Key Rate Duration
Key rate duration measures a bond portfolio's or security's price sensitivity to a change in yield at a specific maturity point on the yield curve while holding all other maturity yields constant, enabling precise identification of which parts of the yield curve a portfolio is most exposed to.
Traditional duration measures — modified duration, effective duration — assume that the entire yield curve shifts in parallel: every maturity point moves by the same amount. In practice, yield curves rarely shift in parallel. The 2-year might move more than the 10-year, or the 10-year might move independently of the 30-year. Key rate duration (KRD) was developed by Thomas Ho in 1992 to capture this non-parallel shift risk by decomposing total duration into sensitivity measures at each key maturity point.
A typical KRD analysis for a Treasury portfolio might compute durations at six to twelve key rates: 0.25y, 0.5y, 1y, 2y, 3y, 5y, 7y, 10y, 20y, and 30y. Each KRD measures the percentage price change of the portfolio if yields at that specific maturity point rise by 1%, while yields at all other maturity points remain unchanged. The sum of all key rate durations equals the total effective duration of the portfolio.
KRD is particularly valuable for liability-driven investment programs at insurance companies and pension funds. A pension fund with benefit payment obligations concentrated in years 15-25 has a liability KRD profile peaking at those maturities. To hedge effectively, the asset portfolio must match the liability KRD at each key rate, not just total duration. A mismatch — even if total durations are equal — creates residual exposure to non-parallel curve shifts.
For Treasury portfolio managers, KRDs provide the diagnostic framework for yield curve positioning. A portfolio with higher KRD at the 10-year versus the 2-year is explicitly positioned for 10-year yields to outperform 2-year yields (a flattening view). A portfolio with elevated KRD at intermediate maturities relative to both short and long ends is positioned for a concave (humped) yield curve.
KRDs are computed using either analytical methods for bullet bonds (single cash flow at maturity) or simulation methods for bonds with embedded options or uncertain cash flows. For plain-vanilla Treasury securities, KRD computation is straightforward: each cash flow (coupon or principal payment) contributes to KRDs at adjacent key rate maturity points, weighted by linear interpolation between the two nearest key rates.