Key Rate Duration

Key Rate Duration: What it Is and Why it Matters

Key rate duration (KRD) measures a bond or portfolio’s price sensitivity to yield changes at specific points along the yield curve. Unlike effective duration, which assumes a parallel shift of the entire yield curve, KRD isolates the impact of non‑parallel, point‑specific movements—useful because real-world yield‑curve changes are often uneven.

Formula

KRD at a given key maturity is typically calculated as:

KRD = (P− − P+) / (2 × Δy × P0)

Where:
* P0 = original price
* P+ = price after a Δy increase in yield at the specific key rate
* P− = price after a Δy decrease in yield at that key rate
* Δy = size of the yield shock (in decimal form, e.g., 0.01 for 1%)

Interpreting the result: KRD is expressed in years (duration units) and approximates the percentage price change for a 1.00% (100 basis points) yield change at that maturity. For smaller shocks, scale linearly.

Calculation Example

Suppose a bond has:
* P0 = $1,000
* P+ (yield +1%) = $970
* P− (yield −1%) = $1,040

KRD = ($1,040 − $970) / (2 × 0.01 × $1,000) = $70 / $20 = 3.5

Interpretation: A 1% increase in the yield at that key maturity would be expected to reduce the bond’s price by roughly 3.5%, all else equal.

Relationship to Effective Duration

Calculate KRDs at a set of key maturities (commonly the standard points along the Treasury spot curve). The sum of the KRDs across those maturities approximates the portfolio’s effective duration. Thus, KRDs decompose effective duration into term‑structure‑specific sensitivities.

Practical Uses

• Portfolio risk analysis: Identify which parts of the yield curve drive price volatility.
• Relative value and security selection: Compare two bonds’ KRD profiles to see which is more sensitive at short, intermediate, or long maturities.
• Hedging: Design targeted hedges for exposure concentrated at specific maturities without over‑hedging other parts of the curve.
• Scenario analysis: Model non‑parallel yield curve moves (steepening, flattening, twists) by applying shocks to relevant key rates and aggregating KRD effects.

Example comparison: If Bond A has 1‑year KRD = 0.5 and 5‑year KRD = 0.9, while Bond B has 1‑year KRD = 1.2 and 5‑year KRD = 0.3, Bond A is less sensitive at the short end and more sensitive at the intermediate term than Bond B.

Limitations and Considerations

• KRD assumes isolated shifts at a single key rate while holding other rates constant—real shifts are often correlated across maturities.
• Results depend on the choice and spacing of key maturities and the size of Δy used for shocks.
• For very large yield moves, duration‑based linear approximations become less accurate; consider convexity or full re‑pricing.

Bottom Line

Key rate duration gives a more nuanced view of interest‑rate risk across the yield curve than single‑number measures like effective duration. By quantifying sensitivity at individual maturities, KRD helps investors analyze, compare, and hedge term‑structure exposures in a targeted way.