Alpha as Ambiguity: Robust Mean-Variance Portfolio Analysis

Authors

  • Fabio Maccheroni,

    1. Dept. of Decision Sciences and IGIER, Università Bocconi, Via Sarfatti 25, 20136, Milano, Italy; fabio.maccheroni@unibocconi.it
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  • Massimo Marinacci,

    1. Dept. of Decision Sciences and IGIER, Università Bocconi, Via Sarfatti 25, 20136, Milano, Italy; massimo.marinacci@unibocconi.it
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  • Doriana Ruffino

    1. Dept. of Finance, University of Minnesota, 321 19th Avenue South, Minneapolis, MN 55455, U.S.A.; druffino@umn.edu
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    • We thank Pauline Barrieu, David Bates, Emanuele Borgonovo, Veronica Roberta Cappelli, John Cochrane, Marco Giacoletti, Massimo Guidolin, Lars Hansen, Sujoy Mukerji, Fulvio Ortu, Andrea Resti, Alessandro Sbuelz, Claudio Tebaldi, Piero Veronese, the co-editor, four anonymous referees, and especially Giulia Brancaccio and Simone Cerreia-Vioglio for helpful comments. The financial support of the European Research Council (Advanced Grant, BRSCDP-TEA), the AXA-Bocconi Chair, and the Carlson School of Management at the University of Minnesota (Dean's Research Grant) is gratefully acknowledged.


Abstract

We derive the analogue of the classic Arrow–Pratt approximation of the certainty equivalent under model uncertainty as described by the smooth model of decision making under ambiguity of Klibanoff, Marinacci, and Mukerji (2005). We study its scope by deriving a tractable mean-variance model adjusted for ambiguity and solving the corresponding portfolio allocation problem. In the problem with a risk-free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher ambiguity aversion only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In particular, a positive alpha corresponds to a long position in the ambiguous asset, a negative alpha corresponds to a short position in the ambiguous asset, and greater ambiguity aversion reduces optimal exposure to ambiguity. The analytical tractability of the enhanced Arrow–Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of model uncertainty on equilibrium asset prices.

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