On Bond Portfolio Management
Vladislav Kargin
TL;DR
The paper addresses optimal bond portfolio management under cross-maturity correlation. It models correlations as a smooth function of maturity differences and solves the resulting Markowitz-style problem in a Hilbert space using Padé-based correlation estimation and Wiener-Hopf factorization, yielding Y_hat = (1/(2 gamma)) [P_plus A_times]^{-1} E_hat and a corresponding utility. Key contributions include (i) generalized Padé estimation of the correlation function, (ii) an explicit operator-inversion formula for the optimal allocation, and (iii) arbitrage and near-arbitrage criteria derived from the correlation-operator framework. An empirical application to historical Treasury data demonstrates that the generalized Padé approach captures cross-maturity correlations more accurately than classical Padé, and the resulting portfolio achieves lower variance with positive returns compared with a benchmark that ignores correlations. The work provides a practical, extensible framework for bond portfolio management that can incorporate alternative correlation estimators and supports formal arbitrage checks.
Abstract
This paper describes a new method of bond portfolio optimization based on stochastic string models of correlation structure in bond returns. The paper shows how to approximate correlation function of bond returns, compute the optimal portfolio allocation using Wiener-Hopf factorization, and check whether a collection of bonds presents arbitrage opportunities.