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A Note on the Three–Portfolios Matching Problem
Author(s) -
Trojani Fabio,
Vanini Paolo,
Vignola Luigi
Publication year - 2002
Publication title -
european financial management
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.311
H-Index - 64
eISSN - 1468-036X
pISSN - 1354-7798
DOI - 10.1111/1468-036x.00202
Subject(s) - portfolio , matching (statistics) , transaction cost , portfolio optimization , application portfolio management , replicating portfolio , selection (genetic algorithm) , post modern portfolio theory , asset allocation , modern portfolio theory , economics , computer science , actuarial science , process (computing) , microeconomics , finance , project portfolio management , mathematics , statistics , management , artificial intelligence , project management , operating system
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.