Robust Bond Portfolio Construction via Convex-Concave Saddle Point Optimization

TL;DR

This paper introduces a convex optimization approach for robust bond portfolio construction that accurately estimates worst-case values under yield curve uncertainties and incorporates them into portfolio optimization.

Contribution

It presents a novel convex-concave saddle point optimization method to include worst-case bond portfolio values directly in the construction process.

Findings

Sensitivity-based estimates are conservative and underestimate worst-case values.

The exact worst-case value can be efficiently computed via convex optimization.

The method enables robust long-only bond portfolio design with worst-case considerations.

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.