Key rate duration (KRD) is a measure of how much the price of a bond—or a bond portfolio—changes when the yield at a single point (a “key” maturity) on the yield curve shifts by a given amount, while yields at all other maturities are held constant. It isolates sensitivity to movements at particular maturities (for example, the 2‑year or the 10‑year) rather than assuming a parallel shift of the entire curve.
Why it matters: many real world yield‑curve moves are non‑parallel (steepening, flattening, humps). KRD reveals which parts of the curve drive most of a bond’s or portfolio’s interest‑rate risk and helps design hedges targeted at those maturities.
Key takeaways
– KRD measures bond price sensitivity to a change in yield at one maturity point on the curve, holding others constant.
– It’s useful for non‑parallel yield curve risk analysis and targeted hedging.
– The set of KRDs across all key maturities sums to the effective duration (approx.), so the full curve decomposition reproduces total duration risk.
– KRD is usually computed for several standard maturities (e.g., 1m, 3m, 6m, 1y, 2y, 3y, 5y, 7y, 10y, 20y, 30y).
The formula for key rate duration
Compute prices when the key rate is bumped up and down while keeping all other rates unchanged. Using a symmetric bump of size Δy (in decimal form), the key rate duration at that key is
KRD = (P_down − P_up) / (2 × Δy × P0)
where:
– P0 = base (initial) clean price,
– P_up = price when the key rate is increased by Δy,
– P_down = price when the key rate is decreased by Δy,
– Δy is the bump size (e.g., 0.01 for 1%), and
– KRD is expressed in years (same unit as duration).
Interpretation in dollar terms:
– Approximate dollar price change for a 1% change at that key = −KRD × P0 × 0.01.
– DV01 (dollar value of 1 basis point, bps = 0.01%) at that key ≈ KRD × P0 × 0.0001.
Calculating key rate duration — step‑by‑step
1. Choose key maturities
• Typical choices: 1m, 3m, 6m, 1y, 2y, 3y, 5y, 7y, 10y, 20y, 30y (11 key rates), but you can select a subset relevant to your portfolio.
2. Select bump size Δy
• Common practice uses ±1% (±100 bps) for duration-scale intuition, but many practitioners use ±1 bp (or ±5–10 bps) to reduce non‑linearity error. The KRD formula above assumes a symmetric bump; keep bump consistent across keys.
3. Construct the base zero‑coupon (spot) or par curve
• Use market data (Treasury spot curve, swap curve, or an OAS‑adjusted curve for corporates). Interpolate smoothly between key points as needed.
4. For each key rate:
a. Create two shifted curves: one with the key rate increased by Δy and one decreased by Δy, leaving all other rates unchanged.
b. Reprice the bond using each shifted curve (use your valuation model that maps cash flows to the spot/par curve).
c. Compute KRD with the formula above.
5. For portfolios
• Compute each bond’s KRD for each key and convert to dollar durations: Dollar KRD_i = KRD_i × Price_i × Δy (for 1% → Δy = 0.01). Sum across bonds to get portfolio dollar KRD for each key. Optionally convert back to portfolio KRD by dividing by portfolio market value.
6. Check consistency with effective duration
• The sum of KRDs across all key maturities should approximate the portfolio’s effective duration (small discrepancies may arise from interpolation/curve conventions and bump sizes).
Example (numeric, single bond)
• Base price P0 = $1,000.
– Price when key yield is +1%: P_up = $970.
– Price when key yield is −1%: P_down = $1,040.
– Δy = 0.01.
KRD = (1,040 − 970) / (2 × 0.01 × 1,000) = 70 / 20 = 3.5.
Interpretation: the bond behaves as if it has 3.5 years of sensitivity to a 1% move at that key. The approximate dollar loss for a 1% rise at that key = −3.5 × 1,000 × 0.01 = −$35. DV01 at that key ≈ 3.5 × 1,000 × 0.0001 = $0.35 per 1 bp.
How to use KRD in practice — practical steps
1. Map the curve exposures
• Compute KRDs across chosen maturities for each security to see where risk concentrates (short, intermediate, long).
2. Compare securities
• Use relative KRDs to compare two bonds: a higher KRD at a given key means greater sensitivity to moves at that maturity.
3. Build targeted hedges
• To neutralize exposure at a specific key, use liquid instruments (Treasuries, futures, interest‑rate swaps, FRAs) whose KRD profile offsets the portfolio’s KRD at that key. Hedging multiple keys may require a combination of instruments.
4. Risk decomposition and reporting
• Report portfolio dollar KRDs by key to show where non‑parallel risk sits. Use heat‑maps or bar charts for communication.
5. Scenario analysis
• Use KRDs to approximate price change under non‑parallel scenarios (apply the approximate linear price change per key and sum across keys). For larger moves, reprice under the full scenario (reconstruct the curve) as linear KRD approximations may be inaccurate.
6. Rebalance and monitor
• Recompute KRDs regularly (market moves and trades change risk). Rebalance hedges as necessary.
Limitations and cautions
• Local linear approximation: KRD uses finite differences and is an approximation; convexity and large moves can make it inaccurate.
– Model and curve dependence: results depend on the yield‑curve construction, interpolation, and discounting conventions. For callable or mortgage‑backed securities, option features require option‑adjusted models (KRD becomes OAS‑dependent).
– Isolating a pure single-point move is stylized—real yields often move in correlated ways across maturities.
– Choice of bump size matters: too large a bump can distort KRD via convexity; too small may be noisy in market data or pricing models.
Checklist for implementation (spreadsheet or system)
– Collect instrument cash flows and market curve (spot/par).
– Decide key points and bump size.
– Implement curve shifting that only changes the selected key point.
– Reprice base, up, and down curves per security.
– Compute KRD and convert to dollar terms.
– Aggregate to portfolio level and produce reports.
Bottom line
Key rate duration decomposes interest‑rate risk across the yield curve so you can see where a bond or portfolio is sensitive to non‑parallel moves. It’s a valuable tool for risk monitoring and constructing targeted hedges, but it requires careful curve construction, attention to bump sizes, and understanding of approximation limits.
Source
– Investopedia: “Key Rate Duration” .