Sensitivity Analysis for International Bond Allocation Problems

Pierre Brugiere and Christian Lopez
CEREMADE, URA 749, Université Paris 9 Dauphine
Brugiere@ceremade.dauphine.fr
Lopez@ceremade.dauphine.fr

Abstract

This paper deals with the problem of the construction of an optimal international bond portfolio, in a mean-variance framework, under various linear or non linear convex asset allocation constraints. In our numerical experiments we use the Frank and Wolfe algorithm because it converges and features admissible portfolios at every numerical optimization step. It also efficiently treats a lot of linear constraints with robustness.

We study the problem of the sensitivity of the best achievable expected return, and asset allocation, for the optimal portfolio, relatively to the expected return and variance-covariance matrix assumptions. We also point out the sabilization effect of the convex nonlinear constraints, on the optimal asset allocation. We also give the origins of such constraints in real fund management problem.

To settle the problem precisely, we first derive the analytical expression of the allocation for the optimal mean-variance portfolio and of its total expected return relatively to a given expected return vector and variance-covariance matrix. We then point out, by derivating this portfolio with respect to the assumptions made on the bonds that the total expected return is stable, whereas the bond allocation may be unstable. We also observe numerically that the addition of linear constraints (as Markowitz did) gives the same results. Then by using a regularization technique, we add to the preceding linear constraints, different constraints which involve convex combinations of the absolute value of the asset allocation. Numerical experiments show that this approach is much less sensitive.

We then use this sensitivity analysis as a risk indicator for our optimal portfolio.

Keywords: Bond portfolio management, sensitivity analysis, quadratic programming, Frank and Wolfe algorithm, efficient frontier, convex programming, regularization technique, risk analysis.