SERIES 65 | FINANCIAL REGULATION COURSES
Key rate duration is a fixed income risk measure that quantifies a bond's or portfolio's price sensitivity to a change in yield at a specific maturity point on the yield curve while all other maturities are held constant — providing a more precise and analytically complete picture of interest rate risk than standard effective duration, which assumes that all yields across all maturities move by the same amount simultaneously in a parallel shift.
Why Standard Duration Is Insufficient
Standard modified duration and effective duration are powerful and widely used measures of interest rate risk, but both rest on a critical simplifying assumption: the entire yield curve shifts in parallel — every maturity point rises or falls by the same number of basis points at the same time. In practice, parallel shifts are relatively rare. The yield curve far more commonly changes shape — it steepens when long-term rates rise more than short-term rates, flattens when long-term rates fall relative to short-term rates, or undergoes a twist or butterfly shift where intermediate maturities move differently from both the short and long ends.
When the yield curve does not shift in parallel, a single duration number — even a well-calculated effective duration — cannot accurately predict how a portfolio's value will change. A bond with a ten-year effective duration may behave very differently from another bond with the same effective duration if their cash flows are distributed differently across the yield curve and if the curve steepens rather than shifts in parallel. The ten-year bond whose cash flows are concentrated near the ten-year point will respond primarily to changes in the ten-year yield. A bond whose cash flows are spread across multiple maturities will respond to changes across the entire curve in proportion to how its cash flows are distributed.
Key rate duration solves this problem by measuring sensitivity to each point on the yield curve independently.
The Definition and Formula
Key rate duration measures the sensitivity of a bond's value to a one percent — one hundred basis point — change in the yield at a specific maturity point on the yield curve, holding all other maturity yields constant.
The formula for the key rate duration at maturity k is expressed as follows. Key rate duration at k equals the difference between the bond's price when the yield at maturity k decreases by one percent and the bond's price when the yield at maturity k increases by one percent, divided by two times one percent times the bond's original price. In mathematical notation, key rate duration at k equals the quantity price at negative shock minus price at positive shock divided by the quantity two times 0.01 times the original price.
This formula is structurally identical to the effective duration formula, except that the yield shock is applied only to a single point on the curve rather than to the entire curve simultaneously. The result is a duration measured in years that represents the percentage price change per one hundred basis point change in that specific yield.
A Worked Example
Consider a bond currently priced at one thousand dollars. A one percent increase in the five-year yield, holding all other maturities constant, reduces the bond's price to nine hundred and seventy dollars. A one percent decrease in the five-year yield, holding all other maturities constant, increases the bond's price to one thousand and forty dollars.
The five-year key rate duration is one thousand and forty minus nine hundred and seventy, divided by two times zero point zero one times one thousand. This equals seventy divided by twenty, equalling three point five years. The bond's price is expected to change by approximately three point five percent for each one hundred basis point change in the five-year yield specifically, assuming no change in yields at other maturities.
The Vector of Key Rate Durations
Rather than producing a single number, key rate duration analysis produces a vector — a set of durations, one for each key maturity point along the yield curve being analysed. Common key rate points are the three-month, one-year, two-year, three-year, five-year, seven-year, ten-year, twenty-year, and thirty-year maturities, though the specific points used depend on the analytical framework and the available liquid benchmark instruments at each maturity.
Each key rate duration in the vector tells the analyst how sensitive the portfolio is to changes in yield at that specific maturity. A portfolio concentrated in five to seven year maturities will show large key rate durations at the five-year and seven-year points and small key rate durations at the two-year and thirty-year points, because yield changes at those distant points have little effect on the portfolio's value.
One fundamental mathematical property confirms the internal consistency of key rate duration analysis: the sum of all key rate durations across all maturity points equals the bond's effective duration. If a bond has an effective duration of six years and key rate durations are calculated at the one-year, three-year, five-year, seven-year, and ten-year points, those five key rate durations must sum to six years. This additive property allows analysts to verify their key rate duration calculations and to confirm that the total interest rate risk captured by the key rate framework equals the total risk captured by effective duration for a parallel shift scenario.
