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Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis

  • Fabio Maccheroni
  • Massimo Marinacci
  • Doriana Ruffino

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as defined by the smooth model of decision making under ambiguity of Klibanoff, Marinacci and Mukerji (2005). We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty. In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset. The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 81 (2013)
Issue (Month): 3 (05)
Pages: 1075-1113

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Handle: RePEc:ecm:emetrp:v:81:y:2013:i:3:p:1075-1113
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  1. Massimo Marinacci & Fabio Maccheroni & Aldo Rustichini & Marco Taboga, 2005. "Portfolio Selection with Monotone Mean-Variance Preferences," Finance 0502014, EconWPA.
  2. Ju, Nengjiu & Miao, Jianjun, 2009. "Ambiguity, Learning, and Asset Returns," MPRA Paper 14737, University Library of Munich, Germany, revised Apr 2009.
  3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  4. Huberman, Gur, 2001. "Familiarity Breeds Investment," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 659-80.
  5. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Documents de travail du Centre d'Economie de la Sorbonne 11032, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
  7. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
  8. Judson A. Caskey, 2009. "Information in Equity Markets with Ambiguity-Averse Investors," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3595-3627, September.
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