CFA Level I Exam · Interest Rate Risk and Return

Portfolio Duration and Yield Curve Risk Explained

Updated 7 October 2026 · Fact-checked

Portfolio duration is the weighted average of the durations of the bonds in the portfolio, using market value weights. It estimates the percentage price change for a parallel yield curve shift. It is unreliable when the curve twists or steepens, because bonds of different maturities face different yield changes.

Understand Portfolio Duration and Yield Curve Risk

A bond's duration tells you how much its price moves when its yield changes. A portfolio holds many bonds. Instead of repricing each bond, you can summarize the portfolio with one number: its duration.

There are two ways to get portfolio duration. The first is the weighted average of bond durations. You weight each bond's duration by its share of total portfolio market value. The second is the cash flow yield approach: you treat all portfolio cash flows as one bond, find its IRR, and compute duration from that. This is theoretically more accurate but harder to do. The weighted average is the simpler and more commonly used method.

The weighted average has a key limitation. It assumes every bond's yield changes by the same amount, which is a parallel shift. In real markets, short rates and long rates often move by different amounts. The curve can steepen, flatten or twist. Two portfolios with the same duration can then lose or gain different amounts. This is yield curve risk, also called shaping risk. A barbell portfolio (short and long bonds) and a bullet portfolio (intermediate bonds) can have equal durations but react differently to a non-parallel move.

The weighted average measure also has a second weakness. It is only a first-order estimate, so it is accurate for small yield changes. For large changes you need convexity too.

Yield volatility links to all this. Interest rate risk depends on two things: how sensitive the price is to yield (duration) and how much yields actually move (yield volatility). A high-duration bond in a stable-yield environment may carry less realised risk than a lower-duration bond whose yield swings widely. Short-term yields tend to be more volatile than long-term yields, which can partly offset a long bond's higher duration. Also, yield changes on different bonds are not perfectly correlated, which is why a single duration number cannot capture everything.

Key formulas to remember

Portfolio duration (weighted average): D_p = w₁D₁ + w₂D₂ + … + wₙDₙ; Weights are each bond's market value ÷ total portfolio market value, not par value. Use the same type of duration (e.g. modified or effective) for every bond.
Approximate price change: %ΔPV ≈ −D × ΔYield; D is modified (or effective) duration. Valid for small, parallel yield changes. Add a convexity adjustment for larger moves.
Portfolio money duration: Money duration_p = Σ (money duration of each bond); Money durations are in currency units and are measured for the same yield change, so they simply add up. Dividing the summed money duration by total portfolio market value gives the portfolio modified duration.
Weights: wᵢ = MVᵢ ÷ Σ MV; Weights must sum to 1 (100%).

How to solve Portfolio Duration and Yield Curve Risk questions

Use this method for any question on portfolio duration or yield curve risk.

1Read the question. Decide whether it asks for a calculation, a price change estimate, or a concept about shifts.
2List each bond's market value and duration. Use market value, not par, unless the question says otherwise.
3Compute each weight: bond market value ÷ total market value.
4Multiply each weight by its duration and sum to get portfolio duration.
5If asked for a price change, apply −D × ΔYield. Convert basis points to decimals: 50 bp = 0.005.
6Check the assumption: is the shift parallel? If the question describes a steepening, flattening or twist, say the single duration number is unreliable.
7For concept questions, compare duration with yield volatility: risk = sensitivity × how much yields move.
8Eliminate the two wrong options by checking sign (yields up means prices down) and size (the result should lie between the lowest and highest bond duration).

Quickest way: Sanity-check shortcut for weighted duration

When to use it: Use it when options are close and you have about 90 seconds.

Portfolio duration must lie between the smallest and largest bond duration. Drop any option outside that range.
If weights are roughly equal, the answer is near the simple average.
If one bond has a large weight, the answer sits closer to that bond's duration.
On a calculator, enter w × D for each bond and add. Keep weights as decimals.
For price change, take duration × yield change and attach the opposite sign to the yield move.

