How does immunization work when I have multiple liabilities at different dates?

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AcadiFi · Accepted Answer

Multiple-liability immunization requires matching more than just the aggregate duration. The industry uses THREE main approaches, each progressively more robust. APPROACH 1: AGGREGATE DURATION MATCHING Compute weighted-average duration of liabilities, then build a portfolio with the same duration. Simple but insufficient — it ignores the dispersion of cash flows. APPROACH 2: DURATION + CONVEXITY MATCHING (Redington) Match both duration and convexity of assets to liabilities. Protects against small parallel shifts of any magnitude. Still fails on non-parallel shifts. APPROACH 3: KEY-RATE DURATION MATCHING (Ho, 1992) Define 'key rates' along the yield curve (2y, 5y, 10y, 20y, 30y) and match each key-rate duration of assets to the corresponding liability key-rate duration. Protects against non-parallel shifts. Case: Sandridge Pension has: - $8M due in 3 years - $12M due in 7 years - $15M due in 12 years - $10M due in 20 years Aggregate PV (at 4.5% flat): ~ $26.7M. Aggregate duration ≈ 9.2. Duration-only: buy 10-year bonds (D≈8.2) plus some 15-year bonds — duration 9.2. Misses cash-flow dispersion. Key-rate approach: buy bonds at 2y, 5y, 10y, 20y that match the key-rate durations of each liability tranche. Result: portfolio neutralizes any combination of curve shifts and twists. Preferred in practice: CASH-FLOW MATCHING for near-term liabilities (0-5 years, where liquidity allows exact matching) + DURATION/KEY-RATE IMMUNIZATION for longer liabilities. This hybrid (COMBINATION MATCHING) reduces rebalancing frequency and credit risk for near-term obligations while maintaining flexibility for longer tails. ```mermaid flowchart LR A[Multi-Liab] --> B[Compute
Key-Rate D] B --> C[Build Port
match KRDs] C --> D[Rebalance] ``` M² (M-squared): measures dispersion; lower M² = more bullet-like = less reinvestment risk.

How does immunization work when I have multiple liabilities at different dates?

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