Portfolio Selection With Monotone Mean‐variance Preferences

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.

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

“…fulfills (N), (C), (T) but not the monotonicity property (M); see for instance, Maccheroni et al (2009). This can be corrected by slightly modifying its dual representation.…”

“…This allows us to prove existence and uniqueness of an equilibrium under general assumptions by backward induction. Typical examples of translation invariant preferences are those induced by expected exponential utility, the monotone mean-variance preferences of Maccheroni et al (2009), mean-risk type preferences where risk is measured with a convex risk measure, optimized certainty equivalentsà la Teboulle (1986, 1987) or the divergence utilities of Cherny and Kupper (2009). The assumption of translation invariant preferences is appropriate if, for instance, agents are understood as banks or insurance companies which evaluate investments in terms of expected values and risk capital, that is, buffer capital that needs to be held to make an investment acceptable from a risk management point of view.…”

Ambiguity in asset pricing and portfolio choice: a review of the literature

“…Maccheroni et al (2009) prove that |ω *   | ≥ |ω *   | so that MMVP-optimal portfolios are always more leveraged than MVP-ones, simply because some favorable investment opportunities are discarded by MVP-agents (because of preferences' non-monotonicity) and exploited by MMVP-investors. 49 Under MMVP, Maccheroni et al derive a monotone version of the standard CAPM.…”

Optimal portfolio with vector expected utility

“…Furthermore, these averages are not computed under KMM preference's second order probability but under a modified law that puts more weights on pessimistic priors. Maccheroni et al (2009) build from the variational model mean-variance preferences which are monotone. Applied to the optimal portfolio, they lead to another generalisation of Markowitz' results where the unconditional means and variances are replaced by moments conditioned on the wealth not exceeding a given threshold: the investor ignores the most favourable parts of the distributions, parts which lead to high variances hence to the non monotonicity of the original mean-variance preferences.…”