Common mistakes in Portfolio Duration and Yield Curve Risk

Weighting by par value instead of market value
Par values are easy to read from a bond list, and students forget that prices differ from par.
Fix: Always use market value (price plus accrued interest where given) unless the question states otherwise.
Averaging durations without weights
A simple average feels quick and often looks close.
Fix: Compute weights first. Only use a simple average if market values are equal.
Assuming portfolio duration protects against any yield curve move
One number seems to summarise all risk.
Fix: Remember it assumes a parallel shift. Under steepening, flattening or twists, equal-duration portfolios can perform differently.
Getting the sign wrong on price change
Students forget the minus sign in −D × ΔYield.
Fix: Yields up means prices down; yields down means prices up. Check the sign before choosing an option.
Ignoring yield volatility when judging interest rate risk
Students treat duration as the whole of interest rate risk.
Fix: Interest rate risk depends on both duration and how much yields move. A longer bond may have lower yield volatility.
Forgetting to convert basis points
Rushing under time pressure.
Fix: Write 1 bp = 0.0001 and convert before multiplying.

Worked examples

Example 1

A portfolio holds three bonds. Bond A: market value €40 million, modified duration 2.0. Bond B: market value €35 million, modified duration 5.0. Bond C: market value €25 million, modified duration 9.0. What is the portfolio duration? Options: A) 4.8, B) 5.9, C) 6.4

Show the solution

Total market value = 40 + 35 + 25 = €100 million.
Weights: A = 0.40, B = 0.35, C = 0.25.
Weighted durations: 0.40 × 2.0 = 0.80; 0.35 × 5.0 = 1.75; 0.25 × 9.0 = 2.25.
Sum: 0.80 + 1.75 + 2.25 = 4.80.
Check: 4.80 lies between 2.0 and 9.0.

Answer: Portfolio duration is 4.80, so option A.

Example 2

A USD bond portfolio has a duration of 4.8 and the yield curve shifts up in parallel by 50 basis points. Estimate the percentage change in portfolio value. Options: A) −9.60%, B) −2.40%, C) +2.40%

Show the solution

Yields rise, so the price change is negative. This eliminates C.
ΔYield = 50 bp = 0.005.
%ΔPV ≈ −4.8 × 0.005 = −0.024.
Convert to a percentage: −2.40%.
A would result from using 200 bp (2.0%) instead of 50 bp, so it is wrong.

Answer: The portfolio value falls by about 2.40%, so option B. This holds only for a small, parallel shift.

Exam tips

If a question says the curve steepens, flattens or twists, expect the answer to say portfolio duration alone is not enough.
Check that your computed duration lies between the lowest and highest bond duration. This quickly removes a wrong option.
Read whether weights are given as percentages or market values, and whether the question wants duration or money duration.
For yield volatility questions, remember that risk depends on both duration and the size of yield changes. Do not choose the bond with the highest duration automatically.
Keep your calculator for sums of products only. Most weighted duration items need three or four terms.

Practice questions from Interest Rate Risk and Return

Portfolio Duration and Yield Curve Risk in other exams

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

Portfolio Duration and Yield Curve Risk: frequently asked questions

How do you calculate portfolio duration?

Find each bond's weight as its market value divided by total portfolio market value. Multiply each weight by that bond's duration and add the results. The sum is the portfolio duration.

Why does portfolio duration fail for non-parallel yield curve shifts?

The weighted average assumes all bond yields change by the same amount. If short and long yields move differently, bonds of different maturities gain or lose by different amounts. Two portfolios with equal duration can then have different returns.

What is yield curve risk?

It is the risk that the shape of the yield curve changes, for example through steepening, flattening or a twist. It is also called shaping risk. A single duration figure does not capture it.

How does yield volatility relate to interest rate risk?

Interest rate risk depends on price sensitivity to yield (duration) and on how much yields actually change (yield volatility). Higher duration with higher yield volatility means greater risk. Short-term yields tend to be more volatile than long-term yields, which can partly offset a long bond's higher duration.