Liability-Driven and Index-Based Strategies

Insurers, pension plans and individuals with known future spending need bond portfolios that pay those obligations whatever happens to interest rates, while many other investors simply want cheap, reliable bond market exposure. This module covers immunization and cash-flow matching for single and multiple liabilities, sizing derivative overlays, the risks LDI leaves behind, the practical problems of bond indexing and the choice of a fixed-income benchmark.

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What you will learn

1. Evaluate cash-flow matching, immunization and contingent immunization as ways to fund a single liability, including the conditions for immunization and the risks that remain.

A default-free zero maturing on the liability date is the cleanest match: no reinvestment or price risk.
Immunization: market value >= PV of liability, Macaulay duration = horizon, convexity minimized but above the liability's.
Low dispersion (a bullet) limits structural risk from non-parallel shifts; barbells carry more of it.
Rebalance as time passes and yields change; duration drifts away from the remaining horizon.
Contingent immunization allows active management while a cushion exists and forces immunization when it is gone.

2. Compare cash-flow matching, duration matching, derivatives overlays and horizon matching for funding multiple liabilities, and size an overlay with futures or swaps.

Cash-flow matching: build backwards from the last liability; little rate risk, but costly and inflexible.
Duration matching: PV(assets) >= PV(liabilities), BPV(assets) = BPV(liabilities), asset dispersion and convexity above the liabilities'.
Futures needed = BPV gap / futures BPV, with futures BPV = CTD BPV / conversion factor.
Receive-fixed swap notional = BPV gap / swap BPV per unit of notional.
Hedge ratio = BPV of assets (including derivatives) / BPV of liabilities.

3. Assess liability-driven strategies under different interest rate scenarios, choose among swaps and swaptions, and identify the model, spread, curve, collateral and liquidity risks that remain.

Change in surplus is approximately -(BPV_A - BPV_L) x change in yield in bp.
Hedge ratio below 100%: falling rates hurt the surplus; the plan is implicitly betting on rising rates.
Receive-fixed swaps hedge symmetrically; receiver swaptions protect against falling rates and keep the upside for a premium; collars cut the premium.
Residual risks: model, spread, curve, counterparty and collateral, and asset liquidity.
Leveraged hedges need a collateral buffer sized for severe rate rises.

4. Explain why a bond index is hard to replicate and compare full replication, primary risk factor matching, enhanced indexing, pooled funds, total return swaps and futures as ways to gain passive bond exposure.

Bond indexes are hard to replicate: thousands of issues, constant churn, OTC trading, illiquid and evaluated prices.
Primary risk factor matching: match duration, key rate durations, sector, quality, spread duration and issuer exposures with fewer bonds.
Enhanced indexing accepts small, deliberate mismatches to recover costs.
ETFs are accessible but can trade far from NAV in stress; TRS give exact exposure with counterparty risk.
Bond futures provide government duration, not credit exposure.

5. Select and justify a fixed-income benchmark that fits an investor's liabilities, risk tolerance and constraints.

Market-value-weighted bond indexes overweight the biggest borrowers and drift with issuance.
Index duration often lengthens when yields are low, raising rate risk at the worst time.
Liability-driven investors need a benchmark matching liability BPV and key rate profile.
Asset duration needed to match BPVs = liability duration x (PV of liabilities / PV of assets).
Build ratings, currency, ESG and liquidity constraints into the benchmark itself.

Module at a glance

Single liability: PV(assets) >= PV(liability), Macaulay duration = horizon, minimum convexity above the liability's.
Bullets minimize dispersion and structural risk; barbells add convexity and exposure to twists.
Multiple liabilities: match BPVs, keep asset dispersion and convexity just above the liabilities', or cash-flow match.
Overlay sizing: futures = BPV gap / (CTD BPV / CF); swap notional = BPV gap / swap BPV per unit.
Change in surplus is approximately -(BPV_A - BPV_L) x change in yield; underhedged plans lose when rates fall.
Receiver swaptions protect against falling rates and keep the upside; leveraged hedges need collateral buffers.
Bond indexes are matched by risk factors, not bonds; choose benchmarks by money duration and investor needs.

This free module has 5 lessons, 18 practice questions with full explanations and 1 essay case with a model answer.

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