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Portfolio Management Pathway · Liability-Driven and Index-Based Strategies

Liability Hedging with Derivatives and Leverage in LDI

Updated 8 October 2026 · Fact-checked

Liability hedging with derivatives means using interest rate swaps or futures to match the interest rate sensitivity of assets to liabilities. You find the duration gap in money terms (PVBP or BPV), then add receive-fixed swaps or long bond futures to close it. Leverage frees cash for return-seeking assets, but adds credit and liquidity risk.

Understand Liability Hedging with Derivatives and Leverage

A liability-driven investor, such as a defined benefit pension plan, owes cash flows in the future. The present value of those liabilities moves with interest rates. When rates fall, the liability value rises. If assets do not rise by the same amount, the funded status gets worse. The mismatch is the duration gap.

You can close the gap by buying long-duration bonds. This is expensive in cash. A plan with liabilities of 100 and a liability duration of 15 would need to put almost all assets into long bonds. That leaves little for return-seeking assets such as equities, which the plan needs to earn the return that closes a funding shortfall.

Derivatives solve this. A receive-fixed, pay-floating interest rate swap gains value when rates fall, like a long bond position, and needs little cash up front. Bond futures do the same. Held on top of the physical portfolio, they form a derivatives overlay. The plan can keep most assets in a return-seeking portfolio and use the overlay to add the duration it lacks. This is the idea of leverage in LDI: you control more interest rate exposure than the cash you invest.

The key measure is dollar (or currency) sensitivity, not percentage duration alone. Use the price value of a basis point (PVBP) or BPV for assets, liabilities and the hedge instrument. Match the money sensitivity. Then check the hedge: key rate durations tell you if the match holds when the curve twists, not just when it shifts in parallel.

Derivatives bring costs. Swaps carry counterparty credit risk, handled by collateral and central clearing. Futures and cleared swaps need variation margin, paid in cash daily. When rates rise, the hedge loses value and the plan must post cash, even though the liability falls. If the plan cannot raise cash without selling assets at bad prices, it faces a liquidity risk. So the plan must hold a liquidity buffer of cash or high-quality liquid assets. Also watch basis risk, roll risk on futures and swaps, and the fact that the liability curve may not match the hedge curve.

Key rules to remember

Duration gap in money terms
PVBP gap = PVBP(liabilities) − PVBP(assets)
A positive gap means liabilities are more rate-sensitive than assets. Add hedge PVBP equal to the gap.
PVBP of a portfolio
PVBP ≈ Modified duration × Market value × 0.0001
Use the same rate-change basis (1 bp) for assets, liabilities and the hedge.
Number of futures contracts
N = (PVBP gap) ÷ (PVBP per futures contract)
Use the cheapest-to-deliver bond's PVBP adjusted by the conversion factor where the question gives it. Round to a whole number.
Notional of swap needed
Swap notional = (PVBP gap) ÷ (PVBP per unit of swap notional)
A receive-fixed swap has positive PVBP like a long bond (value rises as rates fall). A pay-fixed swap has negative PVBP, so to add asset duration you receive fixed.
Funded ratio
Funded ratio = PV of assets ÷ PV of liabilities
Hedge aims to stabilise this ratio against rate moves.

How to solve Liability Hedging with Derivatives and Leverage questions

Use this order for any liability hedging question. Tie each choice to the client's funded status, risk tolerance and liquidity needs.

  1. 1Read the client: funded status, return need, risk tolerance, liquidity and regulatory limits.
  2. 2Compute the PVBP (or duration × value) of the liabilities and of the current assets.
  3. 3Find the gap = liabilities − assets. Note its sign and size.
  4. 4Choose the instrument that adds the missing sensitivity: receive-fixed swaps or long futures if assets are too short; the opposite if assets are too long.
  5. 5Size the hedge: gap ÷ PVBP per swap notional or per futures contract. Show the division and round contracts.
  6. 6Check residual risks: curve shape (key rate durations), basis risk, counterparty credit risk, margin and collateral needs.
  7. 7Plan liquidity: size a cash or liquid-asset buffer for a rate rise and margin calls.
  8. 8State the recommendation in one or two sentences that link the choice to the client's objectives and constraints.

Quickest way: Gap, divide, then stress the cash

When to use it: Use this for calculation questions that ask how many contracts or what swap notional closes a gap.

