Key Rate Duration
Key Rate Duration (KRD) measures a bond or portfolio's price sensitivity to a 1% (100 basis point) change in the yield at a specific point (key rate) on the yield curve—holding all other key rates constant—enabling a granular decomposition of interest rate risk across the maturity spectrum rather than summarizing it in a single parallel-shift duration number. The sum of all key rate durations equals the effective duration, providing both a total risk measure and a detailed picture of where along the curve the rate sensitivity is concentrated.
Key takeaways
- KRD measures price sensitivity to isolated yield changes at specific maturities (typically 2Y, 5Y, 10Y, 20Y, 30Y), capturing 'twist' and 'butterfly' risk that parallel-shift duration misses.
- For a bullet bond (cash flows concentrated at one maturity), KRD is concentrated at the maturity closest to the cash flow; for a barbell portfolio, KRDs are concentrated at short and long maturities.
- Portfolio managers match KRDs of assets to liabilities (liability-driven investing) to hedge not just total duration but the full yield curve shape sensitivity, protecting against non-parallel yield curve shifts.
- Mortgage-backed securities have complex KRD profiles that shift dramatically with interest rate levels due to prepayment optionality, requiring dynamic KRD estimation using option-adjusted models.
- KRD is calculated using finite difference methods: shocking each key rate by a small amount (e.g., ±25 bps) while holding other key rates constant, computing the resulting price change, and scaling to a 100 bps (1%) shock.
Explanation
Key Rate Duration extends the concept of effective duration—which measures price sensitivity to a parallel shift across all maturities simultaneously—to capture the more realistic scenario of non-parallel yield curve changes. In practice, interest rate movements are rarely parallel: the Federal Reserve may raise short-term rates while long-term rates rise less (flattening), or long-term yields may rise while short rates stay anchored (bear steepening). These non-parallel shifts create profit and loss for fixed-income portfolios that effective duration alone cannot predict.
The calculation of KRDs uses a finite difference approach applied to specific 'key rates' that are chosen to represent the most important points on the yield curve. A typical set of key rates includes: 3-month, 2-year, 5-year, 10-year, 20-year, and 30-year maturities. For each key rate, the pricing model shocks that specific yield by a small amount (typically ±25 basis points, then scaled to 100 bps) while holding all other key rates constant, using linear interpolation to determine how intermediate maturities are affected by the local shock. The KRD at that key rate equals the percentage price change divided by the yield change in percentage points.
The interpretation of KRD profiles reveals important information about a portfolio's yield curve exposure. A bullet portfolio concentrated in 10-year bonds will have nearly all its KRD in the 10-year key rate bucket and minimal KRDs elsewhere. A barbell portfolio with equal allocations to 2-year and 30-year bonds will have KRDs concentrated at the short and long ends, with minimal sensitivity to 10-year rate changes. Two portfolios with identical total effective durations but different KRD profiles will perform very differently in a yield curve twist (when long rates rise and short rates fall, or vice versa)—the barbell is long the spread between 30-year and 2-year rates (positive position in a bull flattening), while the bullet is exposed only to the 10-year rate.
For liability-driven investing (LDI), KRD matching between assets and liabilities is the precise tool for immunizing a pension fund or insurance company against interest rate risk. A pension fund with liabilities concentrated at 20-30 year maturities will have high KRDs in the long end; matching these with long-duration assets (30-year Treasury bonds, long corporate bonds, long duration swaps) creates a KRD-matched portfolio that is insensitive to any parallel or non-parallel yield curve shift. Residual KRD mismatches—inevitable in practice given discrete asset choices—represent managed risk positions reflecting the portfolio manager's views on yield curve shape.
Mortgage-backed securities present one of the most complex KRD analysis challenges in fixed income. MBS cash flows are path-dependent due to homeowner prepayment behavior, which accelerates when rates fall and slows when rates rise. This creates negative convexity (effective duration shortens in lower rate environments) and complex, non-stationary KRD profiles. At current rate levels, an MBS may have a KRD profile concentrated at 7-10 year maturities; if rates fall 100 basis points, prepayments accelerate, and the MBS's KRD profile collapses toward 3-5 year maturities. Accurately modeling this dynamic KRD behavior requires Monte Carlo simulation of interest rate paths and corresponding prepayment dynamics—a computationally intensive process that risk management systems must run continuously.
Formula
KRD_n = -(ΔP/P) / Δy_n; where Δy_n is a 1% change in key rate n with all other key rates held constant; Σ KRD_n = Effective Duration
Example
A pension fund has liability cash flows concentrated between 15 and 30 years, with key rate duration exposures of 0.5 in 2Y, 0.8 in 5Y, 2.1 in 10Y, 4.5 in 20Y, and 6.2 in 30Y (total effective duration = 14.1 years). Its current asset portfolio has KRDs of: 0.4 (2Y), 1.2 (5Y), 4.1 (10Y), 3.5 (20Y), and 5.0 (30Y)—total effective duration = 14.2 years. While effective durations nearly match, the portfolio has a KRD mismatch: it is long 10-year duration (assets 4.1 vs. liabilities 2.1) and short 20-year and 30-year duration (assets 3.5 and 5.0 vs. liabilities 4.5 and 6.2). If the yield curve twists (long rates rise relative to mid rates), the pension fund suffers as its liabilities increase more than its assets. To correct this, the portfolio manager sells some 10-year bonds and purchases 20-year and 30-year bonds (or enters receive-fixed 20- and 30-year interest rate swaps), aligning the KRD profiles.
Related terms
Asset Backed Security Bankers Acceptance Basis Bond Convexity Duration Effective Duration Interest Rate Interpolation Investment Grade Monte Carlo Simulation Negative Convexity