Portfolio Management Pathway · Yield Curve Strategies

Yield Curve Dynamics and Duration Measures Explained

Updated 8 October 2026 · Fact-checked

Yield curve dynamics describe how the curve moves: a change in level (parallel shift), steepness (twist) or curvature (butterfly). Effective duration measures price sensitivity to a parallel shift. Key rate duration measures sensitivity to a change at one maturity. Money duration converts duration into currency terms.

Understand Yield Curve Dynamics and Duration Measures

A yield curve plots yields against maturity. Bonds at different maturities do not always move by the same amount. So a single duration number can hide risk.

Three factors describe most curve moves. Level is a parallel shift: all yields rise or fall by about the same amount. Steepness is the gap between long and short yields. It changes when short rates and long rates move by different amounts (a steepening or flattening). Curvature is the shape of the middle of the curve relative to the short and long ends. It changes when the medium-term yields move differently from the short and long ends (a butterfly move). Level is usually the largest driver of bond returns, then steepness, then curvature.

Effective duration measures price change for a parallel shift in the benchmark yield curve. It works for bonds with embedded options because it uses full repricing, not a formula based on fixed cash flows. It tells you nothing about non-parallel moves. Two portfolios can have the same effective duration and very different exposure to a flattening.

Key rate duration (also called partial duration) fixes this. You shift the yield at one key maturity, such as 2, 5, 10 or 30 years, and hold the others constant. You then reprice the bond. The key rate durations show where on the curve the exposure sits. For a bond with fixed cash flows, the key rate durations sum to approximately the effective duration. Their pattern also tells you how a barbell, bullet or ladder responds to a twist or butterfly.

Money duration is duration expressed in currency. It is the effective duration times the position's market value. Price value of a basis point (PVBP) is the money change for a 1 bp yield move. These measures let you size positions and compare a bond portfolio with a liability or a derivative hedge. Duration is a first-order estimate. For large moves, add convexity.

Key rules to remember

Effective duration: EffDur = (PV₋ − PV₊) ÷ (2 × PV₀ × ΔCurve); PV₋ is the price after the curve falls by ΔCurve, PV₊ after it rises. ΔCurve is in decimals, e.g. 0.0025 for 25 bps. This is for a parallel shift of the benchmark curve.
Approximate price change from duration: %ΔPV ≈ −EffDur × ΔYield; Add the convexity term when the move is large: + ½ × Convexity × (ΔYield)².
Key rate duration: KRD(k) = (PV₋ − PV₊) ÷ (2 × PV₀ × Δy_k); Only the yield at key maturity k is shifted. Other key rates stay unchanged.
Sum of key rate durations: Σ KRD(k) ≈ EffDur; Holds approximately for a bond or portfolio with fixed cash flows. Portfolio KRD at a point is the market-value-weighted average of the bond KRDs.
Money duration: Money duration = EffDur × Market value; Expressed in currency. Often shown per 100 of par for a bond.
Price value of a basis point: PVBP ≈ Money duration × 0.0001; The approximate money change for a 1 bp change in yield.
Portfolio duration: Dur_p = Σ w_i × Dur_i; Weights are market-value weights. This is correct for a parallel shift of the curve.

How to solve Yield Curve Dynamics and Duration Measures questions

Use this order for any question on curve shifts and duration measures. It keeps the link between the shift and the exposure clear.

1Read the command word and the client objective. Decide whether you must calculate, identify the exposure, or recommend a position.
2Classify the curve move: level (parallel), steepness (twist) or curvature (butterfly). Note the direction and size at each maturity.
3Pick the right measure. Use effective duration for a parallel shift. Use key rate durations for any non-parallel shift. Use money duration or PVBP for currency amounts.
4Compute the price effect. For each key rate, multiply −KRD by that key rate's yield change, then sum. For a parallel shift, use −EffDur × ΔYield.
5Convert to currency by multiplying the percent change by market value, or use money duration × yield change.
6Add convexity only if the move is large or the question gives convexity.
7State the result with its sign and units, then give a one-line conclusion tied to the client objective, such as whether the portfolio gains or loses from the move.

Quickest way: Key rate duration shortcut

When to use it: Use when a question gives key rate durations and the yield changes at each key rate, and asks for the percent price change.

Write each key rate duration beside its yield change in decimals.
Multiply each pair and put a minus sign in front.
Add the results to get the percent price change.
Check the sign: a rise in yields where you hold the duration must give a loss.
Multiply by the market value if the answer is needed in currency.

