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.
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