Shaping Risk — What Key Rate Duration Reveals
The primary analytical contribution of key rate duration is the identification and quantification of shaping risk — a bond's or portfolio's sensitivity to changes in the shape of the yield curve rather than simply its level.
A portfolio with identical effective duration to its benchmark but with key rate durations that differ substantially from the benchmark at specific maturities is exposed to shaping risk. If the yield curve steepens — long rates rise while short rates are unchanged — the portfolio's performance relative to the benchmark will depend on whether the portfolio is overweight or underweight long-duration key rates compared to the benchmark. A portfolio overweight the thirty-year key rate duration relative to its benchmark will underperform when long rates rise, regardless of whether its total effective duration matches the benchmark.
This distinction between level risk — captured by effective duration — and shaping risk — captured by the profile of key rate durations across the curve — is what makes key rate duration an essential analytical tool for active fixed income portfolio managers who take intentional positions along the yield curve rather than simply matching benchmark duration.
Portfolio Application — Yield Curve Strategies
The CFA Institute's fixed income curriculum identifies key rate duration as the primary tool for evaluating a portfolio's sensitivity using key rate durations of the portfolio and its benchmark, which is essential for discussing yield curve strategies across currencies and evaluating the expected return and risks of any yield curve positioning.
Active yield curve managers take positions based on their forecasts of how the yield curve shape will change. A manager who expects the yield curve to steepen — long rates rising relative to short rates — will deliberately position the portfolio with higher key rate duration at the short end and lower key rate duration at the long end compared to the benchmark, seeking to benefit from the underperformance of long bonds as their yields rise. A manager who expects the curve to flatten does the opposite. These tactical yield curve positions, expressed through the key rate duration profile, cannot be evaluated using effective duration alone.
Immunisation strategies — designed to ensure that a fixed income portfolio produces a target return regardless of how interest rates change — require matching not only the effective duration of assets to the investment horizon but also matching the key rate duration profile of assets to that of liabilities when liabilities have cash flows at multiple maturity points. A pension fund with liabilities spread across fifteen, twenty, and thirty-year maturities must match its assets' key rate durations at each of those specific points, not merely match total effective duration, to achieve true immunisation against non-parallel yield curve shifts.
Key Rate Duration and Bonds with Embedded Options
Key rate duration is particularly valuable for analysing bonds with embedded options — callable bonds, puttable bonds, and mortgage-backed securities — whose effective duration changes as rates change and whose price sensitivity varies differently across the yield curve than for option-free bonds.
A callable bond's price is capped near the call price when rates fall, creating negative convexity at low rate levels. This capping occurs specifically in the maturity range of the call option — the key rate duration at maturities near the expected call date will reflect the call option's effect, showing reduced price sensitivity compared to an equivalent option-free bond at the same maturity. Key rate duration analysis therefore reveals where the embedded option is distorting interest rate sensitivity in a way that a single effective duration number cannot communicate.
Examination Relevance and Key Takeaways
Key rate duration is tested on the Series 65 examination in the context of fixed income risk measurement, yield curve analysis, portfolio immunisation, and active yield curve management strategies.
The key points to retain are these.
Key rate duration measures a bond's or portfolio's price sensitivity to a one hundred basis point change in yield at one specific maturity point on the yield curve while all other maturity yields remain unchanged — distinguishing it from effective duration which assumes a parallel shift in all yields simultaneously.
The formula is structurally identical to effective duration but applies the yield shock only to a single point. The result is a vector of durations, one per key maturity point, that together reveal the full interest rate risk profile across the yield curve.
The sum of all key rate durations equals the bond's effective duration, confirming internal consistency. Key rate duration identifies and quantifies shaping risk — sensitivity to changes in the shape rather than merely the level of the yield curve — which is essential for active yield curve strategies involving intentional overweights or underweights at specific curve maturities.
Effective duration is adequate for parallel shift scenarios but provides no information about non-parallel shift risk; key rate duration is required whenever the yield curve shape is expected to change through steepening, flattening, or twisting. Portfolio immunisation requires matching key rate durations of assets to liabilities when liability cash flows are distributed across multiple maturities, not merely matching total effective duration.
