Key rate duration measures a bond's price sensitivity to a yield change at:

Every maturity at once, by an equal amount

One specific maturity, all others held constant

The shortest maturity the portfolio holds

The weighted average maturity of the holdings

Modified duration and effective duration both rest on which simplifying assumption?

Yields move in proportion to time to maturity

Short rates move while long rates stay fixed

The whole curve moves by the same amount at once

The issuer's credit spread stays unchanged throughout

In practice, movements of the yield curve are:

More often changes of shape than parallel shifts

More often parallel shifts than changes of shape

Almost always confined to the shortest maturities

Evenly divided between rises and falls each year

The yield curve is said to steepen when:

Short rates rise more than long rates do

Long rates rise more than short rates do

All maturities rise by the same amount

The middle of the curve moves on its own

Two bonds share an effective duration of ten years. Under a non-parallel move they may still behave differently because:

Their issuers carry different credit ratings

Their coupons are paid on different calendar dates

Their cash flows sit at different points on the curve

They are quoted on different trading venues

In the key rate duration formula, dividing by twice the shock size serves to:

Adjust for compounding between the two shocked prices

Convert the result from years into percentage points

Remove the effect of coupons paid during the period

Average the upward and downward price responses

In the key rate duration formula, the numerator is:

The down-shock price minus the up-shock price

The up-shock price minus the down-shock price

The original price minus the up-shock price

The sum of the two shocked prices, halved

A single effective duration figure and a key rate duration vector differ in that only the vector:

Can be calculated for a bond that pays no coupon

Distinguishes a curve steepening from a parallel shift

Is expressed as a number of years

Requires the bond's current market price as an input

A key rate duration is expressed in years, but is read as:

The share of the portfolio held at that point

The number of years until the cash flows arrive

A percentage price move per hundred basis points

The size of the move being made to that yield

Which maturity points are used in a key rate vector depends on:

The coupon dates of the largest holding

A fixed schedule published by the regulator

The framework and the liquid benchmarks available

The credit quality of the issuers involved

A portfolio concentrated in five to seven year maturities will show key rate durations that are:

Negative at every point beyond seven years

Small near those maturities and large far from them

Roughly equal at every point on the curve

Large near those maturities and small far from them

Across all maturity points, the key rate durations sum to:

One, once the figures are scaled

A manager expects yields at the long end to fall while the short end holds steady. The curve is:

Steepening, as the gap between the ends widens

Flattening, as the gap between the ends narrows

Shifting in parallel, with both ends moving alike

Inverting, with short rates above long rates

A portfolio whose effective duration matches its benchmark exactly:

Will differ from it only when rates move sharply

Will track it closely under any curve movement

Will differ from it only if credit quality differs

May still differ from it at particular maturities

A single effective duration figure captures exposure to a parallel move. Exposure to a non-parallel move is captured instead by:

The portfolio's weighted average coupon rate

The convexity of the longest holding it owns

The spread between its yield and the benchmark's

A manager who expects the curve to steepen will position the portfolio with:

Every maturity weighted equally across the curve

Long maturities emphasised and short ones reduced

Short maturities emphasised and long ones reduced

No position taken until the move has occurred

A tactical position taken along the yield curve cannot be evaluated using:

The manager's stated benchmark index

The key rate profile on its own

The portfolio's average credit rating

An immunisation strategy is designed to produce:

A target return whatever rates do

The highest return the market allows

A return free of any credit exposure

Income paid on a fixed monthly date

A pension fund's liabilities fall due at fifteen, twenty and thirty years. True immunisation requires the assets to match:

The total figure only, which subsumes the points

The profile at each of those points, not just the total

The coupon income arising in each of those years

The credit quality of the sponsor at each date

When rates fall, a callable bond's price is:

Reduced below its earlier level

On a callable bond, the option's effect on interest rate sensitivity shows up at:

Maturities beyond the stated redemption date

The very shortest maturities on the curve

Every maturity in equal proportion

The technique is especially valuable for which instruments?

Callable bonds, puttable bonds and mortgage-backed paper

Treasury bills, commercial paper and repurchase agreements

Common shares, preference shares and warrants

Currency forwards, futures and interest rate swaps

Immunisation begins by matching the duration of the assets to:

The average coupon of the assets

A mortgage-backed security's key rate durations shift markedly after a sharp fall in rates. The most likely cause is:

The benchmark curve has been rebased to new points

Its credit rating has been downgraded by an agency

Expected prepayments have pulled its cash flows earlier

Its coupon has been reset by the loan servicer

The managers for whom this analysis is essential are those who:

Invest exclusively outside fixed income

Match the benchmark's total figure exactly

Hold only cash and short-dated bills

Take deliberate positions along the curve

Key Rate Duration: Definition, Formula and Examples

What Is Key Rate Duration?

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 Macaulay 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 greater price sensitivity at the call date than an equivalent option-free bond, while the callable bond’s key rate duration at its final maturity is lower. 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.