PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES

Authors: Maccheroni, Fabio¹; Marinacci, Massimo²; Rustichini, Aldo³; Taboga, Marco⁴

Source: Mathematical Finance, Volume 19, Number 3, July 2009 , pp. 487-521(35)

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Abstract:

We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone and are therefore not economically meaningful. The functional associated with this new class of preferences is the best approximation of the mean-variance functional among those which are monotonic. We solve the portfolio selection problem and we derive a monotone version of the capital asset pricing model (CAPM), which has two main features: (i) it is, unlike the standard CAPM model, arbitrage free, (ii) it has empirically testable CAPM-like relations. The monotone CAPM has thus a sounder theoretical foundation than the standard CAPM and a comparable empirical tractability.

Keywords: monotone mean-variance; portfolio selection; capital asset pricing model; monotone approximation

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9965.2009.00376.x

Affiliations: 1: Departments of Decision Sciences and of Economics, Dondena and IGIER, Università Bocconi 2: Collegio Carlo Alberto, Università di Torino 3: University of Minnesota 4: Research Department, Banca d'Italia

Publication date: 2009-07-01