Robust Bond Portfolio Construction via Convex-Concave Saddle Point Optimization

Paper: arXiv 2212.02570

Authors: Eric Luxenberg, Philipp Schiele, Stephen Boyd

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly rigorous mathematical framework for robust bond portfolio construction using convex-concave saddle point optimization. However, it is primarily theoretical, lacking extensive empirical backtesting or real-world dataset validation.

Research Flowchart

  flowchart TD
    A[Goal: Robust Long-Only Bond Portfolio via Worst-Case Optimization] --> B[Inputs: Convex set of yield curves, spreads, & portfolio sensitivities]
    B --> C[Methodology: Compare Sensitivity Estimates vs Exact Worst-Case Value]
    C --> D[Computational Step: Solve Tractable Convex Optimization Problem]
    D --> E[Optimization Framework: Convex-Concave Saddle Point Optimization]
    E --> F[Findings: Sensitivity estimates are conservative; Exact method yields optimal robust portfolio]