Robust Bond Portfolio Construction via Convex-Concave Saddle Point Optimization

TL;DR

The paper addresses robust analysis and portfolio construction for long-only bond portfolios under a worst-case framework across yield curves and spreads. It shows that the exact worst-case change in value can be obtained by solving a convex optimization problem, while a duration-based linearization provides a conservative bound. By reformulating the robust construction as a convex-concave saddle point problem, and using duality to reduce to a single convex problem, the authors enable efficient solving via disciplined saddle point programming (DSP). They demonstrate extensions to multiple yield curves and constrained forms, and validate the approach with real-data-like examples showing meaningful shifts toward shorter maturities under risk, thus offering a practical, scalable method for robust bond portfolio design.

Abstract

The minimum (worst case) value of a long-only portfolio of bonds, over a convex set of yield curves and spreads, can be estimated by its sensitivities to the points on the yield curve. We show that sensitivity based estimates are conservative, \ie, underestimate the worst case value, and that the exact worst case value can be found by solving a tractable convex optimization problem. We then show how to construct a long-only bond portfolio that includes the worst case value in its objective or as a constraint, using convex-concave saddle point optimization.

Figures (5)

• Figure 1: The nominal portfolio weights.
• Figure 2: Historical mean values of (annualized) yield and spreads. The nominal yield and spreads, date 2022-9-12, are also shown.
• Figure 3: Worst (annualized) yield curve and spreads for the two uncertainty sets, using the exact and linearized methods.
• Figure 4: Turnover distance to the nominal portfolio, for two uncertainty sets, using both the exact and linearized methods.
• Figure 5: Portfolio holdings, for both uncertainty sets for $\lambda \in \{1,5,15\}$.