Duration measures look contradictory when candidates memorize each label separately. Modified duration, effective duration, and key rate duration are not competing definitions of the same number. They answer different versions of the same risk question: which interest rate changed, did the cash flows change, and is the curve move parallel or local?
The CFA exam often tests this distinction through language rather than heavy math. A stem may say the bond is option-free, the benchmark curve shifts, the change is at one maturity node, or the bond has rate-sensitive cash flows. Each phrase points to a different measure.
The Decision Starts With The Rate Shock
Before choosing a duration measure, identify the rate movement:
The exam trap is using a familiar label before reading the shock. A question about a one-year node and a ten-year node is not asking for a single parallel-shift measure. A question about a callable bond is not solved cleanly by assuming promised cash flows stay fixed.
Modified Duration: Fixed Cash Flows And The Bond's Own Yield
Modified duration estimates the percentage price change for a small change in the bond's yield to maturity, assuming cash flows do not change.
For an option-free fixed-rate bond, that assumption is usually reasonable for a small yield change. If a bond has modified duration of 6.4, a 0.25% rise in yield implies an approximate price change of:
-6.4 x 0.25% = -1.60%
That is a local approximation, not a full revaluation. It is most comfortable when the bond has fixed promised cash flows and the stem does not introduce benchmark curve nodes or embedded options.
Why Modified Duration Can Equal Effective Duration
For a plain option-free bond, effective duration and modified duration can be very close if the effective-duration model uses a small parallel benchmark shift and the bond's spread is unchanged. Both are capturing roughly the same first-order price response.
They are not identical by definition. They can align because the assumptions line up:
- cash flows are fixed
- the rate move is small
- the curve shift is parallel
- the valuation model and yield change are economically consistent
Once any of those assumptions breaks, the measures can separate.
Effective Duration: Model Prices Under Up And Down Curve Shifts
Effective duration estimates sensitivity by repricing the bond when the benchmark curve moves up and down. It is especially useful when expected cash flows may change with rates.
The simplified structure is:
effective duration = (price if rates fall - price if rates rise) / (2 x original price x curve shock)
Suppose Linden Coast Power has a callable bond priced at 101.20. A model prices it at 103.10 after a 25 basis point benchmark decline and 98.40 after a 25 basis point benchmark increase.
Effective duration is approximately:
(103.10 - 98.40) / (2 x 101.20 x 0.0025) = 9.29
That number reflects more than discounting fixed cash flows. If the model changes call probabilities when rates move, the effective duration includes that option-sensitive behavior.
Key Rate Duration: Where On The Curve The Exposure Sits
Key rate duration measures sensitivity to a change at a specific maturity point on the benchmark curve while other points are held constant or moved according to the model's key-rate setup.
That makes it a curve-shape measure. It helps answer questions like:
- Is the bond more exposed to the two-year rate or the ten-year rate?
- What happens if short rates rise but long rates are unchanged?
- How should a portfolio hedge a twist rather than a parallel shift?
Assume Cedar Bay Income Fund owns a bond portfolio with the following key rate durations:
| Curve node | Key rate duration |
|---|---|
| 2-year | 0.8 |
| 5-year | 2.1 |
| 10-year | 3.4 |
| 30-year | 0.7 |
If only the 10-year node rises by 20 basis points, the approximate price effect is:
-3.4 x 0.20% = -0.68%
Using total duration would miss the point because the shock is local, not parallel.
Why The Sum Of Key Rate Durations Can Matter
When every relevant curve node shifts by the same small amount, the sum of key rate durations can approximate the portfolio's sensitivity to a parallel curve move.
In the Cedar Bay example:
0.8 + 2.1 + 3.4 + 0.7 = 7.0
If the full curve shifts up 20 basis points and the key-rate setup covers the relevant curve exposure, the approximate total effect is:
-7.0 x 0.20% = -1.40%
That does not mean key rate duration and effective duration are always interchangeable. It means the partial exposures can add up to a parallel-shift sensitivity when the measurement setup and assumptions are aligned.
Where The Measures Stop Agreeing
The bridge breaks when the rate move is not a simple parallel shift, when cash flows can change, or when the key-rate grid does not capture the relevant curve exposure.
Nonparallel Curve Movement
If the two-year node rises and the ten-year node falls, total effective duration is too blunt. Key rate durations are built for that shape question.
Embedded Or Behavioral Options
Callable bonds, putable bonds, mortgage-backed securities, and other option-sensitive instruments can change expected cash flows when rates move. Modified duration assumes fixed cash flows, so it can become unreliable. Effective duration is usually preferred because the up-rate and down-rate prices can incorporate changing expected cash flows.
Spread Versus Benchmark Movement
If the stem asks about spread widening over the benchmark curve, spread duration may be the relevant measure. If it asks about a benchmark node, key rate duration is in play. If it asks about the bond's own yield for fixed cash flows, modified duration may be enough.
Worked Example: Parallel Versus Twist
Assume North Pier Pension Trust holds an option-free bond portfolio priced at 50,000,000. Its key rate durations are:
| Node | Key rate duration |
|---|---|
| 2-year | 1.2 |
| 5-year | 2.6 |
| 10-year | 2.9 |
| 30-year | 0.5 |
Total key-rate exposure is 7.2.
Scenario 1: Parallel Increase
All nodes rise 15 basis points.
Approximate percentage change:
-7.2 x 0.15% = -1.08%
Approximate value change:
-1.08% x 50,000,000 = -540,000
Here, summed key rate durations behave like a parallel-shift sensitivity.
Scenario 2: Curve Twist
The 2-year node rises 30 basis points, the 5-year node rises 10 basis points, the 10-year node falls 5 basis points, and the 30-year node is unchanged.
Approximate percentage change:
-(1.2 x 0.30%) - (2.6 x 0.10%) - (2.9 x -0.05%) - (0.5 x 0.00%)
= -0.36% - 0.26% + 0.145% = -0.475%
Approximate value change:
-0.475% x 50,000,000 = -237,500
The summed duration of 7.2 would not by itself tell you this answer. You need the location of the exposure and the direction of each node move.
Exam Framing
For CFA fixed-income questions, read the stem in this order:
- Instrument: option-free bond, callable bond, putable bond, mortgage-backed security, or portfolio.
- Rate source: own yield, benchmark curve, spread, or specific curve node.
- Curve shape: parallel move or nonparallel move.
- Cash-flow behavior: fixed promised cash flows or rate-sensitive expected cash flows.
- Output requested: percentage price change, node exposure, measure selection, or interpretation.
The safest mental model is:
- Modified duration: fixed cash flows and the bond's own yield.
- Effective duration: model-based benchmark shift, especially when cash flows can change.
- Key rate duration: exposure to specific curve maturity nodes.
- Sum of key rate durations: possible bridge to parallel-shift sensitivity when assumptions align.
That bridge is useful because it turns duration from a vocabulary list into a map of the actual interest-rate shock.