What is key rate duration and when should I use it instead of regular modified duration?

Question

AcadiFi · Accepted Answer

Key rate duration (KRD) solves one of the biggest limitations of traditional duration: the assumption that the entire yield curve shifts in parallel. In reality, the short end, belly, and long end of the curve often move independently.

## Concept

A key rate duration measures the sensitivity of a bond's (or portfolio's) price to a change in yield at ONE specific maturity point on the curve, while holding all other rates constant.

**If you have key rate durations at maturities 2Y, 5Y, 10Y, and 30Y:**

Delta_P / P = -(KRD_2 x Delta_y_2) - (KRD_5 x Delta_y_5) - (KRD_10 x Delta_y_10) - (KRD_30 x Delta_y_30)

**The sum of all KRDs equals the bond's total modified duration.** This is a useful check.

## Worked Example

Stonebridge Pension Fund holds a portfolio with these key rate durations:

| Key Rate | KRD |
|---|---|
| 2-year | 0.8 |
| 5-year | 2.1 |
| 10-year | 3.5 |
| 30-year | 1.9 |
| **Total** | **8.3** |

This confirms the portfolio's modified duration is 8.3.

Now suppose a yield curve steepening scenario:
- 2Y rate: -25 bps
- 5Y rate: unchanged
- 10Y rate: +15 bps
- 30Y rate: +40 bps

**Price change:**
Delta_P/P = -(0.8 x -0.0025) - (2.1 x 0) - (3.5 x 0.0015) - (1.9 x 0.004)
Delta_P/P = +0.0020 - 0 - 0.00525 - 0.0076
Delta_P/P = **-1.085%**

Compare this to what regular duration would predict for the average shift:
Average shift = (-25 + 0 + 15 + 40) / 4 = +7.5 bps
Delta_P/P (modified dur) = -8.3 x 0.00075 = -0.623%

The KRD estimate (-1.085%) is almost twice the modified duration estimate (-0.623%) because the portfolio has significant exposure to the 10Y and 30Y points, which rose the most.

```mermaid
flowchart LR
    subgraph Parallel["Modified Duration"]
        MD["Single number
Assumes parallel shift"]
    end
    subgraph NonParallel["Key Rate Durations"]
        KRD2["KRD 2Y = 0.8"] 
        KRD5["KRD 5Y = 2.1"]
        KRD10["KRD 10Y = 3.5"]
        KRD30["KRD 30Y = 1.9"]
    end
    NonParallel -->|"Sum = Total MD"| Parallel
    NonParallel -->|"Better for steepening,
flattening, twists"| RESULT["More Accurate
Risk Estimate"]
```

## When to Use KRD

- Portfolios with **barbell structures** (concentrated at short and long maturities)
- **Liability-driven investing** where liability cash flows cluster at specific maturities
- **Mortgage-backed securities** with complex cash flow patterns
- Any scenario involving **non-parallel curve movements**

Practice KRD problems in our FRM question bank.

What is key rate duration and when should I use it instead of regular modified duration?

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