  1. Write PVBP for liabilities and assets in currency per 1 bp.
  2. Subtract to get the gap. Keep the sign.
  3. Divide the gap by the hedge's PVBP per unit.
  4. Type the number alone if the command word is calculate.
  5. Add one line on margin, collateral or liquidity if the question asks for risks or a recommendation.

Common mistakes in Liability Hedging with Derivatives and Leverage

  • Matching percentage durations instead of money sensitivity.

    Assets and liabilities have different sizes, so equal durations feel like a match.

    Fix: Always convert to PVBP or duration × market value. Hedge the money gap.

  • Choosing the wrong swap side.

    Students remember 'pay fixed' from the usual hedging examples.

    Fix: To add asset duration, the plan receives fixed, which gains when rates fall. Pay-fixed reduces duration. Check by asking who gains if rates fall.

  • Ignoring margin and collateral calls.

    The hedge is seen only as an economic offset to liabilities.

    Fix: State that a rate rise forces variation margin in cash, so hold a liquid buffer.

  • Assuming a parallel shift only.

    One duration number hides curve shape.

    Fix: Mention key rate durations when the liability cash flows are spread along the curve, and match them at several points.

  • Forgetting that leverage adds risk.

    Students focus on the return-seeking benefit.

    Fix: Name counterparty, liquidity and basis risk, and say how the plan limits each, such as clearing and collateral.

  • Giving a long list with no link to the client.

    Students recall all risks from the reading.

    Fix: Pick the points that matter to this client and justify the recommendation in a few words.

Worked examples

Example 1

A pension plan has liabilities of 400 million with modified duration 14. Its bond portfolio is 150 million with modified duration 8. The rest is in equities with no rate sensitivity. A futures contract has PVBP of 90 per contract (currency units per 1 bp). How many long futures contracts close the gap?

Show the solution
  1. Liability PVBP = 14 × 400,000,000 × 0.0001 = 560,000.
  2. Asset PVBP = 8 × 150,000,000 × 0.0001 = 120,000.
  3. Gap = 560,000 − 120,000 = 440,000.
  4. Assets are less sensitive, so the plan needs a long position that gains when rates fall: buy futures.
  5. Contracts = 440,000 ÷ 90 = 4,888.9, about 4,889.

Answer: Buy about 4,889 futures contracts.

Example 2

A plan has a funded ratio of 85% and needs higher returns. Its trustees will not sell equities to buy long bonds. Recommend how to hedge interest rate risk, and state one key risk.

Show the solution
  1. The plan is underfunded and needs return, so it should keep the equity holdings.
  2. Selling equities for long bonds would cut expected return and slow recovery of the funded status.
  3. Add a derivatives overlay: receive-fixed swaps or long bond futures sized to the PVBP gap.
  4. This adds liability-matching duration with little cash, so the return-seeking portfolio stays intact.
  5. Key risk: a rise in rates produces losses on the hedge and margin or collateral calls. Hold a buffer of cash or liquid assets and use cleared or collateralised contracts to limit counterparty risk.

Answer: Use a receive-fixed swap or long futures overlay to close the PVBP gap and keep equities for return. Hold a liquidity buffer for margin calls caused by rising rates.

Exam tips

  • For calculation items, show PVBP of liabilities, assets and hedge on separate lines, then type the final number clearly.
  • Read the command word. 'Justify' needs a reason tied to the client, 'identify' needs only the item.
  • If asked for the swap position, check direction by who gains when rates fall.
  • Always give liquidity or margin risk when a question mentions leverage or derivatives.
  • In item sets, a hedge is often asked to be sized with current numbers: recompute the gap after any change in assets or liabilities.

Liability Hedging with Derivatives and Leverage: frequently asked questions

Why use derivatives instead of buying long bonds for LDI?

Derivatives need little cash up front. The plan can add duration while keeping assets in return-seeking investments. The trade-off is margin, collateral and counterparty risk.

How do I close a duration gap using futures?

Compute the PVBP of liabilities and assets and take the difference. Divide that gap by the PVBP of one futures contract. Buy futures if assets need more duration, sell if they need less.

What is the main liquidity risk in an LDI overlay?

When rates rise, hedge positions lose value and need cash for variation margin. The plan must keep liquid assets so it need not sell assets at a bad time.

Does matching duration remove all interest rate risk?

No. It protects mainly against parallel shifts. Curve twists, basis differences and convexity can still cause a mismatch, so key rate durations are used to refine the hedge.