Article

Portfolio Selection with Monotone Mean-Variance Preferences

SSRN Electronic Journal 01/2009; 19(3):487-521. DOI: 10.2139/ssrn.1148724
Source: RePEc

ABSTRACT

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.

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    • "hold if unique values of expected returns, variances and covariances are replaced by averages of these moments calculated for all the distributions of asset returns considered by the DM. 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 "
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    ABSTRACT: We study the optimal portfolio selected by an investor who conforms to Siniscalchi (2009)’s Vector Expected Utility’s (VEU) axioms and who is ambiguity averse. To this end, we derive a mean–variance preference generalised to ambiguity from the second-order Taylor-Young expansion of the VEU certainty equivalent. We apply this Mean Variance Variability preference to the static two-assets portfolio problem and deduce asset allocation results which extend the mean–variance analysis to ambiguity in the VEU framework. Our criterion has attractive features: it is axiomatically well-founded and analytically tractable, it is therefore well suited for applications to asset pricing as proved by a novel analysis of the home-bias puzzle with two ambiguous assets.
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    • "Nevertheless , it is well known that mean-variance functional is not monotone and this is a serious drawback. Namely, Maccheroni et al. [10] gave a simple example when an investor with mean-variance preferences may strictly prefer less to more, thus violating one of the most compelling principles of economic rationality. For this reason, they created a new 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. "
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    ABSTRACT: This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the problem of optimizing the mentioned functional in a market with a stochastic interest rate. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to derive the optimal investment strategy and the value function.
    Full-text · Article · Apr 2014
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    • "The purpose is to describe an optimal financial strategy which an investor can follow in order to maximize his performance criterion which is a modification of the monotone mean-variance functional. Let us recall that Maccheroni et al. [13] introduce a functional given by "
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    ABSTRACT: We consider an incomplete market with a non-tradable stochastic factor and an investment problem with optimality criterion based on a functional which is a modification of a monotone mean-variance preferences. We formulate it as a stochastic differential game problem and use Hamilton Jacobi Bellman Isaacs equations to derive the optimal investment strategy and the value function. Finally, we show that our solution coincides with the solution to classical mean-variance problem with risk aversion coefficient which is dependent on stochastic factor.
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