Efficient Portfolios with Endogenous Liabilities

Swiss Banking Institute Working Paper No. WP L3

26 Pages Posted: 23 Apr 2003

See all articles by Markus Leippold

Markus Leippold

University of Zurich - Department of Banking and Finance; University of Zurich - Faculty of Economics, Business Administration and Information Technology

Paolo Vanini

University of Basel

Fabio Trojani

Swiss Finance Institute; University of Geneva

Date Written: April 2005

Abstract

We study the optimal policies and mean-variance frontiers (MVF) of a multiperiod mean-variance optimization of assets and liabilities (AL). Our model allows for a contemporaneous optimization of the balance-sheet as a whole. This makes the analysis more challenging than in a setting based on purely exogenous liabilities. We show that under general conditions on the joint AL dynamics the arising optimal policies and MVF can be decomposed in an orthogonal set of basis returns. Such a decomposition is derived using a geometric formalism based on exterior algebra which simplifies the computations when liabilities are endogenous. As a special case, the geometric representation in Leippold, Trojani and Vanini (2004) for the exogenous liabilities case follows directly. We apply such a decomposition to study the structure of optimal policies and MVF under endogenous liabilities and show how to obtain MVF representations that substantially improve analytical descriptions and numerical analysis. We finally illustrate the methodology by studying the impact of the rebalancing frequency on the MVF and by highlighting in a numerical example the main differences arising when liabilities are exogenous and when they are endogenous.

Keywords: Assets and Liabilities, Mean-Variance Frontiers, Markowitz Model, Endogenous Liabilities, Grassmann Algebra

JEL Classification: G12, G13, E43

Suggested Citation

Leippold, Markus and Vanini, Paolo and Trojani, Fabio, Efficient Portfolios with Endogenous Liabilities (April 2005). Swiss Banking Institute Working Paper No. WP L3, Available at SSRN: https://ssrn.com/abstract=388080 or http://dx.doi.org/10.2139/ssrn.388080

Markus Leippold (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

University of Zurich - Faculty of Economics, Business Administration and Information Technology ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Paolo Vanini

University of Basel ( email )

Petersplatz 1
Basel, CH-4003
Switzerland

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva, Geneva
Switzerland

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
554
Abstract Views
3,790
rank
61,372
PlumX Metrics