Duration and the Mechanics of Rate Shocks
Duration translates a specified yield change into an approximate price response. It does not explain why yields move, predict the next move, or summarize every risk of a bond. Its value comes from stating exactly which sensitivity is being measured.
Identify the duration definition and yield convention, express rate shocks in decimal units, and use convexity or full repricing when the linear approximation is inadequate. Examine curve twists, embedded options, and spread exposure separately. Reconcile price effects with income and cash-flow timing before describing a scenario as a holding-period return.
Distinguish duration from maturity
Maturity states when a bond's final contractual payment occurs. Duration describes cash-flow timing or price sensitivity under a specified definition. A coupon bond pays part of its value before final maturity, so the two measures differ. Two securities maturing on the same day can have different duration because their coupons, yields, and cash-flow features differ. A maturity label alone is insufficient for comparing interest-rate exposure.
CFA Institute's Yield-Based Bond Duration Measures and Properties distinguishes Macaulay duration, modified duration, money duration, and price value of a basis point. Modified duration measures proportional price sensitivity to a bond's own yield under fixed-cash-flow assumptions. Macaulay duration is a discounted cash-flow timing measure. Identify the particular measure rather than carrying a number called duration between models that use different definitions.
Calculate a synthetic first-order price response
Assume an illustrative bond position worth USD 10 million with modified duration of 6.5. For a 75-basis-point yield increase, the first-order proportional price change is negative 6.5 multiplied by 0.0075, or negative 4.875%. The estimated price loss is USD 487,500. The inputs are synthetic and describe an instantaneous sensitivity, not expected performance over the coming year.
One basis point is 0.0001 in decimal yield units. The position's approximate price value of a basis point is USD 10 million times 6.5 times 0.0001, or USD 6,500. Confusing 75 basis points with 0.75 or with 75 creates enormous errors. Show the shock conversion and sign explicitly, and state that the price value changes as the bond's price and duration change.
Add convexity without claiming exactness
Continue the synthetic example with annual convexity of 55 under the same yield convention. The second-order adjustment is one-half times 55 times 0.0075 squared, approximately positive 0.1547%. Adding it to the duration estimate gives a price change near negative 4.7203%, or a USD 472,031 loss after rounding. Income, elapsed time, and transaction costs remain excluded.
CFA Institute's Yield-Based Bond Convexity and Portfolio Properties explains why curvature matters more for larger yield changes. With a 75-basis-point decline and the same synthetic parameters, the duration-plus-convexity estimate is positive 5.0297%, not merely the opposite of the estimated decline. This asymmetry applies to the stated option-free approximation; callable securities can behave differently. Full cash-flow repricing remains preferable when the move or instrument complexity makes local approximations unreliable.
Test curve twists rather than only parallel shifts
A single duration number compresses exposure across maturities. A two-year yield and a thirty-year yield rarely move by exactly the same amount in every episode. Key-rate sensitivities describe exposure to selected curve points under a defined interpolation and bumping method. They allow a researcher to distinguish two portfolios that have similar overall duration but concentrate their sensitivities at different maturities.
For an illustrative decomposition, assign key-rate durations of 2 at the short point and 4 at the long point. If the short yield falls 25 basis points while the long yield rises 50, the linear effect is positive 0.5% minus 2%, or negative 1.5%. A parallel-shift summary would miss this combination. The example ignores cross-effects and requires a coherent curve construction before being applied to real securities.
Recognize instruments whose cash flows can change
A callable bond's expected redemption timing can change when rates move. Mortgage prepayments and floating coupons create other forms of conditional cash flow. Applying fixed-cash-flow modified duration mechanically can misstate these exposures. Effective duration instead reprices under benchmark-curve shocks with a model for changing cash flows. Its output depends on that model, not solely on the instrument's observed coupon and maturity.
CFA Institute's Overview of Fixed-Income Portfolio Management discusses effective measures and spread sensitivity alongside duration. For corporate bonds, distinguish benchmark-rate changes from credit-spread changes. For inflation-linked bonds, identify whether the shock concerns real yields or inflation assumptions. An interest-rate sensitivity is only one part of an instrument's risk profile; it does not absorb credit deterioration, liquidity discounts, or a change in the assumed exercise behavior.
Reconcile the price shock with the research horizon
An instantaneous shock calculation holds time fixed. A six-month investment result also includes coupon accrual, reinvestment, changes in maturity, and the curve at the endpoint. Carry and roll-down need explicit conventions, particularly if the curve changes during the period. Adding the starting yield to a duration loss is at most a simplified attribution, not a universally correct total-return identity.
A fixed payment held to maturity has different interim price exposure from its ultimate contractual redemption, subject to issuer performance. That does not make its economic rate sensitivity disappear before maturity. Nor does an unchanged redemption amount guarantee a particular real return. Match the question to the horizon: mark-to-market loss, realized sale proceeds, and eventual purchasing power are separate outcomes that should not share an unlabeled chart axis.
Keep a transparent sensitivity record
Record the position value, price basis, settlement date, coupon conventions, yield input, duration definition, convexity units, and shock size. Show whether the calculation reprices a security or estimates an index. For derivatives, specify notional, contract multiplier, and the mapping to underlying rate exposure; a small cash outlay does not imply a small duration position. Retain both the formula and the resulting currency amount.
Review discrepancies between approximation and repricing rather than treating them automatically as data errors. They may reveal curvature, optionality, or a convention mismatch. A sound conclusion reports which exposure explains the calculated move and which risks were left out. It is a conditional sensitivity statement with traceable assumptions, not a forecast of the yield path or a recommendation about the appropriate amount of duration today.
What to retain
- Duration must be defined and matched to the instrument and yield convention.
- Convexity improves a local price approximation but does not make it a total return.
- Curve twists, optionality, and spread movements require additional exposure measures.
Source notes
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Version 1, 15 October 2026. First publication. Illustrative calculations are identified in context; source observations retain their stated dates.