Level III Core · Swaps, Forwards, and Futures Strategies

Interest Rate Swaps for Duration Management

Updated 8 October 2026 · Fact-checked

Swaps change portfolio duration without trading bonds. A receive-fixed swap adds duration. A pay-fixed swap reduces it. The notional needed is: (target duration − current duration) ÷ swap duration × portfolio value, where swap duration is the fixed-leg duration minus the floating-leg duration.

Understand Interest Rate Swaps for Duration Management

A portfolio manager often wants to change interest rate sensitivity without selling bonds. Selling bonds costs money, creates tax events and may be hard in illiquid markets. A swap changes duration quickly and cheaply, and the bond holdings stay in place.

Think of a plain vanilla swap as two bonds. The receive-fixed side is long a fixed-rate bond and short a floating-rate bond. The floating-rate bond has a duration close to zero, because its coupon resets to market rates. So the swap's duration is roughly the duration of the fixed leg minus the floating leg, which is close to the fixed-leg duration.

This gives the direction rule. Receive-fixed acts like owning a longer-duration bond, so it increases portfolio duration. Pay-fixed acts like being short that bond, so it decreases portfolio duration. The swap gains value for a receive-fixed party when rates fall, and for a pay-fixed party when rates rise.

The size of the change depends on the notional. Think in terms of money duration. The portfolio's money duration plus the swap's money duration should equal the target money duration. Solve for the notional.

In the exam, link the choice to the client. A manager who expects rates to rise, or a liability-driven investor with a duration gap to close, will choose the swap that moves duration in the right direction. Always state the direction and the reason.

Key rules to remember

Swap duration: Swap duration (receive fixed) = Duration of fixed leg − Duration of floating leg; For pay fixed, the sign reverses. The floating leg duration is usually a fraction of a year, close to the time to the next reset.
Notional for target duration: Notional = [(Target duration − Current duration) ÷ Swap duration] × Portfolio value; Always enter the swap duration as the receive-fixed figure (fixed leg minus floating leg). Then a positive notional means receive fixed and a negative notional means pay fixed.
Money duration balance: Portfolio value × Current duration + Notional × Swap duration = Portfolio value × Target duration; This is the same relationship as the notional formula, just rearranged. It is a good check.
Direction rule: Receive fixed → duration up. Pay fixed → duration down.; Floating-leg duration is near zero, so the fixed leg drives the result.

How to solve Interest Rate Swaps for Duration Management questions

Use this method for any swap-duration question. Show your numbers clearly. A correct number typed on its own earns full credit, and only the number of responses asked for is evaluated, in the order given.

1Write down the portfolio value, current duration and target duration.
2Decide the direction. If target is above current, receive fixed. If target is below current, pay fixed.
3Find the swap duration: fixed-leg duration minus floating-leg duration. If the question gives the swap duration directly, use it.
4Apply the formula: (Target − Current) ÷ Swap duration × Portfolio value.
5Check the sign. With the swap duration entered as the receive-fixed figure, a positive answer means receive fixed. A negative answer means pay fixed. Quote the absolute notional.
6Check by money duration: portfolio money duration plus swap money duration should equal the target money duration.
7State the answer in the format asked: notional amount, position, and the new duration. Add one line linking to the client's need if the command word asks you to justify.

Quickest way: Money duration shortcut

When to use it: Use it when the question gives portfolio value, two durations and a swap duration, and asks for the notional.

Compute the duration gap: target minus current.
Multiply the gap by portfolio value to get the money duration needed.
Divide by the swap duration to get the notional.
Pick the position from the sign: gap up means receive fixed, gap down means pay fixed.
Do a one-line reasonableness check: a bigger gap or a shorter swap duration needs a bigger notional.

Common mistakes in Interest Rate Swaps for Duration Management

Choosing the wrong position, for example pay fixed to lengthen duration.
Students think about the cash flows they pay rather than the bond they are effectively long or short.
Fix: Remember that receive fixed means long a fixed-rate bond, so duration goes up. Pay fixed means short it, so duration goes down.
Using the fixed-leg duration alone as the swap duration when the question gives a floating-leg duration.
The rule that floating duration is close to zero gets treated as always exactly zero.
Fix: If the question gives a floating-leg duration, subtract it. Use zero only when the question says to ignore it.
Applying the duration gap to the notional rather than to portfolio value.
The formula looks like a ratio, and the roles of the terms get mixed up.
Fix: Portfolio value goes in the numerator. The swap duration is the only divisor.
Forgetting that the swap's duration depends on its remaining life and fixed rate, not the portfolio's duration.
Students reuse the portfolio duration as the swap duration.
Fix: Read the swap's terms. Use the duration figure given for the swap legs.
Reporting a negative notional without saying which side to take.
The sign from the formula is treated as the final answer.
Fix: Translate the sign into a position and give the notional as a positive amount.
Not justifying the recommendation when the command word is 'justify' or 'explain'.
Students stop after the calculation.
Fix: Add one sentence tying the position to the manager's rate view or the client's liability duration.