Common mistakes in Yield Curve Dynamics and Duration Measures

Using effective duration to estimate the effect of a steepening or flattening.
Effective duration is the only duration most candidates remember, so they apply it to every move.
Fix: Effective duration assumes a parallel shift. For a twist or butterfly, use key rate durations at each maturity.
Mixing up what steepness and curvature mean.
Both involve non-parallel moves, and the names sound similar.
Fix: Steepness is long yield minus short yield. Curvature is about the middle of the curve versus the ends. Match the term to the maturities that move.
Entering basis points as whole numbers in the formula.
The question says 25 bps and candidates type 25.
Fix: Convert to decimals first: 25 bps = 0.0025. Check the answer is a sensible size.
Dropping the minus sign, so a yield rise shows a gain.
Candidates focus on the arithmetic and forget the inverse price-yield relationship.
Fix: Write −KRD × Δy every time. Sanity-check: yields up on a long-duration position means a price loss.
Saying two portfolios with equal duration have equal risk.
Duration is treated as a full risk measure.
Fix: Equal effective duration only means equal sensitivity to a parallel shift. Compare their key rate duration profiles.
Treating money duration as a percent figure.
The word duration suggests years or a percent.
Fix: Money duration is in currency. Duration times market value. Divide by 10,000 for PVBP.

Worked examples

Example 1

A portfolio has a market value of $50 million. Its key rate durations are: 2-year 0.40, 5-year 1.10, 10-year 2.20, 30-year 1.50. The yield curve steepens: the 2-year yield falls by 20 bps, the 5-year falls by 10 bps, the 10-year is unchanged and the 30-year rises by 30 bps. Estimate the percent and dollar change in portfolio value.

Show the solution

Convert to decimals: 2-year −0.0020, 5-year −0.0010, 10-year 0, 30-year +0.0030.
2-year: −0.40 × (−0.0020) = +0.0008.
5-year: −1.10 × (−0.0010) = +0.0011.
10-year: −2.20 × 0 = 0.
30-year: −1.50 × 0.0030 = −0.0045.
Sum: 0.0008 + 0.0011 + 0 − 0.0045 = −0.0026, which is −0.26%.
Dollar change: −0.0026 × $50,000,000 = −$130,000.

Answer: The portfolio falls by about 0.26%, or about $130,000. The gains at the short end are outweighed by the loss on the 30-year exposure.

Example 2

A bond position has a market value of $4,000,000. Using a 25 bp parallel shift in the benchmark curve, the bond's price is 101.625 after a fall in yields and 98.375 after a rise in yields, per 100 of par, from a starting price of 100.00. Calculate the effective duration implied by these prices, the money duration of the position, and the approximate dollar change for a 40 bp parallel rise.

Show the solution

Effective duration = (PV₋ − PV₊) ÷ (2 × PV₀ × ΔCurve) = (101.625 − 98.375) ÷ (2 × 100 × 0.0025).
Numerator: 101.625 − 98.375 = 3.25. Denominator: 2 × 100 × 0.0025 = 0.50.
Effective duration = 3.25 ÷ 0.50 = 6.5.
Money duration = 6.5 × $4,000,000 = $26,000,000.
For +40 bps: %ΔPV ≈ −6.5 × 0.0040 = −0.0260, or −2.60%.
Dollar change: −0.0260 × $4,000,000 = −$104,000.

Answer: Implied effective duration is 6.5. Money duration is $26,000,000. A 40 bp parallel rise implies a loss of about $104,000 before any convexity adjustment.

Exam tips

For any non-parallel shift, go straight to key rate durations. Write each KRD times its yield change in a column, then add.
Show every step of the calculation. A correct number typed alone earns full credit, but a worked line protects you if the final figure is wrong.
Obey the command word. If asked to identify the curve move, name it (steepening, flattening, butterfly) and stop. If asked to justify, link the move to the maturity exposure in one sentence.
Read the units: bps to decimals, per 100 of par versus total market value.
In a recommendation, tie the duration positioning to the client's liability or objective, such as which key rate to match.

Yield Curve Dynamics and Duration Measures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Yield Curve Dynamics and Duration Measures: frequently asked questions

What is the difference between a parallel and a non-parallel yield curve shift?

In a parallel shift, yields at all maturities change by about the same amount, so only the level changes. In a non-parallel shift, yields change by different amounts, so steepness or curvature changes. Effective duration covers the first. Key rate durations are needed for the second.

How do you calculate effective duration?

Reprice the bond after the benchmark curve falls and rises by the same small amount. Then compute (PV₋ − PV₊) ÷ (2 × PV₀ × ΔCurve). Use decimals for the curve change.

What does key rate duration tell you that effective duration does not?

It shows where on the curve the price sensitivity sits. Each key rate duration measures the price response to a change at one maturity only. That lets you assess exposure to steepening, flattening and butterfly moves.

What is money duration used for?

It states interest rate exposure in currency by multiplying effective duration by market value. Multiplying by 0.0001 gives the approximate price value of a basis point. It helps size positions and hedges.

Do key rate durations add up to effective duration?

For a bond or portfolio with fixed cash flows, they sum approximately to effective duration. The sum is a consistency check. It is an approximation, not an exact identity in every case.