How does key rate duration hedging work and why is it superior to simple duration matching?

Question

AcadiFi · Accepted Answer

Key rate duration (KRD) measures a bond's price sensitivity to a change in yield at a specific maturity point on the curve while holding all other rates constant. A portfolio has a vector of KRDs rather than a single duration number.

**Why Simple Duration Matching Fails:**

Modified duration assumes the entire yield curve shifts in parallel. In reality, curves steepen, flatten, twist, and butterfly. Two portfolios with identical modified duration can have very different KRD profiles and respond differently to non-parallel shifts.

**Worked Example -- Ashford Pension Fund (fictional)**

Ashford's liability has key rate durations at the 2-year, 5-year, 10-year, and 30-year points:

| Maturity Point | Liability KRD | Portfolio KRD (Before) | Gap | Action |
|---|---|---|---|---|
| 2-year | 0.5 | 1.8 | +1.3 | Sell short-end exposure |
| 5-year | 1.2 | 2.5 | +1.3 | Sell intermediate |
| 10-year | 3.0 | 1.5 | -1.5 | Buy 10-year bonds/swaps |
| 30-year | 8.0 | 3.0 | -5.0 | Buy long-end bonds/swaps |
| **Total Duration** | **12.7** | **8.8** | **-3.9** | |

Even if Ashford adds bonds to match total duration at 12.7, the portfolio would still be mismatched along the curve. A bear flattener (short rates up, long rates stable) would hurt the over-weighted short end while not benefiting the under-weighted long end.

**Hedging with KRD Matching:**

\`\`\`mermaid
flowchart TD
    A[Calculate Liability KRD at Each Point] --> B[Calculate Portfolio KRD at Each Point]
    B --> C[Identify KRD Gaps at Each Maturity]
    C --> D{Gap at Each Point?}
    D -->|Positive Gap| E[Sell Exposure or Add Receiver Swaps]
    D -->|Negative Gap| F[Buy Bonds or Add Payer Swaps]
    E --> G[Rebalance Until All KRDs Match]
    F --> G
    G --> H[Portfolio Immunized Against Non-Parallel Shifts]
\`\`\`

In practice, traders use interest rate swaps at specific tenors to fill KRD gaps because swaps are liquid, capital-efficient, and allow precise maturity targeting. A common approach uses 2-year, 5-year, 10-year, and 30-year swaps to match the four primary KRD buckets.

How does key rate duration hedging work and why is it superior to simple duration matching?

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