Worked examples

Example 1

A bond portfolio is worth $200 million and has a duration of 4.0. The manager wants a duration of 6.0 using a swap. The swap's fixed-leg duration is 5.0 and the floating-leg duration is 0.5 for a receive-fixed position. Calculate the notional and state the position.

Show the solution

Portfolio value = $200 million. Current duration = 4.0. Target duration = 6.0.
Target is above current, so the manager receives fixed.
Swap duration = 5.0 − 0.5 = 4.5.
Notional = (6.0 − 4.0) ÷ 4.5 × $200 million.
= 2.0 ÷ 4.5 × $200 million = 0.4444 × $200 million = $88.89 million.
Check: money duration needed = 2.0 × $200 million = $400 million. Swap money duration = 4.5 × $88.89 million = $400 million. It matches.

Answer: Receive fixed on a notional of about $88.89 million raises portfolio duration from 4.0 to 6.0.

Example 2

A pension fund holds a €500 million bond portfolio with a duration of 7.5. The manager expects rates to rise and wants a duration of 5.0. A pay-fixed swap is available. Its receive-fixed duration is 6.0 (fixed leg 6.25 minus floating leg 0.25). Calculate the notional and explain the position.

Show the solution

Portfolio value = €500 million. Current duration = 7.5. Target duration = 5.0.
Target is below current, so duration must fall. The manager pays fixed.
Swap duration for the receive-fixed side = 6.25 − 0.25 = 6.0.
Notional = (5.0 − 7.5) ÷ 6.0 × €500 million.
= −2.5 ÷ 6.0 × €500 million = −0.41667 × €500 million = −€208.33 million.
The negative sign means the position is pay fixed. The notional is €208.33 million.
Check: portfolio money duration falls by 2.5 × €500 million = €1,250 million. Pay-fixed swap money duration = −6.0 × €208.33 million = −€1,250 million. It matches.
Rationale: if rates rise, bond values fall, but the pay-fixed swap gains value and offsets part of the loss.

Answer: Pay fixed on a notional of about €208.33 million reduces duration from 7.5 to 5.0, which protects the portfolio against rising rates.

Exam tips

Read the command word. 'Calculate' needs a number, with the position stated. 'Justify' needs a reason tied to the client or the rate view.
A correct number typed on its own earns full credit for a calculation. Only the number of responses asked for is evaluated, in the order given, so give exactly what is asked and no extra answers.
In item sets, check whether the answer options include the right size but the wrong position. Direction errors are a common trap.
If the question gives the floating-leg duration, subtract it. If it says to treat the floating leg as zero, do so.
Link to liability-driven cases: a fund with a long liability duration may need to receive fixed to close the gap.

Interest Rate Swaps for Duration Management in other exams

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

Interest Rate Swaps for Duration Management: frequently asked questions

Does a receive-fixed swap increase or decrease duration?

It increases duration. The receive-fixed side behaves like a long position in a fixed-rate bond and a short position in a floating-rate bond. The floating leg has almost no duration, so the net effect is a longer portfolio duration.

How do I calculate the swap notional for a target duration?

Use Notional = (Target duration − Current duration) ÷ Swap duration × Portfolio value. Swap duration is the fixed-leg duration minus the floating-leg duration, the receive-fixed figure. A positive result means receive fixed, and a negative result means pay fixed.

Why is the floating leg's duration close to zero?

A floating-rate coupon resets to the market rate at each reset date. The value of a floating-rate bond therefore returns to par at each reset. Its price sensitivity is only to the time until the next reset, which is short.

When would a manager use a swap instead of futures to change duration?

A swap can be tailored to the exact maturity, notional and reset dates, and it suits longer horizons. Futures are standardised and liquid, but they need margin and may not match the exposure. The choice depends on the client's needs and constraints.