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Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach

Huyen Pham (), Xiaoli Wei and Chao Zhou
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Huyen Pham: LPSM UMR 8001 - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, ENSAE - Ecole Nationale de la Statistique et de l'Analyse Economique - Ecole Nationale de la Statistique et de l'Analyse Economique
Xiaoli Wei: LPSM UMR 8001 - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique
Chao Zhou: NUS - National University of Singapore

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Abstract: This paper is concerned with a multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the effects on portfolio diversification. We prove a separation principle for the associated robust control problem, which allows to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under-diversification, as documented in empirical studies. We explicitly quantify the degree of under-diversification in terms of correlation and Sharpe ratio ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. This extends to the continuous-time setting the results obtained by Garlappi, Uppal and Wang [13], and Liu and Zeng [24] in a one-period model. JEL Classification: G11, C61 MSC Classification: 91G10, 91G80, 60H30

Keywords: Continuous-time Markowitz problem; model uncertainty; ambiguous drift and correlation; separation principle; portfolio diversification (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-rmg and nep-sea
Date: 2018-09-04
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01867133
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