A Note on the Three-Portfolio Matching Problem

14 Pages Posted: 2 Apr 2001

See all articles by Paolo Vanini

Paolo Vanini

University of Basel

Fabio Trojani

Swiss Finance Institute; University of Geneva

Luigi Vignola

Deutsche Bank, Zurich Branch

Date Written: July 25, 2001

Abstract

A typical problem arising in the financial planning for private investors consists in the fact that the initial investor's portfolio, the one determined by the consulting process of the financial institution and the universe of instruments made available to the investor have to be matched/optimized when determining the relevant portfolio choice. We call this problem the three-portfolios matching problem. Clearly, the resulting portfolio selection should be as close as possible to the optimal asset allocation determined by the consulting process of the financial institution. However, the transition from the investor's initial portfolio to the final one is complicated by the presence of transaction costs and some further more specific constraints. Indeed, usually the portfolios under consideration are structured at different aggregation levels, making portfolios comparison and matching more difficult. Further, several investment restrictions have to be satisfied by the final portfolio choice. Finally, the arising portfolio selection process should be sufficiently transparent in order to incorporate the subjective investor's trade-off between the objectives 'optimal portfolio matching' and 'minimal portfolio transition costs.' In this paper, we solve the three-portfolios matching problem analytically for a simplified setting that illustrates the main features of the arising solutions and numerically for the more general situation.

Keywords: Transaction Costs, Portfolio Matching, Portfolio Selection

JEL Classification: G2, G11, G14, G21

Suggested Citation

Vanini, Paolo and Trojani, Fabio and Vignola, Luigi, A Note on the Three-Portfolio Matching Problem (July 25, 2001). Available at SSRN: https://ssrn.com/abstract=265690 or http://dx.doi.org/10.2139/ssrn.265690

Paolo Vanini (Contact Author)

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

Luigi Vignola

Deutsche Bank, Zurich Branch ( email )

Uraniastrasse 9
Zurich
Switzerland
+41 44 227 33 51 (Phone)

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