Robust Asset-Liability Management

Tjeerd de Vries and Alexis Akira Toda

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Abstract: Financial institutions often cannot replicate long-dated liabilities with available bonds, especially when leverage and collateral constraints bind. We characterize the feasible portfolio that minimizes, to first order, the worst equity loss over a prespecified set of yield curve changes. The solution accommodates general deterministic liabilities and portfolio constraints and includes duration and convexity matching as special cases. The minimized loss measures the economic capital buffer needed to absorb the specified interest rate stress. Under an $\ell^2$ stress set, the portfolio is a constrained generalized least squares projection. A portfolio representation shows how additional stress directions can reduce reliance on unstable exact hedges. In U.S. Treasury applications, robust immunization delivers the best or nearly best funding performance for most liabilities and constraints. Simulated and historical dynamic exercises also show modest leverage, turnover, and transaction costs.

Date: 2023-10, Revised 2026-09
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