A Note on the Three-Portfolios Matching Problem

13 Pages Posted: 13 Feb 2003

See all articles by Fabio Trojani

Fabio Trojani

Swiss Finance Institute; University of Geneva

Paolo Vanini

University of Basel

Luigi Vignola

Deutsche Bank, Zurich Branch


A typical problem arising in 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/optimised 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.

Suggested Citation

Trojani, Fabio and Vanini, Paolo and Vignola, Luigi, A Note on the Three-Portfolios Matching Problem. Available at SSRN: https://ssrn.com/abstract=369168

Fabio Trojani (Contact Author)

Swiss Finance Institute ( email )

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

University of Geneva ( email )

Geneva, Geneva

Paolo Vanini

University of Basel ( email )

Petersplatz 1
Basel, CH-4003

Luigi Vignola

Deutsche Bank, Zurich Branch ( email )

Uraniastrasse 9
+41 44 227 33 51 (Phone)

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