to replicate a benchmark's KRD profile with fewer securities — a process called stratified sampling. Rather than holding all 10,000+ bonds in the Bloomberg US Aggregate, an index fund might hold 200-500 securities chosen to match the benchmark's KRD at each tenor bucket within a tight tolerance (e.g., ±0.05 KRD at each bucket). KRD is also the key tool for attribution: tracking error decomposed into KRD mismatch sources tells you whether your over- or underperformance came from being long or short at specific curve points. See quant finance resources for related portfolio optimization and risk decomposition tools.

How does key rate duration relate to CFA Level 3 exam topics?

KRD is explicitly covered in the CFA Level 3 fixed income curriculum under "Yield Curve Strategies" and "Curve-Based Risk Measures." The exam tests: (1) why KRD is more informative than duration alone for non-parallel curve moves; (2) how to aggregate portfolio KRDs; (3) the relationship between KRD profiles and barbell vs bullet positioning; (4) factor decomposition of KRD into level, slope, and curvature components; and (5) using KRDs to structure duration-neutral curve trades. The Level 3 exam increasingly tests portfolio-level applications rather than single-bond calculations — knowing how to read and act on a KRD mismatch table is a core exam skill. See bond duration and convexity for the foundational duration concepts that KRD builds on.